model_identification-decoupled-actions.ipynb

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   "cell_type": "markdown",
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   "source": [
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    "        code_show = !code_show\n",
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    "    $( document ).ready(code_toggle);\n",
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   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# PART | (DECOUPLED ACTIONS)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Quadcopter represent a very interesting control problem, with their very simple design and high agility they are extremely versatile, multirotors are used across a wide spectrum of fields, starting from aerial photography to emergency response and disaster relief. A quadcopter consist of four independent rotors and 6 degrees of freedom(three translational and three rotational), quadcopters are considered under-actuated, because to have 6 degrees of translational and rotational of freedom, translational and rotational motion are coupled, resulting in a highly nonlinear flight dynamics[1]. The aim of this work is to utilize model-based reinforcement learning methods, to do effective and adaptive motion planning and obstacle avoidance.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Table of content:\n",
    "\n",
    "#### 1. Unit testing\n",
    "#### 2. Data preperation\n",
    "#### 3. Data exploration\n",
    "#### 4. Model identification\n",
    "#### &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; &nbsp;3.1 Velocity-based models\n",
    "        4.1.1 MLP\n",
    "        4.1.2 Gradient Boost\n",
    "#### 5. Models evaluation\n",
    "        5.1 MLP\n",
    "        5.2 Gradient Boost\n",
    "#### 6. Model verification\n",
    "    6.1 Integrating predictions (Multi-step ahead)\n",
    "    6.2 Building 2d Simulator based on learned Model"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import sys\n",
    "sys.path.append('..')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Pixiedust database opened successfully\n"
     ]
    },
    {
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       "\n",
       "        <div style=\"margin:10px\">\n",
       "            <a href=\"https://github.com/ibm-watson-data-lab/pixiedust\" target=\"_new\">\n",
       "                <img src=\"https://github.com/ibm-watson-data-lab/pixiedust/raw/master/docs/_static/pd_icon32.png\" style=\"float:left;margin-right:10px\"/>\n",
       "            </a>\n",
       "            <span>Pixiedust version 1.1.0</span>\n",
       "        </div>\n",
       "        "
      ],
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       "<IPython.core.display.HTML object>"
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     "metadata": {},
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    {
     "data": {
      "text/html": [
       "<div>Warning: You are not running the latest version of PixieDust. Current is 1.1.0, Latest is 1.1.7</div>"
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      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
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     "metadata": {},
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    {
     "data": {
      "text/html": [
       "\n",
       "                <div>Please copy and run the following command in a new cell to upgrade: <span style=\"background-color:#ececec;font-family:monospace;padding:0 5px\">!pip install --user --upgrade pixiedust</span></div>\n",
       "            "
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
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     "metadata": {},
     "output_type": "display_data"
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    {
     "data": {
      "text/html": [
       "<div>Please restart kernel after upgrading.</div>"
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      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
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   ],
   "source": [
    "from bokeh.plotting import figure, show, output_notebook\n",
    "from bokeh.io import show, output_file\n",
    "\n",
    "import pixiedust\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "import pandas as pd\n",
    "import numpy as np\n",
    "\n",
    "from pyquaternion import Quaternion \n",
    "from Utilities import *\n",
    "\n",
    "from sklearn.utils import shuffle"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "%matplotlib inline\n",
    "np.random.seed=1"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Dataset:"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<img src='images/airsim.gif'>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Microsoft Airsim simulator was used to collect training data, data was collected at 10 hz over the duration of 50 minutes. Data collection consist of quadcopter being controlled manually by user, and for each action user takes the corresponding initial and next states are recorded, which can be formulated as follows ([a0, a1, a2, a3]t, s0, s1)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {},
   "outputs": [],
   "source": [
    "path1 = '../datasets/10hz-m.csv'\n",
    "dataset = pd.read_csv(path1)[:-6000]\n",
    "\n",
    "length, width = dataset.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "29631"
      ]
     },
     "execution_count": 46,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "length"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {},
   "outputs": [],
   "source": [
    "euler = np.zeros((length, 3))\n",
    "\n",
    "for i, row in dataset.iterrows():\n",
    "    q = row[['scalar', 'i', 'j', 'k']].values\n",
    "    euler[i] = toEulerianAngle(q)\n",
    "    \n",
    "for i, c in enumerate(['roll', 'pitch', 'yaw']):\n",
    "    dataset[c] = euler[:, i]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Dataset consist of 29631 training instances collected over 50 minutes"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {},
   "outputs": [],
   "source": [
    "limit = length\n",
    "train = int(0.8 * limit)\n",
    "\n",
    "X, y = getXyVelocityModel(dataset, limit=limit, frequency=10.0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.preprocessing import StandardScaler\n",
    "\n",
    "X, y = StandardScaler().fit_transform(X_), StandardScaler().fit_transform(y_)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Data is split in to train/test datasets 80%, 20%"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {},
   "outputs": [],
   "source": [
    "xTrain, yTrain = shuffle(X[:train], y[:train])\n",
    "xTest, yTest = X[train:], y[train:] "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Model Inputs"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Index(['dXB', 'dYB', 'dZB', 'dRoll', 'dPitch', 'dYaw', 'roll', 'pitch',\n",
       "       'moveForward', 'yawCCW', 'yawCW', 'hover'],\n",
       "      dtype='object')"
      ]
     },
     "execution_count": 50,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X.columns"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Model outputs"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Index(['dXB', 'dYB', 'dZB', 'dRoll', 'dPitch', 'dYaw'], dtype='object')"
      ]
     },
     "execution_count": 51,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "y.columns"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "metadata": {},
   "outputs": [],
   "source": [
    "plot_limit = 300\n",
    "frequency = 10.0"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Unit test (rotations, numerical integration, data verification)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 102,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Unit test passed!!\n"
     ]
    },
    {
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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f7845cab6d8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "gen2 = integrateTrajectoryVelocityBody(position=dataset.loc[0, ['x', 'y', 'z']].values,\n",
    "                                       orientation=Quaternion(dataset.loc[0, ['scalar', 'i', 'j', 'k']].values),\n",
    "                                       linearVelocities=y[['dXB', 'dYB', 'dZB']].values,\n",
    "                                       angularVelocities=y[['dRoll', 'dPitch', 'dYaw']].values,\n",
    "                                       frequency=frequency * np.ones((plot_limit, )))\n",
    "\n",
    "plt.figure(num=None, figsize=(20, 10), dpi=80, facecolor='w', edgecolor='k')\n",
    "\n",
    "for i in range(1, plot_limit):\n",
    "    # ------------------\n",
    "    plt.subplot(1, 2, 1)\n",
    "    plt.legend(['True'], fontsize=16)\n",
    "    plt.title('Trajectory: True', fontdict={'fontsize':20})\n",
    "    \n",
    "    pTrue = dataset.loc[i, ['x', 'y', 'z']]\n",
    "    oTrue = dataset.loc[i, ['roll', 'pitch', 'yaw']]\n",
    "    plt.scatter(pTrue[0], pTrue[1], color='darkgrey')\n",
    "    \n",
    "    # -----------------\n",
    "    plt.subplot(1, 2, 2)\n",
    "    plt.legend(['Integrated'], fontsize=16)\n",
    "    plt.title('Trajectory: Integrated', fontdict={'fontsize':20})\n",
    "    \n",
    "    o, p, _, _ = next(gen2)\n",
    "    plt.scatter(p[0], p[1], color='blue') \n",
    "    \n",
    "    try:\n",
    "        assert(np.allclose(p.astype(np.float64), pTrue.astype(np.float64)))\n",
    "    except:\n",
    "        print('Unit test failed! at: {} after {} seconds'.format(i, int(i/frequency)))\n",
    "        break\n",
    "    \n",
    "    if i == plot_limit - 1:\n",
    "        print('Unit test passed!!')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Data Exploration \n",
    "units are m/s and rad/s"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>dXB</th>\n",
       "      <th>dYB</th>\n",
       "      <th>dZB</th>\n",
       "      <th>dRoll</th>\n",
       "      <th>dPitch</th>\n",
       "      <th>dYaw</th>\n",
       "      <th>roll</th>\n",
       "      <th>pitch</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>count</th>\n",
       "      <td>3.563100e+04</td>\n",
       "      <td>3.563100e+04</td>\n",
       "      <td>35631.000000</td>\n",
       "      <td>3.563100e+04</td>\n",
       "      <td>3.563100e+04</td>\n",
       "      <td>3.563100e+04</td>\n",
       "      <td>3.563100e+04</td>\n",
       "      <td>3.563100e+04</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>mean</th>\n",
       "      <td>-1.437218e-02</td>\n",
       "      <td>-2.688410e-02</td>\n",
       "      <td>-0.001864</td>\n",
       "      <td>-1.192942e-03</td>\n",
       "      <td>8.375298e-03</td>\n",
       "      <td>8.444422e-02</td>\n",
       "      <td>3.371103e-03</td>\n",
       "      <td>-1.568176e-02</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>std</th>\n",
       "      <td>1.282397e+00</td>\n",
       "      <td>1.299051e+00</td>\n",
       "      <td>0.250865</td>\n",
       "      <td>4.585740e-02</td>\n",
       "      <td>7.250722e-01</td>\n",
       "      <td>5.128511e-01</td>\n",
       "      <td>3.230076e-02</td>\n",
       "      <td>1.460400e-01</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>min</th>\n",
       "      <td>-3.877071e+00</td>\n",
       "      <td>-3.876497e+00</td>\n",
       "      <td>-4.311520</td>\n",
       "      <td>-3.237352e-01</td>\n",
       "      <td>-2.636127e+00</td>\n",
       "      <td>-1.047195e+00</td>\n",
       "      <td>-1.076750e-01</td>\n",
       "      <td>-3.600370e-01</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>25%</th>\n",
       "      <td>-5.448388e-01</td>\n",
       "      <td>-6.268908e-01</td>\n",
       "      <td>-0.043713</td>\n",
       "      <td>-7.641260e-03</td>\n",
       "      <td>-7.685219e-02</td>\n",
       "      <td>-1.866346e-06</td>\n",
       "      <td>-9.812929e-04</td>\n",
       "      <td>-1.111820e-01</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>50%</th>\n",
       "      <td>-9.956547e-10</td>\n",
       "      <td>-1.087952e-09</td>\n",
       "      <td>0.016056</td>\n",
       "      <td>-2.388220e-07</td>\n",
       "      <td>7.312088e-08</td>\n",
       "      <td>1.075034e-07</td>\n",
       "      <td>2.281902e-07</td>\n",
       "      <td>-1.829759e-09</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>75%</th>\n",
       "      <td>5.202256e-01</td>\n",
       "      <td>5.312344e-01</td>\n",
       "      <td>0.121287</td>\n",
       "      <td>2.756100e-03</td>\n",
       "      <td>1.222911e-01</td>\n",
       "      <td>1.492053e-01</td>\n",
       "      <td>9.429372e-03</td>\n",
       "      <td>6.466343e-02</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>max</th>\n",
       "      <td>3.763646e+00</td>\n",
       "      <td>3.860891e+00</td>\n",
       "      <td>0.743202</td>\n",
       "      <td>3.292113e-01</td>\n",
       "      <td>2.627451e+00</td>\n",
       "      <td>1.047195e+00</td>\n",
       "      <td>1.074887e-01</td>\n",
       "      <td>3.576003e-01</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                dXB           dYB           dZB         dRoll        dPitch  \\\n",
       "count  3.563100e+04  3.563100e+04  35631.000000  3.563100e+04  3.563100e+04   \n",
       "mean  -1.437218e-02 -2.688410e-02     -0.001864 -1.192942e-03  8.375298e-03   \n",
       "std    1.282397e+00  1.299051e+00      0.250865  4.585740e-02  7.250722e-01   \n",
       "min   -3.877071e+00 -3.876497e+00     -4.311520 -3.237352e-01 -2.636127e+00   \n",
       "25%   -5.448388e-01 -6.268908e-01     -0.043713 -7.641260e-03 -7.685219e-02   \n",
       "50%   -9.956547e-10 -1.087952e-09      0.016056 -2.388220e-07  7.312088e-08   \n",
       "75%    5.202256e-01  5.312344e-01      0.121287  2.756100e-03  1.222911e-01   \n",
       "max    3.763646e+00  3.860891e+00      0.743202  3.292113e-01  2.627451e+00   \n",
       "\n",
       "               dYaw          roll         pitch  \n",
       "count  3.563100e+04  3.563100e+04  3.563100e+04  \n",
       "mean   8.444422e-02  3.371103e-03 -1.568176e-02  \n",
       "std    5.128511e-01  3.230076e-02  1.460400e-01  \n",
       "min   -1.047195e+00 -1.076750e-01 -3.600370e-01  \n",
       "25%   -1.866346e-06 -9.812929e-04 -1.111820e-01  \n",
       "50%    1.075034e-07  2.281902e-07 -1.829759e-09  \n",
       "75%    1.492053e-01  9.429372e-03  6.466343e-02  \n",
       "max    1.047195e+00  1.074887e-01  3.576003e-01  "
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "dataset[X.columns[:-4]].describe()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 119,
   "metadata": {},
   "outputs": [],
   "source": [
    "action_counts = dataset['aName'].value_counts()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Actions sets consist of [Yaw-Clockwise, Yaw-AntiClockwise, Move-Forward, Hover]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<img src='images/roll.gif' width=\"500\" height=\"600\">"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Distribution of actions"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 162,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "\n",
       "<div class=\"bk-root\">\n",
       "    <div class=\"bk-plotdiv\" id=\"5960ab65-9de1-4efe-b377-5e11ecbd974d\"></div>\n",
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Application\",\"version\":\"0.12.13\"}};\n",
       "  var render_items = [{\"docid\":\"83378174-6853-4651-a474-6e6043639997\",\"elementid\":\"5960ab65-9de1-4efe-b377-5e11ecbd974d\",\"modelid\":\"9ec735ab-b264-4702-b92b-3fd559c5c98a\"}];\n",
       "  root.Bokeh.embed.embed_items_notebook(docs_json, render_items);\n",
       "\n",
       "  }\n",
       "  if (root.Bokeh !== undefined) {\n",
       "    embed_document(root);\n",
       "  } else {\n",
       "    var attempts = 0;\n",
       "    var timer = setInterval(function(root) {\n",
       "      if (root.Bokeh !== undefined) {\n",
       "        embed_document(root);\n",
       "        clearInterval(timer);\n",
       "      }\n",
       "      attempts++;\n",
       "      if (attempts > 100) {\n",
       "        console.log(\"Bokeh: ERROR: Unable to run BokehJS code because BokehJS library is missing\")\n",
       "        clearInterval(timer);\n",
       "      }\n",
       "    }, 10, root)\n",
       "  }\n",
       "})(window);"
      ],
      "application/vnd.bokehjs_exec.v0+json": ""
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     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "l = np.array(list(action_counts.items()))\n",
    "\n",
    "p = figure(x_range=l[:,0], plot_height=400, plot_width=950)\n",
    "p.vbar(x=l[:,0], top=l[:, 1], width=0.45)\n",
    "show(p)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Data ranges"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 155,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "\n",
       "<div class=\"bk-root\">\n",
       "    <div class=\"bk-plotdiv\" id=\"66f171f4-45d8-4ef3-a1a2-f281bd98fff3\"></div>\n",
       "</div>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
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      "application/javascript": [
       "(function(root) {\n",
       "  function embed_document(root) {\n",
       "    \n",
       "  var docs_json = 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Application\",\"version\":\"0.12.13\"}};\n",
       "  var render_items = [{\"docid\":\"41c060d4-b3f2-4c34-8508-92f6381928f4\",\"elementid\":\"66f171f4-45d8-4ef3-a1a2-f281bd98fff3\",\"modelid\":\"fd0e62c0-9246-47bb-8390-56104bafb7dc\"}];\n",
       "  root.Bokeh.embed.embed_items_notebook(docs_json, render_items);\n",
       "\n",
       "  }\n",
       "  if (root.Bokeh !== undefined) {\n",
       "    embed_document(root);\n",
       "  } else {\n",
       "    var attempts = 0;\n",
       "    var timer = setInterval(function(root) {\n",
       "      if (root.Bokeh !== undefined) {\n",
       "        embed_document(root);\n",
       "        clearInterval(timer);\n",
       "      }\n",
       "      attempts++;\n",
       "      if (attempts > 100) {\n",
       "        console.log(\"Bokeh: ERROR: Unable to run BokehJS code because BokehJS library is missing\")\n",
       "        clearInterval(timer);\n",
       "      }\n",
       "    }, 10, root)\n",
       "  }\n",
       "})(window);"
      ],
      "application/vnd.bokehjs_exec.v0+json": ""
     },
     "metadata": {
      "application/vnd.bokehjs_exec.v0+json": {
       "id": "fd0e62c0-9246-47bb-8390-56104bafb7dc"
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "ranges = dataset[X.columns[:-4]].describe()\n",
    "max_min = pd.DataFrame({'field':a, 'max':c['max'], 'min':c['min']} for a, c in ranges.to_dict().items())\n",
    "\n",
    "p = figure(x_range=np.array(max_min.field), plot_height=400, plot_width=950)\n",
    "p.vbar(x=np.array(max_min.field), top=max_min['max'].values, width=0.9)\n",
    "p.vbar(x=np.array(max_min.field), top=max_min['min'].values, width=0.9, color='purple')\n",
    "show(p)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Velocity based models"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.metrics import mean_squared_error\n",
    "from sklearn.multioutput import MultiOutputRegressor"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### MLP Regressor with grid-search with cross-validation over model parameters"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.model_selection import GridSearchCV\n",
    "from sklearn.neural_network import MLPRegressor\n",
    "\n",
    "parameters = {'hidden_layer_sizes':[(36, )], 'alpha': np.geomspace(1e-7, 1e-1, 40)}\n",
    "clf = GridSearchCV(MLPRegressor(max_iter=int(10e3), random_state=10, early_stopping=True), parameters, n_jobs=-1).fit(xTrain, yTrain)\n",
    "\n",
    "mlp_cv = clf.best_estimator_"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### best estimator resulting from Gridsearchcv"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "MLPRegressor(activation='relu', alpha=0.002030917620904739, batch_size='auto',\n",
       "       beta_1=0.9, beta_2=0.999, early_stopping=True, epsilon=1e-08,\n",
       "       hidden_layer_sizes=(36,), learning_rate='constant',\n",
       "       learning_rate_init=0.001, max_iter=10000, momentum=0.9,\n",
       "       nesterovs_momentum=True, power_t=0.5, random_state=10, shuffle=True,\n",
       "       solver='adam', tol=0.0001, validation_fraction=0.1, verbose=False,\n",
       "       warm_start=False)"
      ]
     },
     "execution_count": 55,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "mlp_cv"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "metadata": {},
   "outputs": [],
   "source": [
    "yPredicted = pd.DataFrame(mlp_cv.predict(xTest), columns=y.columns)\n",
    "    \n",
    "mlp = MLPRegressor(hidden_layer_sizes=clf.best_params_['hidden_layer_sizes'],\n",
    "                   alpha=clf.best_params_['alpha'], max_iter=int(10e8), random_state=10).fit(X, y)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Gradient Boost  Trees"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 66,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "MultiOutputRegressor(estimator=GradientBoostingRegressor(alpha=0.9, criterion='friedman_mse', init=None,\n",
       "             learning_rate=0.1, loss='huber', max_depth=5,\n",
       "             max_features=None, max_leaf_nodes=None,\n",
       "             min_impurity_decrease=0.0, min_impurity_split=None,\n",
       "             min_samples_leaf=1, min_samples_split=2,\n",
       "             min_weight_fraction_leaf=0.0, n_estimators=100,\n",
       "             presort='auto', random_state=None, subsample=1.0, verbose=0,\n",
       "             warm_start=False),\n",
       "           n_jobs=1)"
      ]
     },
     "execution_count": 66,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sklearn.ensemble import GradientBoostingRegressor\n",
    "\n",
    "gradient = MultiOutputRegressor(GradientBoostingRegressor(max_depth=5, loss='huber'))\\\n",
    "          .fit(xTrain, yTrain)\n",
    "    \n",
    "gradient"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "metadata": {},
   "outputs": [],
   "source": [
    "def predict(actions, position, orientation, x0, model, frequency=10, limit=100):\n",
    "    for i in range(0, limit):\n",
    "        if i > 0:\n",
    "            roll, pitch, yaw = toEulerianAngle(orientation)\n",
    "            x0 = np.concatenate((linearVelocity, angularVelocity, [roll, pitch] , actions[i]))\n",
    "            \n",
    "        s1 = model.predict(x0.reshape(1, -1)).reshape(6,)\n",
    "        \n",
    "        orientation, position, linearVelocity, angularVelocity=\\\n",
    "        next(integrateTrajectoryVelocityBody(position=position, orientation=orientation,\n",
    "                                             frequency=[frequency],\n",
    "                                             linearVelocities=[s1[[0, 1, 2]]],\n",
    "                                             angularVelocities=[s1[[3, 4, 5]]]))\n",
    "        yield orientation, position, linearVelocity, angularVelocity"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Model Evaluation"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### MLP RMSE on test dataset (units are meter/sec and deg/sec)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "dXB\t 0.035535453276990564\n",
      "dYB\t 0.011087754479871377\n",
      "dZB\t 0.03875872172140789\n",
      "dRoll\t 1.0373325096291517\n",
      "dPitch\t 2.6642217733382485\n",
      "dYaw\t 2.1768318760859002\n"
     ]
    }
   ],
   "source": [
    "error_1 = []\n",
    "for i, c in enumerate(y.columns):\n",
    "    error = mean_squared_error(yPredicted[c], yTest[c]) ** 0.5\n",
    "    error_1.append(error)\n",
    "    print(c + '\\t', np.rad2deg(error) if i > 2 else error)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Gradient Boost RMSE on test dataset (units are meter/sec and deg/sec)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 67,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "dXB\t 0.029079627629033954\n",
      "dYB\t 0.004459438027370283\n",
      "dZB\t 0.01728814101802236\n",
      "dRoll\t 0.7751210419850098\n",
      "dPitch\t 3.8008810957492476\n",
      "dYaw\t 1.51341296611495\n"
     ]
    }
   ],
   "source": [
    "yPredicted_2 = pd.DataFrame(gradient.predict(xTest), columns=y.columns)\n",
    "\n",
    "error_2 = []\n",
    "for i, c in enumerate(y.columns):\n",
    "    error = mean_squared_error(yPredicted_2[c], yTest[c]) ** 0.5\n",
    "    error_2.append(error)\n",
    "    print(c + '\\t', np.rad2deg(error) if i > 2 else error)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Comparing Gradient Boosted Trees vs MLP"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 68,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "MLP is better at predicting:  Index(['dPitch'], dtype='object')\n",
      "Gradient-B-Trees is better at predicting:  Index(['dXB', 'dYB', 'dZB', 'dRoll', 'dYaw'], dtype='object')\n"
     ]
    }
   ],
   "source": [
    "diff = np.array(error_1) - np.array(error_2)\n",
    "\n",
    "print('MLP is better at predicting: ', y.columns[diff < 0])\n",
    "print('Gradient-B-Trees is better at predicting: ', y.columns[diff > 0])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Performance benchmarks (prediction time) averaged across 80000 predictions"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 64,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "MLP takes 2.306706187999225 seconds per prediction\n",
      "GBT takes 45.19367891299771 seconds per prediction\n",
      "----------\n",
      "MLP is 19.59229968173688 faster\n"
     ]
    }
   ],
   "source": [
    "from timeit import timeit\n",
    "\n",
    "t1 = timeit(partial(mlp_cv.predict, np.ones((1, 12))), number=80000)\n",
    "t2 = timeit(partial(gradient.predict, np.ones((1, 12))), number=80000)\n",
    "\n",
    "print('MLP takes {} seconds per prediction'.format(t1))\n",
    "print('GBT takes {} seconds per prediction'.format(t2))\n",
    "\n",
    "print('-' * 10 +'\\nMLP is {} faster'.format(t2/t1))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Gradient Boosted trees are 20 times slower per prediction than MLP "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Integrated trajectories of random samples from test dataset (20 seconds each)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### MLP"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 73,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f08187e3550>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(num=None, figsize=(14, 23), dpi=80, facecolor='w', edgecolor='k')\n",
    "\n",
    "limit = 200\n",
    "\n",
    "for j in range(1, 9):\n",
    "    shift = np.random.randint(xTest.shape[0]-limit)\n",
    "\n",
    "    actions = xTest[['moveForward', 'yawCCW', 'yawCW', 'hover']].values[shift:]\n",
    "    position = dataset.loc[train + shift, ['x', 'y', 'z']].values\n",
    "    orientation = Quaternion(dataset.loc[train + shift, ['scalar', 'i', 'j', 'k']].values)\n",
    "\n",
    "    gen2 = predict(position=position, orientation=orientation, x0=xTest.iloc[shift].values, \n",
    "                   actions=actions, limit=limit, model=mlp_cv)\n",
    "    \n",
    "    for i in range(1, limit):\n",
    "        pl = plt.subplot(4, 2, j)\n",
    "        pTrue = dataset.loc[i+train+shift, ['x', 'y', 'z']]\n",
    "        o, p, _, _ = next(gen2)\n",
    "\n",
    "        plt.scatter(*pTrue[:-1], color='darkgrey', alpha=0.6)\n",
    "        plt.scatter(p[0], p[1], color='blue')\n",
    "        \n",
    "        plt.legend(['True', 'Predicted'], fontsize=9)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 81,
   "metadata": {},
   "outputs": [],
   "source": [
    "# taken from: https://stackoverflow.com/questions/4633177/c-how-to-wrap-a-float-to-the-interval-pi-pi\n",
    "def wrapAroundPi(angle):\n",
    "    return np.arctan2(np.sin(angle), np.cos(angle))\n",
    "\n",
    "def getOrientationErrorGlobal(angularPosition1, angularPosition0, frequency):\n",
    "    return getAverage(m1=angularPosition1, m0=angularPosition0, frequency=frequency, wrap=wrapAngleAroundPi)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 104,
   "metadata": {},
   "outputs": [],
   "source": [
    "pos_error_trials = []\n",
    "velocity_error_trials = []\n",
    "angular_velocity_error_trials = []\n",
    "orientation_error_trials = []\n",
    "\n",
    "for trial in range(10):\n",
    "    pos_error = np.ones((limit, 3))\n",
    "    orientation_error = np.ones((limit, 3))\n",
    "    \n",
    "    velocity_error = np.ones((limit, 3))\n",
    "    angular_velocity_error = np.ones((limit, 3))\n",
    "\n",
    "    shift = np.random.randint(xTest.shape[0]-limit)\n",
    "\n",
    "    actions = xTest[['moveForward', 'yawCCW', 'yawCW', 'hover']].values[shift:]\n",
    "    position = dataset.loc[train + shift, ['x', 'y', 'z']].values\n",
    "    orientation = Quaternion(dataset.loc[train + shift, ['scalar', 'i', 'j', 'k']].values)\n",
    "\n",
    "    gen2 = predict(position=position, orientation=orientation, x0=xTest.iloc[shift].values, \n",
    "                   actions=actions, limit=limit, model=mlp_cv)\n",
    "\n",
    "    for i in range(1, limit):\n",
    "        pTrue = dataset.loc[i+train+shift, ['x', 'y', 'z']]\n",
    "        oTrue = dataset.loc[i+train+shift, ['scalar', 'i', 'j', 'k']]\n",
    "        \n",
    "        vTrue = dataset.loc[i+train+shift, ['dXB', 'dYB', 'dZB']]\n",
    "        wTrue = dataset.loc[i+train+shift, ['dRoll', 'dPitch', 'dYaw']]\n",
    "        o, p, v, w = next(gen2)\n",
    "\n",
    "        pos_error[i -1] = p - pTrue\n",
    "        orientation_error[i -1] = getOrientationErrorGlobal(toEulerianAngle(o) ,toEulerianAngle(oTrue), 1.0)\n",
    "        velocity_error[i -1] = vTrue - v\n",
    "        angular_velocity_error[i-1] = wTrue - w\n",
    "\n",
    "    pos_error_trials.append(pos_error)\n",
    "    orientation_error_trials.append(orientation_error)\n",
    "    velocity_error_trials.append(velocity_error)\n",
    "    angular_velocity_error_trials.append(angular_velocity_error)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 105,
   "metadata": {},
   "outputs": [],
   "source": [
    "averaged_position_error = list(map(lambda ls:\n",
    "                                   np.array(ls).reshape(-1, 3).mean(axis=0) ,zip(*pos_error_trials)))\n",
    "\n",
    "averaged_orientation_error = list(map(lambda ls: \n",
    "                                      np.array(ls).reshape(-1, 3).mean(axis=0) ,zip(*orientation_error_trials)))\n",
    "\n",
    "averaged_velocity_error = list(map(lambda ls: \n",
    "                                   np.array(ls).reshape(-1, 3).mean(axis=0) ,zip(*velocity_error_trials)))\n",
    "\n",
    "averaged_angular_velocity_error = list(map(lambda ls: \n",
    "                                           np.array(ls).reshape(-1, 3).mean(axis=0) ,zip(*angular_velocity_error_trials)))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 106,
   "metadata": {},
   "outputs": [],
   "source": [
    "error_pos = pd.DataFrame(averaged_position_error, columns=['x', 'y', 'z'])\n",
    "error_pos['timestep'] = error_pos.index\n",
    "\n",
    "error_orientation = pd.DataFrame(averaged_orientation_error, columns=['roll', 'pitch', 'yaw'])\n",
    "error_orientation['timestep'] = error_orientation.index\n",
    "\n",
    "error_velocity = pd.DataFrame(averaged_velocity_error, columns=['dXB', 'dYB', 'dZB'])\n",
    "error_velocity['timestep'] = error_velocity.index\n",
    "\n",
    "error_angular_velocity = pd.DataFrame(averaged_angular_velocity_error, columns=['dRoll', 'dPitch', 'dYaw'])\n",
    "error_angular_velocity['timestep'] = error_angular_velocity.index"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## MLP Stats"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Error in linear velocity across (20 seconds) averaged across 10 random trajectories"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 85,
   "metadata": {},
   "outputs": [
    {
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       "  }\n",
       "\n",
       "  var JS_MIME_TYPE = 'application/javascript';\n",
       "  var HTML_MIME_TYPE = 'text/html';\n",
       "  var EXEC_MIME_TYPE = 'application/vnd.bokehjs_exec.v0+json';\n",
       "  var CLASS_NAME = 'output_bokeh rendered_html';\n",
       "\n",
       "  /**\n",
       "   * Render data to the DOM node\n",
       "   */\n",
       "  function render(props, node) {\n",
       "    var script = document.createElement(\"script\");\n",
       "    node.appendChild(script);\n",
       "  }\n",
       "\n",
       "  /**\n",
       "   * Handle when an output is cleared or removed\n",
       "   */\n",
       "  function handleClearOutput(event, handle) {\n",
       "    var cell = handle.cell;\n",
       "\n",
       "    var id = cell.output_area._bokeh_element_id;\n",
       "    var server_id = cell.output_area._bokeh_server_id;\n",
       "    // Clean up Bokeh references\n",
       "    if (id !== undefined) {\n",
       "      Bokeh.index[id].model.document.clear();\n",
       "      delete Bokeh.index[id];\n",
       "    }\n",
       "\n",
       "    if (server_id !== undefined) {\n",
       "      // Clean up Bokeh references\n",
       "      var cmd = \"from bokeh.io.state import curstate; print(curstate().uuid_to_server['\" + server_id + \"'].get_sessions()[0].document.roots[0]._id)\";\n",
       "      cell.notebook.kernel.execute(cmd, {\n",
       "        iopub: {\n",
       "          output: function(msg) {\n",
       "            var element_id = msg.content.text.trim();\n",
       "            Bokeh.index[element_id].model.document.clear();\n",
       "            delete Bokeh.index[element_id];\n",
       "          }\n",
       "        }\n",
       "      });\n",
       "      // Destroy server and session\n",
       "      var cmd = \"import bokeh.io.notebook as ion; ion.destroy_server('\" + server_id + \"')\";\n",
       "      cell.notebook.kernel.execute(cmd);\n",
       "    }\n",
       "  }\n",
       "\n",
       "  /**\n",
       "   * Handle when a new output is added\n",
       "   */\n",
       "  function handleAddOutput(event, handle) {\n",
       "    var output_area = handle.output_area;\n",
       "    var output = handle.output;\n",
       "\n",
       "    // limit handleAddOutput to display_data with EXEC_MIME_TYPE content only\n",
       "    if ((output.output_type != \"display_data\") || (!output.data.hasOwnProperty(EXEC_MIME_TYPE))) {\n",
       "      return\n",
       "    }\n",
       "\n",
       "    var toinsert = output_area.element.find(\".\" + CLASS_NAME.split(' ')[0]);\n",
       "\n",
       "    if (output.metadata[EXEC_MIME_TYPE][\"id\"] !== undefined) {\n",
       "      toinsert[0].firstChild.textContent = output.data[JS_MIME_TYPE];\n",
       "      // store reference to embed id on output_area\n",
       "      output_area._bokeh_element_id = output.metadata[EXEC_MIME_TYPE][\"id\"];\n",
       "    }\n",
       "    if (output.metadata[EXEC_MIME_TYPE][\"server_id\"] !== undefined) {\n",
       "      var bk_div = document.createElement(\"div\");\n",
       "      bk_div.innerHTML = output.data[HTML_MIME_TYPE];\n",
       "      var script_attrs = bk_div.children[0].attributes;\n",
       "      for (var i = 0; i < script_attrs.length; i++) {\n",
       "        toinsert[0].firstChild.setAttribute(script_attrs[i].name, script_attrs[i].value);\n",
       "      }\n",
       "      // store reference to server id on output_area\n",
       "      output_area._bokeh_server_id = output.metadata[EXEC_MIME_TYPE][\"server_id\"];\n",
       "    }\n",
       "  }\n",
       "\n",
       "  function register_renderer(events, OutputArea) {\n",
       "\n",
       "    function append_mime(data, metadata, element) {\n",
       "      // create a DOM node to render to\n",
       "      var toinsert = this.create_output_subarea(\n",
       "        metadata,\n",
       "        CLASS_NAME,\n",
       "        EXEC_MIME_TYPE\n",
       "      );\n",
       "      this.keyboard_manager.register_events(toinsert);\n",
       "      // Render to node\n",
       "      var props = {data: data, metadata: metadata[EXEC_MIME_TYPE]};\n",
       "      render(props, toinsert[0]);\n",
       "      element.append(toinsert);\n",
       "      return toinsert\n",
       "    }\n",
       "\n",
       "    /* Handle when an output is cleared or removed */\n",
       "    events.on('clear_output.CodeCell', handleClearOutput);\n",
       "    events.on('delete.Cell', handleClearOutput);\n",
       "\n",
       "    /* Handle when a new output is added */\n",
       "    events.on('output_added.OutputArea', handleAddOutput);\n",
       "\n",
       "    /**\n",
       "     * Register the mime type and append_mime function with output_area\n",
       "     */\n",
       "    OutputArea.prototype.register_mime_type(EXEC_MIME_TYPE, append_mime, {\n",
       "      /* Is output safe? */\n",
       "      safe: true,\n",
       "      /* Index of renderer in `output_area.display_order` */\n",
       "      index: 0\n",
       "    });\n",
       "  }\n",
       "\n",
       "  // register the mime type if in Jupyter Notebook environment and previously unregistered\n",
       "  if (root.Jupyter !== undefined) {\n",
       "    var events = require('base/js/events');\n",
       "    var OutputArea = require('notebook/js/outputarea').OutputArea;\n",
       "\n",
       "    if (OutputArea.prototype.mime_types().indexOf(EXEC_MIME_TYPE) == -1) {\n",
       "      register_renderer(events, OutputArea);\n",
       "    }\n",
       "  }\n",
       "\n",
       "  \n",
       "  if (typeof (root._bokeh_timeout) === \"undefined\" || force === true) {\n",
       "    root._bokeh_timeout = Date.now() + 5000;\n",
       "    root._bokeh_failed_load = false;\n",
       "  }\n",
       "\n",
       "  var NB_LOAD_WARNING = {'data': {'text/html':\n",
       "     \"<div style='background-color: #fdd'>\\n\"+\n",
       "     \"<p>\\n\"+\n",
       "     \"BokehJS does not appear to have successfully loaded. If loading BokehJS from CDN, this \\n\"+\n",
       "     \"may be due to a slow or bad network connection. Possible fixes:\\n\"+\n",
       "     \"</p>\\n\"+\n",
       "     \"<ul>\\n\"+\n",
       "     \"<li>re-rerun `output_notebook()` to attempt to load from CDN again, or</li>\\n\"+\n",
       "     \"<li>use INLINE resources instead, as so:</li>\\n\"+\n",
       "     \"</ul>\\n\"+\n",
       "     \"<code>\\n\"+\n",
       "     \"from bokeh.resources import INLINE\\n\"+\n",
       "     \"output_notebook(resources=INLINE)\\n\"+\n",
       "     \"</code>\\n\"+\n",
       "     \"</div>\"}};\n",
       "\n",
       "  function display_loaded() {\n",
       "    var el = document.getElementById(\"1ef6a178-ed01-4970-b9c2-c104a4d21bca\");\n",
       "    if (el != null) {\n",
       "      el.textContent = \"BokehJS is loading...\";\n",
       "    }\n",
       "    if (root.Bokeh !== undefined) {\n",
       "      if (el != null) {\n",
       "        el.textContent = \"BokehJS \" + root.Bokeh.version + \" successfully loaded.\";\n",
       "      }\n",
       "    } else if (Date.now() < root._bokeh_timeout) {\n",
       "      setTimeout(display_loaded, 100)\n",
       "    }\n",
       "  }\n",
       "\n",
       "\n",
       "  function run_callbacks() {\n",
       "    try {\n",
       "      root._bokeh_onload_callbacks.forEach(function(callback) { callback() });\n",
       "    }\n",
       "    finally {\n",
       "      delete root._bokeh_onload_callbacks\n",
       "    }\n",
       "    console.info(\"Bokeh: all callbacks have finished\");\n",
       "  }\n",
       "\n",
       "  function load_libs(js_urls, callback) {\n",
       "    root._bokeh_onload_callbacks.push(callback);\n",
       "    if (root._bokeh_is_loading > 0) {\n",
       "      console.log(\"Bokeh: BokehJS is being loaded, scheduling callback at\", now());\n",
       "      return null;\n",
       "    }\n",
       "    if (js_urls == null || js_urls.length === 0) {\n",
       "      run_callbacks();\n",
       "      return null;\n",
       "    }\n",
       "    console.log(\"Bokeh: BokehJS not loaded, scheduling load and callback at\", now());\n",
       "    root._bokeh_is_loading = js_urls.length;\n",
       "    for (var i = 0; i < js_urls.length; i++) {\n",
       "      var url = js_urls[i];\n",
       "      var s = document.createElement('script');\n",
       "      s.src = url;\n",
       "      s.async = false;\n",
       "      s.onreadystatechange = s.onload = function() {\n",
       "        root._bokeh_is_loading--;\n",
       "        if (root._bokeh_is_loading === 0) {\n",
       "          console.log(\"Bokeh: all BokehJS libraries loaded\");\n",
       "          run_callbacks()\n",
       "        }\n",
       "      };\n",
       "      s.onerror = function() {\n",
       "        console.warn(\"failed to load library \" + url);\n",
       "      };\n",
       "      console.log(\"Bokeh: injecting script tag for BokehJS library: \", url);\n",
       "      document.getElementsByTagName(\"head\")[0].appendChild(s);\n",
       "    }\n",
       "  };var element = document.getElementById(\"1ef6a178-ed01-4970-b9c2-c104a4d21bca\");\n",
       "  if (element == null) {\n",
       "    console.log(\"Bokeh: ERROR: autoload.js configured with elementid '1ef6a178-ed01-4970-b9c2-c104a4d21bca' but no matching script tag was found. \")\n",
       "    return false;\n",
       "  }\n",
       "\n",
       "  var js_urls = [\"https://cdn.pydata.org/bokeh/release/bokeh-0.12.13.min.js\", \"https://cdn.pydata.org/bokeh/release/bokeh-widgets-0.12.13.min.js\", \"https://cdn.pydata.org/bokeh/release/bokeh-tables-0.12.13.min.js\", \"https://cdn.pydata.org/bokeh/release/bokeh-gl-0.12.13.min.js\"];\n",
       "\n",
       "  var inline_js = [\n",
       "    function(Bokeh) {\n",
       "      Bokeh.set_log_level(\"info\");\n",
       "    },\n",
       "    \n",
       "    function(Bokeh) {\n",
       "      \n",
       "    },\n",
       "    function(Bokeh) {\n",
       "      console.log(\"Bokeh: injecting CSS: https://cdn.pydata.org/bokeh/release/bokeh-0.12.13.min.css\");\n",
       "      Bokeh.embed.inject_css(\"https://cdn.pydata.org/bokeh/release/bokeh-0.12.13.min.css\");\n",
       "      console.log(\"Bokeh: injecting CSS: https://cdn.pydata.org/bokeh/release/bokeh-widgets-0.12.13.min.css\");\n",
       "      Bokeh.embed.inject_css(\"https://cdn.pydata.org/bokeh/release/bokeh-widgets-0.12.13.min.css\");\n",
       "      console.log(\"Bokeh: injecting CSS: https://cdn.pydata.org/bokeh/release/bokeh-tables-0.12.13.min.css\");\n",
       "      Bokeh.embed.inject_css(\"https://cdn.pydata.org/bokeh/release/bokeh-tables-0.12.13.min.css\");\n",
       "    }\n",
       "  ];\n",
       "\n",
       "  function run_inline_js() {\n",
       "    \n",
       "    if ((root.Bokeh !== undefined) || (force === true)) {\n",
       "      for (var i = 0; i < inline_js.length; i++) {\n",
       "        inline_js[i].call(root, root.Bokeh);\n",
       "      }if (force === true) {\n",
       "        display_loaded();\n",
       "      }} else if (Date.now() < root._bokeh_timeout) {\n",
       "      setTimeout(run_inline_js, 100);\n",
       "    } else if (!root._bokeh_failed_load) {\n",
       "      console.log(\"Bokeh: BokehJS failed to load within specified timeout.\");\n",
       "      root._bokeh_failed_load = true;\n",
       "    } else if (force !== true) {\n",
       "      var cell = $(document.getElementById(\"1ef6a178-ed01-4970-b9c2-c104a4d21bca\")).parents('.cell').data().cell;\n",
       "      cell.output_area.append_execute_result(NB_LOAD_WARNING)\n",
       "    }\n",
       "\n",
       "  }\n",
       "\n",
       "  if (root._bokeh_is_loading === 0) {\n",
       "    console.log(\"Bokeh: BokehJS loaded, going straight to plotting\");\n",
       "    run_inline_js();\n",
       "  } else {\n",
       "    load_libs(js_urls, function() {\n",
       "      console.log(\"Bokeh: BokehJS plotting callback run at\", now());\n",
       "      run_inline_js();\n",
       "    });\n",
       "  }\n",
       "}(window));"
      ],
      "application/vnd.bokehjs_load.v0+json": "\n(function(root) {\n  function now() {\n    return new Date();\n  }\n\n  var force = true;\n\n  if (typeof (root._bokeh_onload_callbacks) === \"undefined\" || force === true) {\n    root._bokeh_onload_callbacks = [];\n    root._bokeh_is_loading = undefined;\n  }\n\n  \n\n  \n  if (typeof (root._bokeh_timeout) === \"undefined\" || force === true) {\n    root._bokeh_timeout = Date.now() + 5000;\n    root._bokeh_failed_load = false;\n  }\n\n  var NB_LOAD_WARNING = {'data': {'text/html':\n     \"<div style='background-color: #fdd'>\\n\"+\n     \"<p>\\n\"+\n     \"BokehJS does not appear to have successfully loaded. If loading BokehJS from CDN, this \\n\"+\n     \"may be due to a slow or bad network connection. Possible fixes:\\n\"+\n     \"</p>\\n\"+\n     \"<ul>\\n\"+\n     \"<li>re-rerun `output_notebook()` to attempt to load from CDN again, or</li>\\n\"+\n     \"<li>use INLINE resources instead, as so:</li>\\n\"+\n     \"</ul>\\n\"+\n     \"<code>\\n\"+\n     \"from bokeh.resources import INLINE\\n\"+\n     \"output_notebook(resources=INLINE)\\n\"+\n     \"</code>\\n\"+\n     \"</div>\"}};\n\n  function display_loaded() {\n    var el = document.getElementById(\"1ef6a178-ed01-4970-b9c2-c104a4d21bca\");\n    if (el != null) {\n      el.textContent = \"BokehJS is loading...\";\n    }\n    if (root.Bokeh !== undefined) {\n      if (el != null) {\n        el.textContent = \"BokehJS \" + root.Bokeh.version + \" successfully loaded.\";\n      }\n    } else if (Date.now() < root._bokeh_timeout) {\n      setTimeout(display_loaded, 100)\n    }\n  }\n\n\n  function run_callbacks() {\n    try {\n      root._bokeh_onload_callbacks.forEach(function(callback) { callback() });\n    }\n    finally {\n      delete root._bokeh_onload_callbacks\n    }\n    console.info(\"Bokeh: all callbacks have finished\");\n  }\n\n  function load_libs(js_urls, callback) {\n    root._bokeh_onload_callbacks.push(callback);\n    if (root._bokeh_is_loading > 0) {\n      console.log(\"Bokeh: BokehJS is being loaded, scheduling callback at\", now());\n      return null;\n    }\n    if (js_urls == null || js_urls.length === 0) {\n      run_callbacks();\n      return null;\n    }\n    console.log(\"Bokeh: BokehJS not loaded, scheduling load and callback at\", now());\n    root._bokeh_is_loading = js_urls.length;\n    for (var i = 0; i < js_urls.length; i++) {\n      var url = js_urls[i];\n      var s = document.createElement('script');\n      s.src = url;\n      s.async = false;\n      s.onreadystatechange = s.onload = function() {\n        root._bokeh_is_loading--;\n        if (root._bokeh_is_loading === 0) {\n          console.log(\"Bokeh: all BokehJS libraries loaded\");\n          run_callbacks()\n        }\n      };\n      s.onerror = function() {\n        console.warn(\"failed to load library \" + url);\n      };\n      console.log(\"Bokeh: injecting script tag for BokehJS library: \", url);\n      document.getElementsByTagName(\"head\")[0].appendChild(s);\n    }\n  };var element = document.getElementById(\"1ef6a178-ed01-4970-b9c2-c104a4d21bca\");\n  if (element == null) {\n    console.log(\"Bokeh: ERROR: autoload.js configured with elementid '1ef6a178-ed01-4970-b9c2-c104a4d21bca' but no matching script tag was found. \")\n    return false;\n  }\n\n  var js_urls = [\"https://cdn.pydata.org/bokeh/release/bokeh-0.12.13.min.js\", \"https://cdn.pydata.org/bokeh/release/bokeh-widgets-0.12.13.min.js\", \"https://cdn.pydata.org/bokeh/release/bokeh-tables-0.12.13.min.js\", \"https://cdn.pydata.org/bokeh/release/bokeh-gl-0.12.13.min.js\"];\n\n  var inline_js = [\n    function(Bokeh) {\n      Bokeh.set_log_level(\"info\");\n    },\n    \n    function(Bokeh) {\n      \n    },\n    function(Bokeh) {\n      console.log(\"Bokeh: injecting CSS: https://cdn.pydata.org/bokeh/release/bokeh-0.12.13.min.css\");\n      Bokeh.embed.inject_css(\"https://cdn.pydata.org/bokeh/release/bokeh-0.12.13.min.css\");\n      console.log(\"Bokeh: injecting CSS: https://cdn.pydata.org/bokeh/release/bokeh-widgets-0.12.13.min.css\");\n      Bokeh.embed.inject_css(\"https://cdn.pydata.org/bokeh/release/bokeh-widgets-0.12.13.min.css\");\n      console.log(\"Bokeh: injecting CSS: https://cdn.pydata.org/bokeh/release/bokeh-tables-0.12.13.min.css\");\n      Bokeh.embed.inject_css(\"https://cdn.pydata.org/bokeh/release/bokeh-tables-0.12.13.min.css\");\n    }\n  ];\n\n  function run_inline_js() {\n    \n    if ((root.Bokeh !== undefined) || (force === true)) {\n      for (var i = 0; i < inline_js.length; i++) {\n        inline_js[i].call(root, root.Bokeh);\n      }if (force === true) {\n        display_loaded();\n      }} else if (Date.now() < root._bokeh_timeout) {\n      setTimeout(run_inline_js, 100);\n    } else if (!root._bokeh_failed_load) {\n      console.log(\"Bokeh: BokehJS failed to load within specified timeout.\");\n      root._bokeh_failed_load = true;\n    } else if (force !== true) {\n      var cell = $(document.getElementById(\"1ef6a178-ed01-4970-b9c2-c104a4d21bca\")).parents('.cell').data().cell;\n      cell.output_area.append_execute_result(NB_LOAD_WARNING)\n    }\n\n  }\n\n  if (root._bokeh_is_loading === 0) {\n    console.log(\"Bokeh: BokehJS loaded, going straight to plotting\");\n    run_inline_js();\n  } else {\n    load_libs(js_urls, function() {\n      console.log(\"Bokeh: BokehJS plotting callback run at\", now());\n      run_inline_js();\n    });\n  }\n}(window));"
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "\n",
       "<div class=\"bk-root\">\n",
       "    <div class=\"bk-plotdiv\" id=\"023019f2-5b8b-45f2-9359-175d4214dcb1\"></div>\n",
       "</div>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "application/javascript": [
       "(function(root) {\n",
       "  function embed_document(root) {\n",
       "    \n",
       "  var docs_json = 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       "  var render_items = [{\"docid\":\"7075133d-e7bf-409e-aa8d-381c7b20fb63\",\"elementid\":\"023019f2-5b8b-45f2-9359-175d4214dcb1\",\"modelid\":\"47be88ff-1dd2-4355-83a8-6da1756e3674\"}];\n",
       "  root.Bokeh.embed.embed_items_notebook(docs_json, render_items);\n",
       "\n",
       "  }\n",
       "  if (root.Bokeh !== undefined) {\n",
       "    embed_document(root);\n",
       "  } else {\n",
       "    var attempts = 0;\n",
       "    var timer = setInterval(function(root) {\n",
       "      if (root.Bokeh !== undefined) {\n",
       "        embed_document(root);\n",
       "        clearInterval(timer);\n",
       "      }\n",
       "      attempts++;\n",
       "      if (attempts > 100) {\n",
       "        console.log(\"Bokeh: ERROR: Unable to run BokehJS code because BokehJS library is missing\")\n",
       "        clearInterval(timer);\n",
       "      }\n",
       "    }, 10, root)\n",
       "  }\n",
       "})(window);"
      ],
      "application/vnd.bokehjs_exec.v0+json": ""
     },
     "metadata": {
      "application/vnd.bokehjs_exec.v0+json": {
       "id": "47be88ff-1dd2-4355-83a8-6da1756e3674"
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "output_notebook()\n",
    "p = figure(plot_width=950, plot_height=400)\n",
    "\n",
    "p.line(error_velocity['timestep'][:-10], error_velocity.dXB[:-10], line_width=2, color='blue', legend='dXB')\n",
    "p.line(error_velocity['timestep'][:-10], error_velocity.dYB[:-10], line_width=2, color='red', legend='dYB')\n",
    "p.line(error_velocity['timestep'][:-10], error_velocity.dZB[:-10], line_width=2, color='purple', legend='dZB')\n",
    "\n",
    "show(p)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Error in angular velocity across (20 seconds) averaged across 10 random trajectories"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 86,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "\n",
       "    <div class=\"bk-root\">\n",
       "        <a href=\"https://bokeh.pydata.org\" target=\"_blank\" class=\"bk-logo bk-logo-small bk-logo-notebook\"></a>\n",
       "        <span id=\"13975323-f97c-4a49-991c-381a5178d8c3\">Loading BokehJS ...</span>\n",
       "    </div>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "application/javascript": [
       "\n",
       "(function(root) {\n",
       "  function now() {\n",
       "    return new Date();\n",
       "  }\n",
       "\n",
       "  var force = true;\n",
       "\n",
       "  if (typeof (root._bokeh_onload_callbacks) === \"undefined\" || force === true) {\n",
       "    root._bokeh_onload_callbacks = [];\n",
       "    root._bokeh_is_loading = undefined;\n",
       "  }\n",
       "\n",
       "  var JS_MIME_TYPE = 'application/javascript';\n",
       "  var HTML_MIME_TYPE = 'text/html';\n",
       "  var EXEC_MIME_TYPE = 'application/vnd.bokehjs_exec.v0+json';\n",
       "  var CLASS_NAME = 'output_bokeh rendered_html';\n",
       "\n",
       "  /**\n",
       "   * Render data to the DOM node\n",
       "   */\n",
       "  function render(props, node) {\n",
       "    var script = document.createElement(\"script\");\n",
       "    node.appendChild(script);\n",
       "  }\n",
       "\n",
       "  /**\n",
       "   * Handle when an output is cleared or removed\n",
       "   */\n",
       "  function handleClearOutput(event, handle) {\n",
       "    var cell = handle.cell;\n",
       "\n",
       "    var id = cell.output_area._bokeh_element_id;\n",
       "    var server_id = cell.output_area._bokeh_server_id;\n",
       "    // Clean up Bokeh references\n",
       "    if (id !== undefined) {\n",
       "      Bokeh.index[id].model.document.clear();\n",
       "      delete Bokeh.index[id];\n",
       "    }\n",
       "\n",
       "    if (server_id !== undefined) {\n",
       "      // Clean up Bokeh references\n",
       "      var cmd = \"from bokeh.io.state import curstate; print(curstate().uuid_to_server['\" + server_id + \"'].get_sessions()[0].document.roots[0]._id)\";\n",
       "      cell.notebook.kernel.execute(cmd, {\n",
       "        iopub: {\n",
       "          output: function(msg) {\n",
       "            var element_id = msg.content.text.trim();\n",
       "            Bokeh.index[element_id].model.document.clear();\n",
       "            delete Bokeh.index[element_id];\n",
       "          }\n",
       "        }\n",
       "      });\n",
       "      // Destroy server and session\n",
       "      var cmd = \"import bokeh.io.notebook as ion; ion.destroy_server('\" + server_id + \"')\";\n",
       "      cell.notebook.kernel.execute(cmd);\n",
       "    }\n",
       "  }\n",
       "\n",
       "  /**\n",
       "   * Handle when a new output is added\n",
       "   */\n",
       "  function handleAddOutput(event, handle) {\n",
       "    var output_area = handle.output_area;\n",
       "    var output = handle.output;\n",
       "\n",
       "    // limit handleAddOutput to display_data with EXEC_MIME_TYPE content only\n",
       "    if ((output.output_type != \"display_data\") || (!output.data.hasOwnProperty(EXEC_MIME_TYPE))) {\n",
       "      return\n",
       "    }\n",
       "\n",
       "    var toinsert = output_area.element.find(\".\" + CLASS_NAME.split(' ')[0]);\n",
       "\n",
       "    if (output.metadata[EXEC_MIME_TYPE][\"id\"] !== undefined) {\n",
       "      toinsert[0].firstChild.textContent = output.data[JS_MIME_TYPE];\n",
       "      // store reference to embed id on output_area\n",
       "      output_area._bokeh_element_id = output.metadata[EXEC_MIME_TYPE][\"id\"];\n",
       "    }\n",
       "    if (output.metadata[EXEC_MIME_TYPE][\"server_id\"] !== undefined) {\n",
       "      var bk_div = document.createElement(\"div\");\n",
       "      bk_div.innerHTML = output.data[HTML_MIME_TYPE];\n",
       "      var script_attrs = bk_div.children[0].attributes;\n",
       "      for (var i = 0; i < script_attrs.length; i++) {\n",
       "        toinsert[0].firstChild.setAttribute(script_attrs[i].name, script_attrs[i].value);\n",
       "      }\n",
       "      // store reference to server id on output_area\n",
       "      output_area._bokeh_server_id = output.metadata[EXEC_MIME_TYPE][\"server_id\"];\n",
       "    }\n",
       "  }\n",
       "\n",
       "  function register_renderer(events, OutputArea) {\n",
       "\n",
       "    function append_mime(data, metadata, element) {\n",
       "      // create a DOM node to render to\n",
       "      var toinsert = this.create_output_subarea(\n",
       "        metadata,\n",
       "        CLASS_NAME,\n",
       "        EXEC_MIME_TYPE\n",
       "      );\n",
       "      this.keyboard_manager.register_events(toinsert);\n",
       "      // Render to node\n",
       "      var props = {data: data, metadata: metadata[EXEC_MIME_TYPE]};\n",
       "      render(props, toinsert[0]);\n",
       "      element.append(toinsert);\n",
       "      return toinsert\n",
       "    }\n",
       "\n",
       "    /* Handle when an output is cleared or removed */\n",
       "    events.on('clear_output.CodeCell', handleClearOutput);\n",
       "    events.on('delete.Cell', handleClearOutput);\n",
       "\n",
       "    /* Handle when a new output is added */\n",
       "    events.on('output_added.OutputArea', handleAddOutput);\n",
       "\n",
       "    /**\n",
       "     * Register the mime type and append_mime function with output_area\n",
       "     */\n",
       "    OutputArea.prototype.register_mime_type(EXEC_MIME_TYPE, append_mime, {\n",
       "      /* Is output safe? */\n",
       "      safe: true,\n",
       "      /* Index of renderer in `output_area.display_order` */\n",
       "      index: 0\n",
       "    });\n",
       "  }\n",
       "\n",
       "  // register the mime type if in Jupyter Notebook environment and previously unregistered\n",
       "  if (root.Jupyter !== undefined) {\n",
       "    var events = require('base/js/events');\n",
       "    var OutputArea = require('notebook/js/outputarea').OutputArea;\n",
       "\n",
       "    if (OutputArea.prototype.mime_types().indexOf(EXEC_MIME_TYPE) == -1) {\n",
       "      register_renderer(events, OutputArea);\n",
       "    }\n",
       "  }\n",
       "\n",
       "  \n",
       "  if (typeof (root._bokeh_timeout) === \"undefined\" || force === true) {\n",
       "    root._bokeh_timeout = Date.now() + 5000;\n",
       "    root._bokeh_failed_load = false;\n",
       "  }\n",
       "\n",
       "  var NB_LOAD_WARNING = {'data': {'text/html':\n",
       "     \"<div style='background-color: #fdd'>\\n\"+\n",
       "     \"<p>\\n\"+\n",
       "     \"BokehJS does not appear to have successfully loaded. If loading BokehJS from CDN, this \\n\"+\n",
       "     \"may be due to a slow or bad network connection. Possible fixes:\\n\"+\n",
       "     \"</p>\\n\"+\n",
       "     \"<ul>\\n\"+\n",
       "     \"<li>re-rerun `output_notebook()` to attempt to load from CDN again, or</li>\\n\"+\n",
       "     \"<li>use INLINE resources instead, as so:</li>\\n\"+\n",
       "     \"</ul>\\n\"+\n",
       "     \"<code>\\n\"+\n",
       "     \"from bokeh.resources import INLINE\\n\"+\n",
       "     \"output_notebook(resources=INLINE)\\n\"+\n",
       "     \"</code>\\n\"+\n",
       "     \"</div>\"}};\n",
       "\n",
       "  function display_loaded() {\n",
       "    var el = document.getElementById(\"13975323-f97c-4a49-991c-381a5178d8c3\");\n",
       "    if (el != null) {\n",
       "      el.textContent = \"BokehJS is loading...\";\n",
       "    }\n",
       "    if (root.Bokeh !== undefined) {\n",
       "      if (el != null) {\n",
       "        el.textContent = \"BokehJS \" + root.Bokeh.version + \" successfully loaded.\";\n",
       "      }\n",
       "    } else if (Date.now() < root._bokeh_timeout) {\n",
       "      setTimeout(display_loaded, 100)\n",
       "    }\n",
       "  }\n",
       "\n",
       "\n",
       "  function run_callbacks() {\n",
       "    try {\n",
       "      root._bokeh_onload_callbacks.forEach(function(callback) { callback() });\n",
       "    }\n",
       "    finally {\n",
       "      delete root._bokeh_onload_callbacks\n",
       "    }\n",
       "    console.info(\"Bokeh: all callbacks have finished\");\n",
       "  }\n",
       "\n",
       "  function load_libs(js_urls, callback) {\n",
       "    root._bokeh_onload_callbacks.push(callback);\n",
       "    if (root._bokeh_is_loading > 0) {\n",
       "      console.log(\"Bokeh: BokehJS is being loaded, scheduling callback at\", now());\n",
       "      return null;\n",
       "    }\n",
       "    if (js_urls == null || js_urls.length === 0) {\n",
       "      run_callbacks();\n",
       "      return null;\n",
       "    }\n",
       "    console.log(\"Bokeh: BokehJS not loaded, scheduling load and callback at\", now());\n",
       "    root._bokeh_is_loading = js_urls.length;\n",
       "    for (var i = 0; i < js_urls.length; i++) {\n",
       "      var url = js_urls[i];\n",
       "      var s = document.createElement('script');\n",
       "      s.src = url;\n",
       "      s.async = false;\n",
       "      s.onreadystatechange = s.onload = function() {\n",
       "        root._bokeh_is_loading--;\n",
       "        if (root._bokeh_is_loading === 0) {\n",
       "          console.log(\"Bokeh: all BokehJS libraries loaded\");\n",
       "          run_callbacks()\n",
       "        }\n",
       "      };\n",
       "      s.onerror = function() {\n",
       "        console.warn(\"failed to load library \" + url);\n",
       "      };\n",
       "      console.log(\"Bokeh: injecting script tag for BokehJS library: \", url);\n",
       "      document.getElementsByTagName(\"head\")[0].appendChild(s);\n",
       "    }\n",
       "  };var element = document.getElementById(\"13975323-f97c-4a49-991c-381a5178d8c3\");\n",
       "  if (element == null) {\n",
       "    console.log(\"Bokeh: ERROR: autoload.js configured with elementid '13975323-f97c-4a49-991c-381a5178d8c3' but no matching script tag was found. \")\n",
       "    return false;\n",
       "  }\n",
       "\n",
       "  var js_urls = [\"https://cdn.pydata.org/bokeh/release/bokeh-0.12.13.min.js\", \"https://cdn.pydata.org/bokeh/release/bokeh-widgets-0.12.13.min.js\", \"https://cdn.pydata.org/bokeh/release/bokeh-tables-0.12.13.min.js\", \"https://cdn.pydata.org/bokeh/release/bokeh-gl-0.12.13.min.js\"];\n",
       "\n",
       "  var inline_js = [\n",
       "    function(Bokeh) {\n",
       "      Bokeh.set_log_level(\"info\");\n",
       "    },\n",
       "    \n",
       "    function(Bokeh) {\n",
       "      \n",
       "    },\n",
       "    function(Bokeh) {\n",
       "      console.log(\"Bokeh: injecting CSS: https://cdn.pydata.org/bokeh/release/bokeh-0.12.13.min.css\");\n",
       "      Bokeh.embed.inject_css(\"https://cdn.pydata.org/bokeh/release/bokeh-0.12.13.min.css\");\n",
       "      console.log(\"Bokeh: injecting CSS: https://cdn.pydata.org/bokeh/release/bokeh-widgets-0.12.13.min.css\");\n",
       "      Bokeh.embed.inject_css(\"https://cdn.pydata.org/bokeh/release/bokeh-widgets-0.12.13.min.css\");\n",
       "      console.log(\"Bokeh: injecting CSS: https://cdn.pydata.org/bokeh/release/bokeh-tables-0.12.13.min.css\");\n",
       "      Bokeh.embed.inject_css(\"https://cdn.pydata.org/bokeh/release/bokeh-tables-0.12.13.min.css\");\n",
       "    }\n",
       "  ];\n",
       "\n",
       "  function run_inline_js() {\n",
       "    \n",
       "    if ((root.Bokeh !== undefined) || (force === true)) {\n",
       "      for (var i = 0; i < inline_js.length; i++) {\n",
       "        inline_js[i].call(root, root.Bokeh);\n",
       "      }if (force === true) {\n",
       "        display_loaded();\n",
       "      }} else if (Date.now() < root._bokeh_timeout) {\n",
       "      setTimeout(run_inline_js, 100);\n",
       "    } else if (!root._bokeh_failed_load) {\n",
       "      console.log(\"Bokeh: BokehJS failed to load within specified timeout.\");\n",
       "      root._bokeh_failed_load = true;\n",
       "    } else if (force !== true) {\n",
       "      var cell = $(document.getElementById(\"13975323-f97c-4a49-991c-381a5178d8c3\")).parents('.cell').data().cell;\n",
       "      cell.output_area.append_execute_result(NB_LOAD_WARNING)\n",
       "    }\n",
       "\n",
       "  }\n",
       "\n",
       "  if (root._bokeh_is_loading === 0) {\n",
       "    console.log(\"Bokeh: BokehJS loaded, going straight to plotting\");\n",
       "    run_inline_js();\n",
       "  } else {\n",
       "    load_libs(js_urls, function() {\n",
       "      console.log(\"Bokeh: BokehJS plotting callback run at\", now());\n",
       "      run_inline_js();\n",
       "    });\n",
       "  }\n",
       "}(window));"
      ],
      "application/vnd.bokehjs_load.v0+json": "\n(function(root) {\n  function now() {\n    return new Date();\n  }\n\n  var force = true;\n\n  if (typeof (root._bokeh_onload_callbacks) === \"undefined\" || force === true) {\n    root._bokeh_onload_callbacks = [];\n    root._bokeh_is_loading = undefined;\n  }\n\n  \n\n  \n  if (typeof (root._bokeh_timeout) === \"undefined\" || force === true) {\n    root._bokeh_timeout = Date.now() + 5000;\n    root._bokeh_failed_load = false;\n  }\n\n  var NB_LOAD_WARNING = {'data': {'text/html':\n     \"<div style='background-color: #fdd'>\\n\"+\n     \"<p>\\n\"+\n     \"BokehJS does not appear to have successfully loaded. If loading BokehJS from CDN, this \\n\"+\n     \"may be due to a slow or bad network connection. Possible fixes:\\n\"+\n     \"</p>\\n\"+\n     \"<ul>\\n\"+\n     \"<li>re-rerun `output_notebook()` to attempt to load from CDN again, or</li>\\n\"+\n     \"<li>use INLINE resources instead, as so:</li>\\n\"+\n     \"</ul>\\n\"+\n     \"<code>\\n\"+\n     \"from bokeh.resources import INLINE\\n\"+\n     \"output_notebook(resources=INLINE)\\n\"+\n     \"</code>\\n\"+\n     \"</div>\"}};\n\n  function display_loaded() {\n    var el = document.getElementById(\"13975323-f97c-4a49-991c-381a5178d8c3\");\n    if (el != null) {\n      el.textContent = \"BokehJS is loading...\";\n    }\n    if (root.Bokeh !== undefined) {\n      if (el != null) {\n        el.textContent = \"BokehJS \" + root.Bokeh.version + \" successfully loaded.\";\n      }\n    } else if (Date.now() < root._bokeh_timeout) {\n      setTimeout(display_loaded, 100)\n    }\n  }\n\n\n  function run_callbacks() {\n    try {\n      root._bokeh_onload_callbacks.forEach(function(callback) { callback() });\n    }\n    finally {\n      delete root._bokeh_onload_callbacks\n    }\n    console.info(\"Bokeh: all callbacks have finished\");\n  }\n\n  function load_libs(js_urls, callback) {\n    root._bokeh_onload_callbacks.push(callback);\n    if (root._bokeh_is_loading > 0) {\n      console.log(\"Bokeh: BokehJS is being loaded, scheduling callback at\", now());\n      return null;\n    }\n    if (js_urls == null || js_urls.length === 0) {\n      run_callbacks();\n      return null;\n    }\n    console.log(\"Bokeh: BokehJS not loaded, scheduling load and callback at\", now());\n    root._bokeh_is_loading = js_urls.length;\n    for (var i = 0; i < js_urls.length; i++) {\n      var url = js_urls[i];\n      var s = document.createElement('script');\n      s.src = url;\n      s.async = false;\n      s.onreadystatechange = s.onload = function() {\n        root._bokeh_is_loading--;\n        if (root._bokeh_is_loading === 0) {\n          console.log(\"Bokeh: all BokehJS libraries loaded\");\n          run_callbacks()\n        }\n      };\n      s.onerror = function() {\n        console.warn(\"failed to load library \" + url);\n      };\n      console.log(\"Bokeh: injecting script tag for BokehJS library: \", url);\n      document.getElementsByTagName(\"head\")[0].appendChild(s);\n    }\n  };var element = document.getElementById(\"13975323-f97c-4a49-991c-381a5178d8c3\");\n  if (element == null) {\n    console.log(\"Bokeh: ERROR: autoload.js configured with elementid '13975323-f97c-4a49-991c-381a5178d8c3' but no matching script tag was found. \")\n    return false;\n  }\n\n  var js_urls = [\"https://cdn.pydata.org/bokeh/release/bokeh-0.12.13.min.js\", \"https://cdn.pydata.org/bokeh/release/bokeh-widgets-0.12.13.min.js\", \"https://cdn.pydata.org/bokeh/release/bokeh-tables-0.12.13.min.js\", \"https://cdn.pydata.org/bokeh/release/bokeh-gl-0.12.13.min.js\"];\n\n  var inline_js = [\n    function(Bokeh) {\n      Bokeh.set_log_level(\"info\");\n    },\n    \n    function(Bokeh) {\n      \n    },\n    function(Bokeh) {\n      console.log(\"Bokeh: injecting CSS: https://cdn.pydata.org/bokeh/release/bokeh-0.12.13.min.css\");\n      Bokeh.embed.inject_css(\"https://cdn.pydata.org/bokeh/release/bokeh-0.12.13.min.css\");\n      console.log(\"Bokeh: injecting CSS: https://cdn.pydata.org/bokeh/release/bokeh-widgets-0.12.13.min.css\");\n      Bokeh.embed.inject_css(\"https://cdn.pydata.org/bokeh/release/bokeh-widgets-0.12.13.min.css\");\n      console.log(\"Bokeh: injecting CSS: https://cdn.pydata.org/bokeh/release/bokeh-tables-0.12.13.min.css\");\n      Bokeh.embed.inject_css(\"https://cdn.pydata.org/bokeh/release/bokeh-tables-0.12.13.min.css\");\n    }\n  ];\n\n  function run_inline_js() {\n    \n    if ((root.Bokeh !== undefined) || (force === true)) {\n      for (var i = 0; i < inline_js.length; i++) {\n        inline_js[i].call(root, root.Bokeh);\n      }if (force === true) {\n        display_loaded();\n      }} else if (Date.now() < root._bokeh_timeout) {\n      setTimeout(run_inline_js, 100);\n    } else if (!root._bokeh_failed_load) {\n      console.log(\"Bokeh: BokehJS failed to load within specified timeout.\");\n      root._bokeh_failed_load = true;\n    } else if (force !== true) {\n      var cell = $(document.getElementById(\"13975323-f97c-4a49-991c-381a5178d8c3\")).parents('.cell').data().cell;\n      cell.output_area.append_execute_result(NB_LOAD_WARNING)\n    }\n\n  }\n\n  if (root._bokeh_is_loading === 0) {\n    console.log(\"Bokeh: BokehJS loaded, going straight to plotting\");\n    run_inline_js();\n  } else {\n    load_libs(js_urls, function() {\n      console.log(\"Bokeh: BokehJS plotting callback run at\", now());\n      run_inline_js();\n    });\n  }\n}(window));"
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "\n",
       "<div class=\"bk-root\">\n",
       "    <div class=\"bk-plotdiv\" id=\"c65c9473-5846-4d14-ba1f-eefc2a4d30ab\"></div>\n",
       "</div>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "application/javascript": [
       "(function(root) {\n",
       "  function embed_document(root) {\n",
       "    \n",
       "  var docs_json = 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       "  var render_items = [{\"docid\":\"c46815c6-c324-435d-9c97-285112ce0365\",\"elementid\":\"c65c9473-5846-4d14-ba1f-eefc2a4d30ab\",\"modelid\":\"5165eeee-4825-4b0d-8457-09896a8fe8ca\"}];\n",
       "  root.Bokeh.embed.embed_items_notebook(docs_json, render_items);\n",
       "\n",
       "  }\n",
       "  if (root.Bokeh !== undefined) {\n",
       "    embed_document(root);\n",
       "  } else {\n",
       "    var attempts = 0;\n",
       "    var timer = setInterval(function(root) {\n",
       "      if (root.Bokeh !== undefined) {\n",
       "        embed_document(root);\n",
       "        clearInterval(timer);\n",
       "      }\n",
       "      attempts++;\n",
       "      if (attempts > 100) {\n",
       "        console.log(\"Bokeh: ERROR: Unable to run BokehJS code because BokehJS library is missing\")\n",
       "        clearInterval(timer);\n",
       "      }\n",
       "    }, 10, root)\n",
       "  }\n",
       "})(window);"
      ],
      "application/vnd.bokehjs_exec.v0+json": ""
     },
     "metadata": {
      "application/vnd.bokehjs_exec.v0+json": {
       "id": "5165eeee-4825-4b0d-8457-09896a8fe8ca"
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "output_notebook()\n",
    "p = figure(plot_width=950, plot_height=400)\n",
    "\n",
    "p.line(error_angular_velocity['timestep'][:-10], error_angular_velocity.dRoll[:-10], line_width=2, color='blue', legend='dRoll')\n",
    "p.line(error_angular_velocity['timestep'][:-10], error_angular_velocity.dPitch[:-10], line_width=2, color='red', legend='dPitch')\n",
    "p.line(error_angular_velocity['timestep'][:-10], error_angular_velocity.dYaw[:-10], line_width=2, color='purple', legend='dYaw')\n",
    "\n",
    "show(p)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Error in position across (20 seconds) averaged across 10 random trajectories"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 87,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "\n",
       "    <div class=\"bk-root\">\n",
       "        <a href=\"https://bokeh.pydata.org\" target=\"_blank\" class=\"bk-logo bk-logo-small bk-logo-notebook\"></a>\n",
       "        <span id=\"1df8e3c7-0ee8-4d72-973c-3ffbdfc71a91\">Loading BokehJS ...</span>\n",
       "    </div>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "application/javascript": [
       "\n",
       "(function(root) {\n",
       "  function now() {\n",
       "    return new Date();\n",
       "  }\n",
       "\n",
       "  var force = true;\n",
       "\n",
       "  if (typeof (root._bokeh_onload_callbacks) === \"undefined\" || force === true) {\n",
       "    root._bokeh_onload_callbacks = [];\n",
       "    root._bokeh_is_loading = undefined;\n",
       "  }\n",
       "\n",
       "  var JS_MIME_TYPE = 'application/javascript';\n",
       "  var HTML_MIME_TYPE = 'text/html';\n",
       "  var EXEC_MIME_TYPE = 'application/vnd.bokehjs_exec.v0+json';\n",
       "  var CLASS_NAME = 'output_bokeh rendered_html';\n",
       "\n",
       "  /**\n",
       "   * Render data to the DOM node\n",
       "   */\n",
       "  function render(props, node) {\n",
       "    var script = document.createElement(\"script\");\n",
       "    node.appendChild(script);\n",
       "  }\n",
       "\n",
       "  /**\n",
       "   * Handle when an output is cleared or removed\n",
       "   */\n",
       "  function handleClearOutput(event, handle) {\n",
       "    var cell = handle.cell;\n",
       "\n",
       "    var id = cell.output_area._bokeh_element_id;\n",
       "    var server_id = cell.output_area._bokeh_server_id;\n",
       "    // Clean up Bokeh references\n",
       "    if (id !== undefined) {\n",
       "      Bokeh.index[id].model.document.clear();\n",
       "      delete Bokeh.index[id];\n",
       "    }\n",
       "\n",
       "    if (server_id !== undefined) {\n",
       "      // Clean up Bokeh references\n",
       "      var cmd = \"from bokeh.io.state import curstate; print(curstate().uuid_to_server['\" + server_id + \"'].get_sessions()[0].document.roots[0]._id)\";\n",
       "      cell.notebook.kernel.execute(cmd, {\n",
       "        iopub: {\n",
       "          output: function(msg) {\n",
       "            var element_id = msg.content.text.trim();\n",
       "            Bokeh.index[element_id].model.document.clear();\n",
       "            delete Bokeh.index[element_id];\n",
       "          }\n",
       "        }\n",
       "      });\n",
       "      // Destroy server and session\n",
       "      var cmd = \"import bokeh.io.notebook as ion; ion.destroy_server('\" + server_id + \"')\";\n",
       "      cell.notebook.kernel.execute(cmd);\n",
       "    }\n",
       "  }\n",
       "\n",
       "  /**\n",
       "   * Handle when a new output is added\n",
       "   */\n",
       "  function handleAddOutput(event, handle) {\n",
       "    var output_area = handle.output_area;\n",
       "    var output = handle.output;\n",
       "\n",
       "    // limit handleAddOutput to display_data with EXEC_MIME_TYPE content only\n",
       "    if ((output.output_type != \"display_data\") || (!output.data.hasOwnProperty(EXEC_MIME_TYPE))) {\n",
       "      return\n",
       "    }\n",
       "\n",
       "    var toinsert = output_area.element.find(\".\" + CLASS_NAME.split(' ')[0]);\n",
       "\n",
       "    if (output.metadata[EXEC_MIME_TYPE][\"id\"] !== undefined) {\n",
       "      toinsert[0].firstChild.textContent = output.data[JS_MIME_TYPE];\n",
       "      // store reference to embed id on output_area\n",
       "      output_area._bokeh_element_id = output.metadata[EXEC_MIME_TYPE][\"id\"];\n",
       "    }\n",
       "    if (output.metadata[EXEC_MIME_TYPE][\"server_id\"] !== undefined) {\n",
       "      var bk_div = document.createElement(\"div\");\n",
       "      bk_div.innerHTML = output.data[HTML_MIME_TYPE];\n",
       "      var script_attrs = bk_div.children[0].attributes;\n",
       "      for (var i = 0; i < script_attrs.length; i++) {\n",
       "        toinsert[0].firstChild.setAttribute(script_attrs[i].name, script_attrs[i].value);\n",
       "      }\n",
       "      // store reference to server id on output_area\n",
       "      output_area._bokeh_server_id = output.metadata[EXEC_MIME_TYPE][\"server_id\"];\n",
       "    }\n",
       "  }\n",
       "\n",
       "  function register_renderer(events, OutputArea) {\n",
       "\n",
       "    function append_mime(data, metadata, element) {\n",
       "      // create a DOM node to render to\n",
       "      var toinsert = this.create_output_subarea(\n",
       "        metadata,\n",
       "        CLASS_NAME,\n",
       "        EXEC_MIME_TYPE\n",
       "      );\n",
       "      this.keyboard_manager.register_events(toinsert);\n",
       "      // Render to node\n",
       "      var props = {data: data, metadata: metadata[EXEC_MIME_TYPE]};\n",
       "      render(props, toinsert[0]);\n",
       "      element.append(toinsert);\n",
       "      return toinsert\n",
       "    }\n",
       "\n",
       "    /* Handle when an output is cleared or removed */\n",
       "    events.on('clear_output.CodeCell', handleClearOutput);\n",
       "    events.on('delete.Cell', handleClearOutput);\n",
       "\n",
       "    /* Handle when a new output is added */\n",
       "    events.on('output_added.OutputArea', handleAddOutput);\n",
       "\n",
       "    /**\n",
       "     * Register the mime type and append_mime function with output_area\n",
       "     */\n",
       "    OutputArea.prototype.register_mime_type(EXEC_MIME_TYPE, append_mime, {\n",
       "      /* Is output safe? */\n",
       "      safe: true,\n",
       "      /* Index of renderer in `output_area.display_order` */\n",
       "      index: 0\n",
       "    });\n",
       "  }\n",
       "\n",
       "  // register the mime type if in Jupyter Notebook environment and previously unregistered\n",
       "  if (root.Jupyter !== undefined) {\n",
       "    var events = require('base/js/events');\n",
       "    var OutputArea = require('notebook/js/outputarea').OutputArea;\n",
       "\n",
       "    if (OutputArea.prototype.mime_types().indexOf(EXEC_MIME_TYPE) == -1) {\n",
       "      register_renderer(events, OutputArea);\n",
       "    }\n",
       "  }\n",
       "\n",
       "  \n",
       "  if (typeof (root._bokeh_timeout) === \"undefined\" || force === true) {\n",
       "    root._bokeh_timeout = Date.now() + 5000;\n",
       "    root._bokeh_failed_load = false;\n",
       "  }\n",
       "\n",
       "  var NB_LOAD_WARNING = {'data': {'text/html':\n",
       "     \"<div style='background-color: #fdd'>\\n\"+\n",
       "     \"<p>\\n\"+\n",
       "     \"BokehJS does not appear to have successfully loaded. If loading BokehJS from CDN, this \\n\"+\n",
       "     \"may be due to a slow or bad network connection. Possible fixes:\\n\"+\n",
       "     \"</p>\\n\"+\n",
       "     \"<ul>\\n\"+\n",
       "     \"<li>re-rerun `output_notebook()` to attempt to load from CDN again, or</li>\\n\"+\n",
       "     \"<li>use INLINE resources instead, as so:</li>\\n\"+\n",
       "     \"</ul>\\n\"+\n",
       "     \"<code>\\n\"+\n",
       "     \"from bokeh.resources import INLINE\\n\"+\n",
       "     \"output_notebook(resources=INLINE)\\n\"+\n",
       "     \"</code>\\n\"+\n",
       "     \"</div>\"}};\n",
       "\n",
       "  function display_loaded() {\n",
       "    var el = document.getElementById(\"1df8e3c7-0ee8-4d72-973c-3ffbdfc71a91\");\n",
       "    if (el != null) {\n",
       "      el.textContent = \"BokehJS is loading...\";\n",
       "    }\n",
       "    if (root.Bokeh !== undefined) {\n",
       "      if (el != null) {\n",
       "        el.textContent = \"BokehJS \" + root.Bokeh.version + \" successfully loaded.\";\n",
       "      }\n",
       "    } else if (Date.now() < root._bokeh_timeout) {\n",
       "      setTimeout(display_loaded, 100)\n",
       "    }\n",
       "  }\n",
       "\n",
       "\n",
       "  function run_callbacks() {\n",
       "    try {\n",
       "      root._bokeh_onload_callbacks.forEach(function(callback) { callback() });\n",
       "    }\n",
       "    finally {\n",
       "      delete root._bokeh_onload_callbacks\n",
       "    }\n",
       "    console.info(\"Bokeh: all callbacks have finished\");\n",
       "  }\n",
       "\n",
       "  function load_libs(js_urls, callback) {\n",
       "    root._bokeh_onload_callbacks.push(callback);\n",
       "    if (root._bokeh_is_loading > 0) {\n",
       "      console.log(\"Bokeh: BokehJS is being loaded, scheduling callback at\", now());\n",
       "      return null;\n",
       "    }\n",
       "    if (js_urls == null || js_urls.length === 0) {\n",
       "      run_callbacks();\n",
       "      return null;\n",
       "    }\n",
       "    console.log(\"Bokeh: BokehJS not loaded, scheduling load and callback at\", now());\n",
       "    root._bokeh_is_loading = js_urls.length;\n",
       "    for (var i = 0; i < js_urls.length; i++) {\n",
       "      var url = js_urls[i];\n",
       "      var s = document.createElement('script');\n",
       "      s.src = url;\n",
       "      s.async = false;\n",
       "      s.onreadystatechange = s.onload = function() {\n",
       "        root._bokeh_is_loading--;\n",
       "        if (root._bokeh_is_loading === 0) {\n",
       "          console.log(\"Bokeh: all BokehJS libraries loaded\");\n",
       "          run_callbacks()\n",
       "        }\n",
       "      };\n",
       "      s.onerror = function() {\n",
       "        console.warn(\"failed to load library \" + url);\n",
       "      };\n",
       "      console.log(\"Bokeh: injecting script tag for BokehJS library: \", url);\n",
       "      document.getElementsByTagName(\"head\")[0].appendChild(s);\n",
       "    }\n",
       "  };var element = document.getElementById(\"1df8e3c7-0ee8-4d72-973c-3ffbdfc71a91\");\n",
       "  if (element == null) {\n",
       "    console.log(\"Bokeh: ERROR: autoload.js configured with elementid '1df8e3c7-0ee8-4d72-973c-3ffbdfc71a91' but no matching script tag was found. \")\n",
       "    return false;\n",
       "  }\n",
       "\n",
       "  var js_urls = [\"https://cdn.pydata.org/bokeh/release/bokeh-0.12.13.min.js\", \"https://cdn.pydata.org/bokeh/release/bokeh-widgets-0.12.13.min.js\", \"https://cdn.pydata.org/bokeh/release/bokeh-tables-0.12.13.min.js\", \"https://cdn.pydata.org/bokeh/release/bokeh-gl-0.12.13.min.js\"];\n",
       "\n",
       "  var inline_js = [\n",
       "    function(Bokeh) {\n",
       "      Bokeh.set_log_level(\"info\");\n",
       "    },\n",
       "    \n",
       "    function(Bokeh) {\n",
       "      \n",
       "    },\n",
       "    function(Bokeh) {\n",
       "      console.log(\"Bokeh: injecting CSS: https://cdn.pydata.org/bokeh/release/bokeh-0.12.13.min.css\");\n",
       "      Bokeh.embed.inject_css(\"https://cdn.pydata.org/bokeh/release/bokeh-0.12.13.min.css\");\n",
       "      console.log(\"Bokeh: injecting CSS: https://cdn.pydata.org/bokeh/release/bokeh-widgets-0.12.13.min.css\");\n",
       "      Bokeh.embed.inject_css(\"https://cdn.pydata.org/bokeh/release/bokeh-widgets-0.12.13.min.css\");\n",
       "      console.log(\"Bokeh: injecting CSS: https://cdn.pydata.org/bokeh/release/bokeh-tables-0.12.13.min.css\");\n",
       "      Bokeh.embed.inject_css(\"https://cdn.pydata.org/bokeh/release/bokeh-tables-0.12.13.min.css\");\n",
       "    }\n",
       "  ];\n",
       "\n",
       "  function run_inline_js() {\n",
       "    \n",
       "    if ((root.Bokeh !== undefined) || (force === true)) {\n",
       "      for (var i = 0; i < inline_js.length; i++) {\n",
       "        inline_js[i].call(root, root.Bokeh);\n",
       "      }if (force === true) {\n",
       "        display_loaded();\n",
       "      }} else if (Date.now() < root._bokeh_timeout) {\n",
       "      setTimeout(run_inline_js, 100);\n",
       "    } else if (!root._bokeh_failed_load) {\n",
       "      console.log(\"Bokeh: BokehJS failed to load within specified timeout.\");\n",
       "      root._bokeh_failed_load = true;\n",
       "    } else if (force !== true) {\n",
       "      var cell = $(document.getElementById(\"1df8e3c7-0ee8-4d72-973c-3ffbdfc71a91\")).parents('.cell').data().cell;\n",
       "      cell.output_area.append_execute_result(NB_LOAD_WARNING)\n",
       "    }\n",
       "\n",
       "  }\n",
       "\n",
       "  if (root._bokeh_is_loading === 0) {\n",
       "    console.log(\"Bokeh: BokehJS loaded, going straight to plotting\");\n",
       "    run_inline_js();\n",
       "  } else {\n",
       "    load_libs(js_urls, function() {\n",
       "      console.log(\"Bokeh: BokehJS plotting callback run at\", now());\n",
       "      run_inline_js();\n",
       "    });\n",
       "  }\n",
       "}(window));"
      ],
      "application/vnd.bokehjs_load.v0+json": "\n(function(root) {\n  function now() {\n    return new Date();\n  }\n\n  var force = true;\n\n  if (typeof (root._bokeh_onload_callbacks) === \"undefined\" || force === true) {\n    root._bokeh_onload_callbacks = [];\n    root._bokeh_is_loading = undefined;\n  }\n\n  \n\n  \n  if (typeof (root._bokeh_timeout) === \"undefined\" || force === true) {\n    root._bokeh_timeout = Date.now() + 5000;\n    root._bokeh_failed_load = false;\n  }\n\n  var NB_LOAD_WARNING = {'data': {'text/html':\n     \"<div style='background-color: #fdd'>\\n\"+\n     \"<p>\\n\"+\n     \"BokehJS does not appear to have successfully loaded. If loading BokehJS from CDN, this \\n\"+\n     \"may be due to a slow or bad network connection. Possible fixes:\\n\"+\n     \"</p>\\n\"+\n     \"<ul>\\n\"+\n     \"<li>re-rerun `output_notebook()` to attempt to load from CDN again, or</li>\\n\"+\n     \"<li>use INLINE resources instead, as so:</li>\\n\"+\n     \"</ul>\\n\"+\n     \"<code>\\n\"+\n     \"from bokeh.resources import INLINE\\n\"+\n     \"output_notebook(resources=INLINE)\\n\"+\n     \"</code>\\n\"+\n     \"</div>\"}};\n\n  function display_loaded() {\n    var el = document.getElementById(\"1df8e3c7-0ee8-4d72-973c-3ffbdfc71a91\");\n    if (el != null) {\n      el.textContent = \"BokehJS is loading...\";\n    }\n    if (root.Bokeh !== undefined) {\n      if (el != null) {\n        el.textContent = \"BokehJS \" + root.Bokeh.version + \" successfully loaded.\";\n      }\n    } else if (Date.now() < root._bokeh_timeout) {\n      setTimeout(display_loaded, 100)\n    }\n  }\n\n\n  function run_callbacks() {\n    try {\n      root._bokeh_onload_callbacks.forEach(function(callback) { callback() });\n    }\n    finally {\n      delete root._bokeh_onload_callbacks\n    }\n    console.info(\"Bokeh: all callbacks have finished\");\n  }\n\n  function load_libs(js_urls, callback) {\n    root._bokeh_onload_callbacks.push(callback);\n    if (root._bokeh_is_loading > 0) {\n      console.log(\"Bokeh: BokehJS is being loaded, scheduling callback at\", now());\n      return null;\n    }\n    if (js_urls == null || js_urls.length === 0) {\n      run_callbacks();\n      return null;\n    }\n    console.log(\"Bokeh: BokehJS not loaded, scheduling load and callback at\", now());\n    root._bokeh_is_loading = js_urls.length;\n    for (var i = 0; i < js_urls.length; i++) {\n      var url = js_urls[i];\n      var s = document.createElement('script');\n      s.src = url;\n      s.async = false;\n      s.onreadystatechange = s.onload = function() {\n        root._bokeh_is_loading--;\n        if (root._bokeh_is_loading === 0) {\n          console.log(\"Bokeh: all BokehJS libraries loaded\");\n          run_callbacks()\n        }\n      };\n      s.onerror = function() {\n        console.warn(\"failed to load library \" + url);\n      };\n      console.log(\"Bokeh: injecting script tag for BokehJS library: \", url);\n      document.getElementsByTagName(\"head\")[0].appendChild(s);\n    }\n  };var element = document.getElementById(\"1df8e3c7-0ee8-4d72-973c-3ffbdfc71a91\");\n  if (element == null) {\n    console.log(\"Bokeh: ERROR: autoload.js configured with elementid '1df8e3c7-0ee8-4d72-973c-3ffbdfc71a91' but no matching script tag was found. \")\n    return false;\n  }\n\n  var js_urls = [\"https://cdn.pydata.org/bokeh/release/bokeh-0.12.13.min.js\", \"https://cdn.pydata.org/bokeh/release/bokeh-widgets-0.12.13.min.js\", \"https://cdn.pydata.org/bokeh/release/bokeh-tables-0.12.13.min.js\", \"https://cdn.pydata.org/bokeh/release/bokeh-gl-0.12.13.min.js\"];\n\n  var inline_js = [\n    function(Bokeh) {\n      Bokeh.set_log_level(\"info\");\n    },\n    \n    function(Bokeh) {\n      \n    },\n    function(Bokeh) {\n      console.log(\"Bokeh: injecting CSS: https://cdn.pydata.org/bokeh/release/bokeh-0.12.13.min.css\");\n      Bokeh.embed.inject_css(\"https://cdn.pydata.org/bokeh/release/bokeh-0.12.13.min.css\");\n      console.log(\"Bokeh: injecting CSS: https://cdn.pydata.org/bokeh/release/bokeh-widgets-0.12.13.min.css\");\n      Bokeh.embed.inject_css(\"https://cdn.pydata.org/bokeh/release/bokeh-widgets-0.12.13.min.css\");\n      console.log(\"Bokeh: injecting CSS: https://cdn.pydata.org/bokeh/release/bokeh-tables-0.12.13.min.css\");\n      Bokeh.embed.inject_css(\"https://cdn.pydata.org/bokeh/release/bokeh-tables-0.12.13.min.css\");\n    }\n  ];\n\n  function run_inline_js() {\n    \n    if ((root.Bokeh !== undefined) || (force === true)) {\n      for (var i = 0; i < inline_js.length; i++) {\n        inline_js[i].call(root, root.Bokeh);\n      }if (force === true) {\n        display_loaded();\n      }} else if (Date.now() < root._bokeh_timeout) {\n      setTimeout(run_inline_js, 100);\n    } else if (!root._bokeh_failed_load) {\n      console.log(\"Bokeh: BokehJS failed to load within specified timeout.\");\n      root._bokeh_failed_load = true;\n    } else if (force !== true) {\n      var cell = $(document.getElementById(\"1df8e3c7-0ee8-4d72-973c-3ffbdfc71a91\")).parents('.cell').data().cell;\n      cell.output_area.append_execute_result(NB_LOAD_WARNING)\n    }\n\n  }\n\n  if (root._bokeh_is_loading === 0) {\n    console.log(\"Bokeh: BokehJS loaded, going straight to plotting\");\n    run_inline_js();\n  } else {\n    load_libs(js_urls, function() {\n      console.log(\"Bokeh: BokehJS plotting callback run at\", now());\n      run_inline_js();\n    });\n  }\n}(window));"
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "\n",
       "<div class=\"bk-root\">\n",
       "    <div class=\"bk-plotdiv\" id=\"70c2ff08-5e0d-4075-8a80-20730f36cba8\"></div>\n",
       "</div>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "application/javascript": [
       "(function(root) {\n",
       "  function embed_document(root) {\n",
       "    \n",
       "  var docs_json = 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Application\",\"version\":\"0.12.13\"}};\n",
       "  var render_items = [{\"docid\":\"4e96510f-f0e6-466e-917f-bf27255d8fd8\",\"elementid\":\"70c2ff08-5e0d-4075-8a80-20730f36cba8\",\"modelid\":\"88a2c5ab-790d-4c70-8e90-f21d234c3635\"}];\n",
       "  root.Bokeh.embed.embed_items_notebook(docs_json, render_items);\n",
       "\n",
       "  }\n",
       "  if (root.Bokeh !== undefined) {\n",
       "    embed_document(root);\n",
       "  } else {\n",
       "    var attempts = 0;\n",
       "    var timer = setInterval(function(root) {\n",
       "      if (root.Bokeh !== undefined) {\n",
       "        embed_document(root);\n",
       "        clearInterval(timer);\n",
       "      }\n",
       "      attempts++;\n",
       "      if (attempts > 100) {\n",
       "        console.log(\"Bokeh: ERROR: Unable to run BokehJS code because BokehJS library is missing\")\n",
       "        clearInterval(timer);\n",
       "      }\n",
       "    }, 10, root)\n",
       "  }\n",
       "})(window);"
      ],
      "application/vnd.bokehjs_exec.v0+json": ""
     },
     "metadata": {
      "application/vnd.bokehjs_exec.v0+json": {
       "id": "88a2c5ab-790d-4c70-8e90-f21d234c3635"
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "output_notebook()\n",
    "p = figure(plot_width=950, plot_height=400)\n",
    "\n",
    "p.line(error_pos['timestep'][:-10], error_pos.x[:-10], line_width=2, color='blue', legend='x')\n",
    "p.line(error_pos['timestep'][:-10], error_pos.y[:-10], line_width=2, color='red', legend='y')\n",
    "p.line(error_pos['timestep'][:-10], error_pos.z[:-10], line_width=2, color='purple', legend='z')\n",
    "\n",
    "show(p)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Error in Orientation (smallest angle) in radians (20 seconds) averaged across 10 random trajectories"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 88,
   "metadata": {
    "pixiedust": {
     "displayParams": {
      "aggregation": "SUM",
      "charttype": "grouped",
      "handlerId": "barChart",
      "keyFields": "timestep",
      "rowCount": "500",
      "valueFields": "roll,pitch,yaw"
     }
    },
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "\n",
       "    <div class=\"bk-root\">\n",
       "        <a href=\"https://bokeh.pydata.org\" target=\"_blank\" class=\"bk-logo bk-logo-small bk-logo-notebook\"></a>\n",
       "        <span id=\"3be80eb3-2207-434c-9311-b8c122ef9506\">Loading BokehJS ...</span>\n",
       "    </div>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "application/javascript": [
       "\n",
       "(function(root) {\n",
       "  function now() {\n",
       "    return new Date();\n",
       "  }\n",
       "\n",
       "  var force = true;\n",
       "\n",
       "  if (typeof (root._bokeh_onload_callbacks) === \"undefined\" || force === true) {\n",
       "    root._bokeh_onload_callbacks = [];\n",
       "    root._bokeh_is_loading = undefined;\n",
       "  }\n",
       "\n",
       "  var JS_MIME_TYPE = 'application/javascript';\n",
       "  var HTML_MIME_TYPE = 'text/html';\n",
       "  var EXEC_MIME_TYPE = 'application/vnd.bokehjs_exec.v0+json';\n",
       "  var CLASS_NAME = 'output_bokeh rendered_html';\n",
       "\n",
       "  /**\n",
       "   * Render data to the DOM node\n",
       "   */\n",
       "  function render(props, node) {\n",
       "    var script = document.createElement(\"script\");\n",
       "    node.appendChild(script);\n",
       "  }\n",
       "\n",
       "  /**\n",
       "   * Handle when an output is cleared or removed\n",
       "   */\n",
       "  function handleClearOutput(event, handle) {\n",
       "    var cell = handle.cell;\n",
       "\n",
       "    var id = cell.output_area._bokeh_element_id;\n",
       "    var server_id = cell.output_area._bokeh_server_id;\n",
       "    // Clean up Bokeh references\n",
       "    if (id !== undefined) {\n",
       "      Bokeh.index[id].model.document.clear();\n",
       "      delete Bokeh.index[id];\n",
       "    }\n",
       "\n",
       "    if (server_id !== undefined) {\n",
       "      // Clean up Bokeh references\n",
       "      var cmd = \"from bokeh.io.state import curstate; print(curstate().uuid_to_server['\" + server_id + \"'].get_sessions()[0].document.roots[0]._id)\";\n",
       "      cell.notebook.kernel.execute(cmd, {\n",
       "        iopub: {\n",
       "          output: function(msg) {\n",
       "            var element_id = msg.content.text.trim();\n",
       "            Bokeh.index[element_id].model.document.clear();\n",
       "            delete Bokeh.index[element_id];\n",
       "          }\n",
       "        }\n",
       "      });\n",
       "      // Destroy server and session\n",
       "      var cmd = \"import bokeh.io.notebook as ion; ion.destroy_server('\" + server_id + \"')\";\n",
       "      cell.notebook.kernel.execute(cmd);\n",
       "    }\n",
       "  }\n",
       "\n",
       "  /**\n",
       "   * Handle when a new output is added\n",
       "   */\n",
       "  function handleAddOutput(event, handle) {\n",
       "    var output_area = handle.output_area;\n",
       "    var output = handle.output;\n",
       "\n",
       "    // limit handleAddOutput to display_data with EXEC_MIME_TYPE content only\n",
       "    if ((output.output_type != \"display_data\") || (!output.data.hasOwnProperty(EXEC_MIME_TYPE))) {\n",
       "      return\n",
       "    }\n",
       "\n",
       "    var toinsert = output_area.element.find(\".\" + CLASS_NAME.split(' ')[0]);\n",
       "\n",
       "    if (output.metadata[EXEC_MIME_TYPE][\"id\"] !== undefined) {\n",
       "      toinsert[0].firstChild.textContent = output.data[JS_MIME_TYPE];\n",
       "      // store reference to embed id on output_area\n",
       "      output_area._bokeh_element_id = output.metadata[EXEC_MIME_TYPE][\"id\"];\n",
       "    }\n",
       "    if (output.metadata[EXEC_MIME_TYPE][\"server_id\"] !== undefined) {\n",
       "      var bk_div = document.createElement(\"div\");\n",
       "      bk_div.innerHTML = output.data[HTML_MIME_TYPE];\n",
       "      var script_attrs = bk_div.children[0].attributes;\n",
       "      for (var i = 0; i < script_attrs.length; i++) {\n",
       "        toinsert[0].firstChild.setAttribute(script_attrs[i].name, script_attrs[i].value);\n",
       "      }\n",
       "      // store reference to server id on output_area\n",
       "      output_area._bokeh_server_id = output.metadata[EXEC_MIME_TYPE][\"server_id\"];\n",
       "    }\n",
       "  }\n",
       "\n",
       "  function register_renderer(events, OutputArea) {\n",
       "\n",
       "    function append_mime(data, metadata, element) {\n",
       "      // create a DOM node to render to\n",
       "      var toinsert = this.create_output_subarea(\n",
       "        metadata,\n",
       "        CLASS_NAME,\n",
       "        EXEC_MIME_TYPE\n",
       "      );\n",
       "      this.keyboard_manager.register_events(toinsert);\n",
       "      // Render to node\n",
       "      var props = {data: data, metadata: metadata[EXEC_MIME_TYPE]};\n",
       "      render(props, toinsert[0]);\n",
       "      element.append(toinsert);\n",
       "      return toinsert\n",
       "    }\n",
       "\n",
       "    /* Handle when an output is cleared or removed */\n",
       "    events.on('clear_output.CodeCell', handleClearOutput);\n",
       "    events.on('delete.Cell', handleClearOutput);\n",
       "\n",
       "    /* Handle when a new output is added */\n",
       "    events.on('output_added.OutputArea', handleAddOutput);\n",
       "\n",
       "    /**\n",
       "     * Register the mime type and append_mime function with output_area\n",
       "     */\n",
       "    OutputArea.prototype.register_mime_type(EXEC_MIME_TYPE, append_mime, {\n",
       "      /* Is output safe? */\n",
       "      safe: true,\n",
       "      /* Index of renderer in `output_area.display_order` */\n",
       "      index: 0\n",
       "    });\n",
       "  }\n",
       "\n",
       "  // register the mime type if in Jupyter Notebook environment and previously unregistered\n",
       "  if (root.Jupyter !== undefined) {\n",
       "    var events = require('base/js/events');\n",
       "    var OutputArea = require('notebook/js/outputarea').OutputArea;\n",
       "\n",
       "    if (OutputArea.prototype.mime_types().indexOf(EXEC_MIME_TYPE) == -1) {\n",
       "      register_renderer(events, OutputArea);\n",
       "    }\n",
       "  }\n",
       "\n",
       "  \n",
       "  if (typeof (root._bokeh_timeout) === \"undefined\" || force === true) {\n",
       "    root._bokeh_timeout = Date.now() + 5000;\n",
       "    root._bokeh_failed_load = false;\n",
       "  }\n",
       "\n",
       "  var NB_LOAD_WARNING = {'data': {'text/html':\n",
       "     \"<div style='background-color: #fdd'>\\n\"+\n",
       "     \"<p>\\n\"+\n",
       "     \"BokehJS does not appear to have successfully loaded. If loading BokehJS from CDN, this \\n\"+\n",
       "     \"may be due to a slow or bad network connection. Possible fixes:\\n\"+\n",
       "     \"</p>\\n\"+\n",
       "     \"<ul>\\n\"+\n",
       "     \"<li>re-rerun `output_notebook()` to attempt to load from CDN again, or</li>\\n\"+\n",
       "     \"<li>use INLINE resources instead, as so:</li>\\n\"+\n",
       "     \"</ul>\\n\"+\n",
       "     \"<code>\\n\"+\n",
       "     \"from bokeh.resources import INLINE\\n\"+\n",
       "     \"output_notebook(resources=INLINE)\\n\"+\n",
       "     \"</code>\\n\"+\n",
       "     \"</div>\"}};\n",
       "\n",
       "  function display_loaded() {\n",
       "    var el = document.getElementById(\"3be80eb3-2207-434c-9311-b8c122ef9506\");\n",
       "    if (el != null) {\n",
       "      el.textContent = \"BokehJS is loading...\";\n",
       "    }\n",
       "    if (root.Bokeh !== undefined) {\n",
       "      if (el != null) {\n",
       "        el.textContent = \"BokehJS \" + root.Bokeh.version + \" successfully loaded.\";\n",
       "      }\n",
       "    } else if (Date.now() < root._bokeh_timeout) {\n",
       "      setTimeout(display_loaded, 100)\n",
       "    }\n",
       "  }\n",
       "\n",
       "\n",
       "  function run_callbacks() {\n",
       "    try {\n",
       "      root._bokeh_onload_callbacks.forEach(function(callback) { callback() });\n",
       "    }\n",
       "    finally {\n",
       "      delete root._bokeh_onload_callbacks\n",
       "    }\n",
       "    console.info(\"Bokeh: all callbacks have finished\");\n",
       "  }\n",
       "\n",
       "  function load_libs(js_urls, callback) {\n",
       "    root._bokeh_onload_callbacks.push(callback);\n",
       "    if (root._bokeh_is_loading > 0) {\n",
       "      console.log(\"Bokeh: BokehJS is being loaded, scheduling callback at\", now());\n",
       "      return null;\n",
       "    }\n",
       "    if (js_urls == null || js_urls.length === 0) {\n",
       "      run_callbacks();\n",
       "      return null;\n",
       "    }\n",
       "    console.log(\"Bokeh: BokehJS not loaded, scheduling load and callback at\", now());\n",
       "    root._bokeh_is_loading = js_urls.length;\n",
       "    for (var i = 0; i < js_urls.length; i++) {\n",
       "      var url = js_urls[i];\n",
       "      var s = document.createElement('script');\n",
       "      s.src = url;\n",
       "      s.async = false;\n",
       "      s.onreadystatechange = s.onload = function() {\n",
       "        root._bokeh_is_loading--;\n",
       "        if (root._bokeh_is_loading === 0) {\n",
       "          console.log(\"Bokeh: all BokehJS libraries loaded\");\n",
       "          run_callbacks()\n",
       "        }\n",
       "      };\n",
       "      s.onerror = function() {\n",
       "        console.warn(\"failed to load library \" + url);\n",
       "      };\n",
       "      console.log(\"Bokeh: injecting script tag for BokehJS library: \", url);\n",
       "      document.getElementsByTagName(\"head\")[0].appendChild(s);\n",
       "    }\n",
       "  };var element = document.getElementById(\"3be80eb3-2207-434c-9311-b8c122ef9506\");\n",
       "  if (element == null) {\n",
       "    console.log(\"Bokeh: ERROR: autoload.js configured with elementid '3be80eb3-2207-434c-9311-b8c122ef9506' but no matching script tag was found. \")\n",
       "    return false;\n",
       "  }\n",
       "\n",
       "  var js_urls = [\"https://cdn.pydata.org/bokeh/release/bokeh-0.12.13.min.js\", \"https://cdn.pydata.org/bokeh/release/bokeh-widgets-0.12.13.min.js\", \"https://cdn.pydata.org/bokeh/release/bokeh-tables-0.12.13.min.js\", \"https://cdn.pydata.org/bokeh/release/bokeh-gl-0.12.13.min.js\"];\n",
       "\n",
       "  var inline_js = [\n",
       "    function(Bokeh) {\n",
       "      Bokeh.set_log_level(\"info\");\n",
       "    },\n",
       "    \n",
       "    function(Bokeh) {\n",
       "      \n",
       "    },\n",
       "    function(Bokeh) {\n",
       "      console.log(\"Bokeh: injecting CSS: https://cdn.pydata.org/bokeh/release/bokeh-0.12.13.min.css\");\n",
       "      Bokeh.embed.inject_css(\"https://cdn.pydata.org/bokeh/release/bokeh-0.12.13.min.css\");\n",
       "      console.log(\"Bokeh: injecting CSS: https://cdn.pydata.org/bokeh/release/bokeh-widgets-0.12.13.min.css\");\n",
       "      Bokeh.embed.inject_css(\"https://cdn.pydata.org/bokeh/release/bokeh-widgets-0.12.13.min.css\");\n",
       "      console.log(\"Bokeh: injecting CSS: https://cdn.pydata.org/bokeh/release/bokeh-tables-0.12.13.min.css\");\n",
       "      Bokeh.embed.inject_css(\"https://cdn.pydata.org/bokeh/release/bokeh-tables-0.12.13.min.css\");\n",
       "    }\n",
       "  ];\n",
       "\n",
       "  function run_inline_js() {\n",
       "    \n",
       "    if ((root.Bokeh !== undefined) || (force === true)) {\n",
       "      for (var i = 0; i < inline_js.length; i++) {\n",
       "        inline_js[i].call(root, root.Bokeh);\n",
       "      }if (force === true) {\n",
       "        display_loaded();\n",
       "      }} else if (Date.now() < root._bokeh_timeout) {\n",
       "      setTimeout(run_inline_js, 100);\n",
       "    } else if (!root._bokeh_failed_load) {\n",
       "      console.log(\"Bokeh: BokehJS failed to load within specified timeout.\");\n",
       "      root._bokeh_failed_load = true;\n",
       "    } else if (force !== true) {\n",
       "      var cell = $(document.getElementById(\"3be80eb3-2207-434c-9311-b8c122ef9506\")).parents('.cell').data().cell;\n",
       "      cell.output_area.append_execute_result(NB_LOAD_WARNING)\n",
       "    }\n",
       "\n",
       "  }\n",
       "\n",
       "  if (root._bokeh_is_loading === 0) {\n",
       "    console.log(\"Bokeh: BokehJS loaded, going straight to plotting\");\n",
       "    run_inline_js();\n",
       "  } else {\n",
       "    load_libs(js_urls, function() {\n",
       "      console.log(\"Bokeh: BokehJS plotting callback run at\", now());\n",
       "      run_inline_js();\n",
       "    });\n",
       "  }\n",
       "}(window));"
      ],
      "application/vnd.bokehjs_load.v0+json": "\n(function(root) {\n  function now() {\n    return new Date();\n  }\n\n  var force = true;\n\n  if (typeof (root._bokeh_onload_callbacks) === \"undefined\" || force === true) {\n    root._bokeh_onload_callbacks = [];\n    root._bokeh_is_loading = undefined;\n  }\n\n  \n\n  \n  if (typeof (root._bokeh_timeout) === \"undefined\" || force === true) {\n    root._bokeh_timeout = Date.now() + 5000;\n    root._bokeh_failed_load = false;\n  }\n\n  var NB_LOAD_WARNING = {'data': {'text/html':\n     \"<div style='background-color: #fdd'>\\n\"+\n     \"<p>\\n\"+\n     \"BokehJS does not appear to have successfully loaded. If loading BokehJS from CDN, this \\n\"+\n     \"may be due to a slow or bad network connection. Possible fixes:\\n\"+\n     \"</p>\\n\"+\n     \"<ul>\\n\"+\n     \"<li>re-rerun `output_notebook()` to attempt to load from CDN again, or</li>\\n\"+\n     \"<li>use INLINE resources instead, as so:</li>\\n\"+\n     \"</ul>\\n\"+\n     \"<code>\\n\"+\n     \"from bokeh.resources import INLINE\\n\"+\n     \"output_notebook(resources=INLINE)\\n\"+\n     \"</code>\\n\"+\n     \"</div>\"}};\n\n  function display_loaded() {\n    var el = document.getElementById(\"3be80eb3-2207-434c-9311-b8c122ef9506\");\n    if (el != null) {\n      el.textContent = \"BokehJS is loading...\";\n    }\n    if (root.Bokeh !== undefined) {\n      if (el != null) {\n        el.textContent = \"BokehJS \" + root.Bokeh.version + \" successfully loaded.\";\n      }\n    } else if (Date.now() < root._bokeh_timeout) {\n      setTimeout(display_loaded, 100)\n    }\n  }\n\n\n  function run_callbacks() {\n    try {\n      root._bokeh_onload_callbacks.forEach(function(callback) { callback() });\n    }\n    finally {\n      delete root._bokeh_onload_callbacks\n    }\n    console.info(\"Bokeh: all callbacks have finished\");\n  }\n\n  function load_libs(js_urls, callback) {\n    root._bokeh_onload_callbacks.push(callback);\n    if (root._bokeh_is_loading > 0) {\n      console.log(\"Bokeh: BokehJS is being loaded, scheduling callback at\", now());\n      return null;\n    }\n    if (js_urls == null || js_urls.length === 0) {\n      run_callbacks();\n      return null;\n    }\n    console.log(\"Bokeh: BokehJS not loaded, scheduling load and callback at\", now());\n    root._bokeh_is_loading = js_urls.length;\n    for (var i = 0; i < js_urls.length; i++) {\n      var url = js_urls[i];\n      var s = document.createElement('script');\n      s.src = url;\n      s.async = false;\n      s.onreadystatechange = s.onload = function() {\n        root._bokeh_is_loading--;\n        if (root._bokeh_is_loading === 0) {\n          console.log(\"Bokeh: all BokehJS libraries loaded\");\n          run_callbacks()\n        }\n      };\n      s.onerror = function() {\n        console.warn(\"failed to load library \" + url);\n      };\n      console.log(\"Bokeh: injecting script tag for BokehJS library: \", url);\n      document.getElementsByTagName(\"head\")[0].appendChild(s);\n    }\n  };var element = document.getElementById(\"3be80eb3-2207-434c-9311-b8c122ef9506\");\n  if (element == null) {\n    console.log(\"Bokeh: ERROR: autoload.js configured with elementid '3be80eb3-2207-434c-9311-b8c122ef9506' but no matching script tag was found. \")\n    return false;\n  }\n\n  var js_urls = [\"https://cdn.pydata.org/bokeh/release/bokeh-0.12.13.min.js\", \"https://cdn.pydata.org/bokeh/release/bokeh-widgets-0.12.13.min.js\", \"https://cdn.pydata.org/bokeh/release/bokeh-tables-0.12.13.min.js\", \"https://cdn.pydata.org/bokeh/release/bokeh-gl-0.12.13.min.js\"];\n\n  var inline_js = [\n    function(Bokeh) {\n      Bokeh.set_log_level(\"info\");\n    },\n    \n    function(Bokeh) {\n      \n    },\n    function(Bokeh) {\n      console.log(\"Bokeh: injecting CSS: https://cdn.pydata.org/bokeh/release/bokeh-0.12.13.min.css\");\n      Bokeh.embed.inject_css(\"https://cdn.pydata.org/bokeh/release/bokeh-0.12.13.min.css\");\n      console.log(\"Bokeh: injecting CSS: https://cdn.pydata.org/bokeh/release/bokeh-widgets-0.12.13.min.css\");\n      Bokeh.embed.inject_css(\"https://cdn.pydata.org/bokeh/release/bokeh-widgets-0.12.13.min.css\");\n      console.log(\"Bokeh: injecting CSS: https://cdn.pydata.org/bokeh/release/bokeh-tables-0.12.13.min.css\");\n      Bokeh.embed.inject_css(\"https://cdn.pydata.org/bokeh/release/bokeh-tables-0.12.13.min.css\");\n    }\n  ];\n\n  function run_inline_js() {\n    \n    if ((root.Bokeh !== undefined) || (force === true)) {\n      for (var i = 0; i < inline_js.length; i++) {\n        inline_js[i].call(root, root.Bokeh);\n      }if (force === true) {\n        display_loaded();\n      }} else if (Date.now() < root._bokeh_timeout) {\n      setTimeout(run_inline_js, 100);\n    } else if (!root._bokeh_failed_load) {\n      console.log(\"Bokeh: BokehJS failed to load within specified timeout.\");\n      root._bokeh_failed_load = true;\n    } else if (force !== true) {\n      var cell = $(document.getElementById(\"3be80eb3-2207-434c-9311-b8c122ef9506\")).parents('.cell').data().cell;\n      cell.output_area.append_execute_result(NB_LOAD_WARNING)\n    }\n\n  }\n\n  if (root._bokeh_is_loading === 0) {\n    console.log(\"Bokeh: BokehJS loaded, going straight to plotting\");\n    run_inline_js();\n  } else {\n    load_libs(js_urls, function() {\n      console.log(\"Bokeh: BokehJS plotting callback run at\", now());\n      run_inline_js();\n    });\n  }\n}(window));"
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "\n",
       "<div class=\"bk-root\">\n",
       "    <div class=\"bk-plotdiv\" id=\"333dafd9-ea25-4392-85d8-4c39f6dcf460\"></div>\n",
       "</div>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "application/javascript": [
       "(function(root) {\n",
       "  function embed_document(root) {\n",
       "    \n",
       "  var docs_json = 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       "  var render_items = [{\"docid\":\"a95c28a0-b630-4aab-b99c-c560c71f81ce\",\"elementid\":\"333dafd9-ea25-4392-85d8-4c39f6dcf460\",\"modelid\":\"c29b050d-7180-4307-937b-9da27f35f7f8\"}];\n",
       "  root.Bokeh.embed.embed_items_notebook(docs_json, render_items);\n",
       "\n",
       "  }\n",
       "  if (root.Bokeh !== undefined) {\n",
       "    embed_document(root);\n",
       "  } else {\n",
       "    var attempts = 0;\n",
       "    var timer = setInterval(function(root) {\n",
       "      if (root.Bokeh !== undefined) {\n",
       "        embed_document(root);\n",
       "        clearInterval(timer);\n",
       "      }\n",
       "      attempts++;\n",
       "      if (attempts > 100) {\n",
       "        console.log(\"Bokeh: ERROR: Unable to run BokehJS code because BokehJS library is missing\")\n",
       "        clearInterval(timer);\n",
       "      }\n",
       "    }, 10, root)\n",
       "  }\n",
       "})(window);"
      ],
      "application/vnd.bokehjs_exec.v0+json": ""
     },
     "metadata": {
      "application/vnd.bokehjs_exec.v0+json": {
       "id": "c29b050d-7180-4307-937b-9da27f35f7f8"
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "output_notebook()\n",
    "p = figure(plot_width=950, plot_height=400)\n",
    "\n",
    "p.line(error_orientation['timestep'][:-10], error_orientation.roll[:-10], line_width=2, color='blue', legend='roll')\n",
    "p.line(error_orientation['timestep'][:-10], error_orientation.pitch[:-10], line_width=2, color='red', legend='pitch')\n",
    "p.line(error_orientation['timestep'][:-10], error_orientation.yaw[:-10], line_width=2, color='purple', legend='yaw')\n",
    "\n",
    "show(p)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Gradient Boosted Trees Stats"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Error in linear velocity across (20 seconds) averaged across 10 random trajectories"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 92,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "\n",
       "    <div class=\"bk-root\">\n",
       "        <a href=\"https://bokeh.pydata.org\" target=\"_blank\" class=\"bk-logo bk-logo-small bk-logo-notebook\"></a>\n",
       "        <span id=\"774504d7-1fba-40c6-a484-46d4ccc18c2b\">Loading BokehJS ...</span>\n",
       "    </div>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "application/javascript": [
       "\n",
       "(function(root) {\n",
       "  function now() {\n",
       "    return new Date();\n",
       "  }\n",
       "\n",
       "  var force = true;\n",
       "\n",
       "  if (typeof (root._bokeh_onload_callbacks) === \"undefined\" || force === true) {\n",
       "    root._bokeh_onload_callbacks = [];\n",
       "    root._bokeh_is_loading = undefined;\n",
       "  }\n",
       "\n",
       "  var JS_MIME_TYPE = 'application/javascript';\n",
       "  var HTML_MIME_TYPE = 'text/html';\n",
       "  var EXEC_MIME_TYPE = 'application/vnd.bokehjs_exec.v0+json';\n",
       "  var CLASS_NAME = 'output_bokeh rendered_html';\n",
       "\n",
       "  /**\n",
       "   * Render data to the DOM node\n",
       "   */\n",
       "  function render(props, node) {\n",
       "    var script = document.createElement(\"script\");\n",
       "    node.appendChild(script);\n",
       "  }\n",
       "\n",
       "  /**\n",
       "   * Handle when an output is cleared or removed\n",
       "   */\n",
       "  function handleClearOutput(event, handle) {\n",
       "    var cell = handle.cell;\n",
       "\n",
       "    var id = cell.output_area._bokeh_element_id;\n",
       "    var server_id = cell.output_area._bokeh_server_id;\n",
       "    // Clean up Bokeh references\n",
       "    if (id !== undefined) {\n",
       "      Bokeh.index[id].model.document.clear();\n",
       "      delete Bokeh.index[id];\n",
       "    }\n",
       "\n",
       "    if (server_id !== undefined) {\n",
       "      // Clean up Bokeh references\n",
       "      var cmd = \"from bokeh.io.state import curstate; print(curstate().uuid_to_server['\" + server_id + \"'].get_sessions()[0].document.roots[0]._id)\";\n",
       "      cell.notebook.kernel.execute(cmd, {\n",
       "        iopub: {\n",
       "          output: function(msg) {\n",
       "            var element_id = msg.content.text.trim();\n",
       "            Bokeh.index[element_id].model.document.clear();\n",
       "            delete Bokeh.index[element_id];\n",
       "          }\n",
       "        }\n",
       "      });\n",
       "      // Destroy server and session\n",
       "      var cmd = \"import bokeh.io.notebook as ion; ion.destroy_server('\" + server_id + \"')\";\n",
       "      cell.notebook.kernel.execute(cmd);\n",
       "    }\n",
       "  }\n",
       "\n",
       "  /**\n",
       "   * Handle when a new output is added\n",
       "   */\n",
       "  function handleAddOutput(event, handle) {\n",
       "    var output_area = handle.output_area;\n",
       "    var output = handle.output;\n",
       "\n",
       "    // limit handleAddOutput to display_data with EXEC_MIME_TYPE content only\n",
       "    if ((output.output_type != \"display_data\") || (!output.data.hasOwnProperty(EXEC_MIME_TYPE))) {\n",
       "      return\n",
       "    }\n",
       "\n",
       "    var toinsert = output_area.element.find(\".\" + CLASS_NAME.split(' ')[0]);\n",
       "\n",
       "    if (output.metadata[EXEC_MIME_TYPE][\"id\"] !== undefined) {\n",
       "      toinsert[0].firstChild.textContent = output.data[JS_MIME_TYPE];\n",
       "      // store reference to embed id on output_area\n",
       "      output_area._bokeh_element_id = output.metadata[EXEC_MIME_TYPE][\"id\"];\n",
       "    }\n",
       "    if (output.metadata[EXEC_MIME_TYPE][\"server_id\"] !== undefined) {\n",
       "      var bk_div = document.createElement(\"div\");\n",
       "      bk_div.innerHTML = output.data[HTML_MIME_TYPE];\n",
       "      var script_attrs = bk_div.children[0].attributes;\n",
       "      for (var i = 0; i < script_attrs.length; i++) {\n",
       "        toinsert[0].firstChild.setAttribute(script_attrs[i].name, script_attrs[i].value);\n",
       "      }\n",
       "      // store reference to server id on output_area\n",
       "      output_area._bokeh_server_id = output.metadata[EXEC_MIME_TYPE][\"server_id\"];\n",
       "    }\n",
       "  }\n",
       "\n",
       "  function register_renderer(events, OutputArea) {\n",
       "\n",
       "    function append_mime(data, metadata, element) {\n",
       "      // create a DOM node to render to\n",
       "      var toinsert = this.create_output_subarea(\n",
       "        metadata,\n",
       "        CLASS_NAME,\n",
       "        EXEC_MIME_TYPE\n",
       "      );\n",
       "      this.keyboard_manager.register_events(toinsert);\n",
       "      // Render to node\n",
       "      var props = {data: data, metadata: metadata[EXEC_MIME_TYPE]};\n",
       "      render(props, toinsert[0]);\n",
       "      element.append(toinsert);\n",
       "      return toinsert\n",
       "    }\n",
       "\n",
       "    /* Handle when an output is cleared or removed */\n",
       "    events.on('clear_output.CodeCell', handleClearOutput);\n",
       "    events.on('delete.Cell', handleClearOutput);\n",
       "\n",
       "    /* Handle when a new output is added */\n",
       "    events.on('output_added.OutputArea', handleAddOutput);\n",
       "\n",
       "    /**\n",
       "     * Register the mime type and append_mime function with output_area\n",
       "     */\n",
       "    OutputArea.prototype.register_mime_type(EXEC_MIME_TYPE, append_mime, {\n",
       "      /* Is output safe? */\n",
       "      safe: true,\n",
       "      /* Index of renderer in `output_area.display_order` */\n",
       "      index: 0\n",
       "    });\n",
       "  }\n",
       "\n",
       "  // register the mime type if in Jupyter Notebook environment and previously unregistered\n",
       "  if (root.Jupyter !== undefined) {\n",
       "    var events = require('base/js/events');\n",
       "    var OutputArea = require('notebook/js/outputarea').OutputArea;\n",
       "\n",
       "    if (OutputArea.prototype.mime_types().indexOf(EXEC_MIME_TYPE) == -1) {\n",
       "      register_renderer(events, OutputArea);\n",
       "    }\n",
       "  }\n",
       "\n",
       "  \n",
       "  if (typeof (root._bokeh_timeout) === \"undefined\" || force === true) {\n",
       "    root._bokeh_timeout = Date.now() + 5000;\n",
       "    root._bokeh_failed_load = false;\n",
       "  }\n",
       "\n",
       "  var NB_LOAD_WARNING = {'data': {'text/html':\n",
       "     \"<div style='background-color: #fdd'>\\n\"+\n",
       "     \"<p>\\n\"+\n",
       "     \"BokehJS does not appear to have successfully loaded. If loading BokehJS from CDN, this \\n\"+\n",
       "     \"may be due to a slow or bad network connection. Possible fixes:\\n\"+\n",
       "     \"</p>\\n\"+\n",
       "     \"<ul>\\n\"+\n",
       "     \"<li>re-rerun `output_notebook()` to attempt to load from CDN again, or</li>\\n\"+\n",
       "     \"<li>use INLINE resources instead, as so:</li>\\n\"+\n",
       "     \"</ul>\\n\"+\n",
       "     \"<code>\\n\"+\n",
       "     \"from bokeh.resources import INLINE\\n\"+\n",
       "     \"output_notebook(resources=INLINE)\\n\"+\n",
       "     \"</code>\\n\"+\n",
       "     \"</div>\"}};\n",
       "\n",
       "  function display_loaded() {\n",
       "    var el = document.getElementById(\"774504d7-1fba-40c6-a484-46d4ccc18c2b\");\n",
       "    if (el != null) {\n",
       "      el.textContent = \"BokehJS is loading...\";\n",
       "    }\n",
       "    if (root.Bokeh !== undefined) {\n",
       "      if (el != null) {\n",
       "        el.textContent = \"BokehJS \" + root.Bokeh.version + \" successfully loaded.\";\n",
       "      }\n",
       "    } else if (Date.now() < root._bokeh_timeout) {\n",
       "      setTimeout(display_loaded, 100)\n",
       "    }\n",
       "  }\n",
       "\n",
       "\n",
       "  function run_callbacks() {\n",
       "    try {\n",
       "      root._bokeh_onload_callbacks.forEach(function(callback) { callback() });\n",
       "    }\n",
       "    finally {\n",
       "      delete root._bokeh_onload_callbacks\n",
       "    }\n",
       "    console.info(\"Bokeh: all callbacks have finished\");\n",
       "  }\n",
       "\n",
       "  function load_libs(js_urls, callback) {\n",
       "    root._bokeh_onload_callbacks.push(callback);\n",
       "    if (root._bokeh_is_loading > 0) {\n",
       "      console.log(\"Bokeh: BokehJS is being loaded, scheduling callback at\", now());\n",
       "      return null;\n",
       "    }\n",
       "    if (js_urls == null || js_urls.length === 0) {\n",
       "      run_callbacks();\n",
       "      return null;\n",
       "    }\n",
       "    console.log(\"Bokeh: BokehJS not loaded, scheduling load and callback at\", now());\n",
       "    root._bokeh_is_loading = js_urls.length;\n",
       "    for (var i = 0; i < js_urls.length; i++) {\n",
       "      var url = js_urls[i];\n",
       "      var s = document.createElement('script');\n",
       "      s.src = url;\n",
       "      s.async = false;\n",
       "      s.onreadystatechange = s.onload = function() {\n",
       "        root._bokeh_is_loading--;\n",
       "        if (root._bokeh_is_loading === 0) {\n",
       "          console.log(\"Bokeh: all BokehJS libraries loaded\");\n",
       "          run_callbacks()\n",
       "        }\n",
       "      };\n",
       "      s.onerror = function() {\n",
       "        console.warn(\"failed to load library \" + url);\n",
       "      };\n",
       "      console.log(\"Bokeh: injecting script tag for BokehJS library: \", url);\n",
       "      document.getElementsByTagName(\"head\")[0].appendChild(s);\n",
       "    }\n",
       "  };var element = document.getElementById(\"774504d7-1fba-40c6-a484-46d4ccc18c2b\");\n",
       "  if (element == null) {\n",
       "    console.log(\"Bokeh: ERROR: autoload.js configured with elementid '774504d7-1fba-40c6-a484-46d4ccc18c2b' but no matching script tag was found. \")\n",
       "    return false;\n",
       "  }\n",
       "\n",
       "  var js_urls = [\"https://cdn.pydata.org/bokeh/release/bokeh-0.12.13.min.js\", \"https://cdn.pydata.org/bokeh/release/bokeh-widgets-0.12.13.min.js\", \"https://cdn.pydata.org/bokeh/release/bokeh-tables-0.12.13.min.js\", \"https://cdn.pydata.org/bokeh/release/bokeh-gl-0.12.13.min.js\"];\n",
       "\n",
       "  var inline_js = [\n",
       "    function(Bokeh) {\n",
       "      Bokeh.set_log_level(\"info\");\n",
       "    },\n",
       "    \n",
       "    function(Bokeh) {\n",
       "      \n",
       "    },\n",
       "    function(Bokeh) {\n",
       "      console.log(\"Bokeh: injecting CSS: https://cdn.pydata.org/bokeh/release/bokeh-0.12.13.min.css\");\n",
       "      Bokeh.embed.inject_css(\"https://cdn.pydata.org/bokeh/release/bokeh-0.12.13.min.css\");\n",
       "      console.log(\"Bokeh: injecting CSS: https://cdn.pydata.org/bokeh/release/bokeh-widgets-0.12.13.min.css\");\n",
       "      Bokeh.embed.inject_css(\"https://cdn.pydata.org/bokeh/release/bokeh-widgets-0.12.13.min.css\");\n",
       "      console.log(\"Bokeh: injecting CSS: https://cdn.pydata.org/bokeh/release/bokeh-tables-0.12.13.min.css\");\n",
       "      Bokeh.embed.inject_css(\"https://cdn.pydata.org/bokeh/release/bokeh-tables-0.12.13.min.css\");\n",
       "    }\n",
       "  ];\n",
       "\n",
       "  function run_inline_js() {\n",
       "    \n",
       "    if ((root.Bokeh !== undefined) || (force === true)) {\n",
       "      for (var i = 0; i < inline_js.length; i++) {\n",
       "        inline_js[i].call(root, root.Bokeh);\n",
       "      }if (force === true) {\n",
       "        display_loaded();\n",
       "      }} else if (Date.now() < root._bokeh_timeout) {\n",
       "      setTimeout(run_inline_js, 100);\n",
       "    } else if (!root._bokeh_failed_load) {\n",
       "      console.log(\"Bokeh: BokehJS failed to load within specified timeout.\");\n",
       "      root._bokeh_failed_load = true;\n",
       "    } else if (force !== true) {\n",
       "      var cell = $(document.getElementById(\"774504d7-1fba-40c6-a484-46d4ccc18c2b\")).parents('.cell').data().cell;\n",
       "      cell.output_area.append_execute_result(NB_LOAD_WARNING)\n",
       "    }\n",
       "\n",
       "  }\n",
       "\n",
       "  if (root._bokeh_is_loading === 0) {\n",
       "    console.log(\"Bokeh: BokehJS loaded, going straight to plotting\");\n",
       "    run_inline_js();\n",
       "  } else {\n",
       "    load_libs(js_urls, function() {\n",
       "      console.log(\"Bokeh: BokehJS plotting callback run at\", now());\n",
       "      run_inline_js();\n",
       "    });\n",
       "  }\n",
       "}(window));"
      ],
      "application/vnd.bokehjs_load.v0+json": "\n(function(root) {\n  function now() {\n    return new Date();\n  }\n\n  var force = true;\n\n  if (typeof (root._bokeh_onload_callbacks) === \"undefined\" || force === true) {\n    root._bokeh_onload_callbacks = [];\n    root._bokeh_is_loading = undefined;\n  }\n\n  \n\n  \n  if (typeof (root._bokeh_timeout) === \"undefined\" || force === true) {\n    root._bokeh_timeout = Date.now() + 5000;\n    root._bokeh_failed_load = false;\n  }\n\n  var NB_LOAD_WARNING = {'data': {'text/html':\n     \"<div style='background-color: #fdd'>\\n\"+\n     \"<p>\\n\"+\n     \"BokehJS does not appear to have successfully loaded. If loading BokehJS from CDN, this \\n\"+\n     \"may be due to a slow or bad network connection. Possible fixes:\\n\"+\n     \"</p>\\n\"+\n     \"<ul>\\n\"+\n     \"<li>re-rerun `output_notebook()` to attempt to load from CDN again, or</li>\\n\"+\n     \"<li>use INLINE resources instead, as so:</li>\\n\"+\n     \"</ul>\\n\"+\n     \"<code>\\n\"+\n     \"from bokeh.resources import INLINE\\n\"+\n     \"output_notebook(resources=INLINE)\\n\"+\n     \"</code>\\n\"+\n     \"</div>\"}};\n\n  function display_loaded() {\n    var el = document.getElementById(\"774504d7-1fba-40c6-a484-46d4ccc18c2b\");\n    if (el != null) {\n      el.textContent = \"BokehJS is loading...\";\n    }\n    if (root.Bokeh !== undefined) {\n      if (el != null) {\n        el.textContent = \"BokehJS \" + root.Bokeh.version + \" successfully loaded.\";\n      }\n    } else if (Date.now() < root._bokeh_timeout) {\n      setTimeout(display_loaded, 100)\n    }\n  }\n\n\n  function run_callbacks() {\n    try {\n      root._bokeh_onload_callbacks.forEach(function(callback) { callback() });\n    }\n    finally {\n      delete root._bokeh_onload_callbacks\n    }\n    console.info(\"Bokeh: all callbacks have finished\");\n  }\n\n  function load_libs(js_urls, callback) {\n    root._bokeh_onload_callbacks.push(callback);\n    if (root._bokeh_is_loading > 0) {\n      console.log(\"Bokeh: BokehJS is being loaded, scheduling callback at\", now());\n      return null;\n    }\n    if (js_urls == null || js_urls.length === 0) {\n      run_callbacks();\n      return null;\n    }\n    console.log(\"Bokeh: BokehJS not loaded, scheduling load and callback at\", now());\n    root._bokeh_is_loading = js_urls.length;\n    for (var i = 0; i < js_urls.length; i++) {\n      var url = js_urls[i];\n      var s = document.createElement('script');\n      s.src = url;\n      s.async = false;\n      s.onreadystatechange = s.onload = function() {\n        root._bokeh_is_loading--;\n        if (root._bokeh_is_loading === 0) {\n          console.log(\"Bokeh: all BokehJS libraries loaded\");\n          run_callbacks()\n        }\n      };\n      s.onerror = function() {\n        console.warn(\"failed to load library \" + url);\n      };\n      console.log(\"Bokeh: injecting script tag for BokehJS library: \", url);\n      document.getElementsByTagName(\"head\")[0].appendChild(s);\n    }\n  };var element = document.getElementById(\"774504d7-1fba-40c6-a484-46d4ccc18c2b\");\n  if (element == null) {\n    console.log(\"Bokeh: ERROR: autoload.js configured with elementid '774504d7-1fba-40c6-a484-46d4ccc18c2b' but no matching script tag was found. \")\n    return false;\n  }\n\n  var js_urls = [\"https://cdn.pydata.org/bokeh/release/bokeh-0.12.13.min.js\", \"https://cdn.pydata.org/bokeh/release/bokeh-widgets-0.12.13.min.js\", \"https://cdn.pydata.org/bokeh/release/bokeh-tables-0.12.13.min.js\", \"https://cdn.pydata.org/bokeh/release/bokeh-gl-0.12.13.min.js\"];\n\n  var inline_js = [\n    function(Bokeh) {\n      Bokeh.set_log_level(\"info\");\n    },\n    \n    function(Bokeh) {\n      \n    },\n    function(Bokeh) {\n      console.log(\"Bokeh: injecting CSS: https://cdn.pydata.org/bokeh/release/bokeh-0.12.13.min.css\");\n      Bokeh.embed.inject_css(\"https://cdn.pydata.org/bokeh/release/bokeh-0.12.13.min.css\");\n      console.log(\"Bokeh: injecting CSS: https://cdn.pydata.org/bokeh/release/bokeh-widgets-0.12.13.min.css\");\n      Bokeh.embed.inject_css(\"https://cdn.pydata.org/bokeh/release/bokeh-widgets-0.12.13.min.css\");\n      console.log(\"Bokeh: injecting CSS: https://cdn.pydata.org/bokeh/release/bokeh-tables-0.12.13.min.css\");\n      Bokeh.embed.inject_css(\"https://cdn.pydata.org/bokeh/release/bokeh-tables-0.12.13.min.css\");\n    }\n  ];\n\n  function run_inline_js() {\n    \n    if ((root.Bokeh !== undefined) || (force === true)) {\n      for (var i = 0; i < inline_js.length; i++) {\n        inline_js[i].call(root, root.Bokeh);\n      }if (force === true) {\n        display_loaded();\n      }} else if (Date.now() < root._bokeh_timeout) {\n      setTimeout(run_inline_js, 100);\n    } else if (!root._bokeh_failed_load) {\n      console.log(\"Bokeh: BokehJS failed to load within specified timeout.\");\n      root._bokeh_failed_load = true;\n    } else if (force !== true) {\n      var cell = $(document.getElementById(\"774504d7-1fba-40c6-a484-46d4ccc18c2b\")).parents('.cell').data().cell;\n      cell.output_area.append_execute_result(NB_LOAD_WARNING)\n    }\n\n  }\n\n  if (root._bokeh_is_loading === 0) {\n    console.log(\"Bokeh: BokehJS loaded, going straight to plotting\");\n    run_inline_js();\n  } else {\n    load_libs(js_urls, function() {\n      console.log(\"Bokeh: BokehJS plotting callback run at\", now());\n      run_inline_js();\n    });\n  }\n}(window));"
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "\n",
       "<div class=\"bk-root\">\n",
       "    <div class=\"bk-plotdiv\" id=\"39020c13-8a39-437e-a8fd-a80e98411c3b\"></div>\n",
       "</div>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "application/javascript": [
       "(function(root) {\n",
       "  function embed_document(root) {\n",
       "    \n",
       "  var docs_json = 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tributes\":{\"bottom_units\":\"screen\",\"fill_alpha\":{\"value\":0.5},\"fill_color\":{\"value\":\"lightgrey\"},\"left_units\":\"screen\",\"level\":\"overlay\",\"line_alpha\":{\"value\":1.0},\"line_color\":{\"value\":\"black\"},\"line_dash\":[4,4],\"line_width\":{\"value\":2},\"plot\":null,\"render_mode\":\"css\",\"right_units\":\"screen\",\"top_units\":\"screen\"},\"id\":\"603c0550-845c-414d-a58d-5cccc8be5198\",\"type\":\"BoxAnnotation\"},{\"attributes\":{},\"id\":\"52807ee6-a42d-484e-a85c-cbf2cd1efd3a\",\"type\":\"BasicTickFormatter\"},{\"attributes\":{\"data_source\":{\"id\":\"d94c7801-dd94-47f4-901a-d4b67d2faf5a\",\"type\":\"ColumnDataSource\"},\"glyph\":{\"id\":\"813d99da-696f-4f77-a05a-540bbc198aec\",\"type\":\"Line\"},\"hover_glyph\":null,\"muted_glyph\":null,\"nonselection_glyph\":{\"id\":\"9a428ee1-b65c-4b92-8d34-19cad6f0d5e1\",\"type\":\"Line\"},\"selection_glyph\":null,\"view\":{\"id\":\"60bf5358-dfef-4fab-9a85-dbe9f6667e79\",\"type\":\"CDSView\"}},\"id\":\"57484a23-a5a3-4047-8ad5-009c069716f8\",\"type\":\"GlyphRenderer\"},{\"attributes\":{\"below\":[{\"id\":\"5f382446-4c0f-4daf-90ff-77172d394c88\",\"type\":\"LinearAxis\"}],\"left\":[{\"id\":\"4b9de3f5-555c-442e-83b8-bb0318d6f2cc\",\"type\":\"LinearAxis\"}],\"plot_height\":400,\"plot_width\":950,\"renderers\":[{\"id\":\"5f382446-4c0f-4daf-90ff-77172d394c88\",\"type\":\"LinearAxis\"},{\"id\":\"536bd016-b28d-4bea-8cfc-8f5a45f75a11\",\"type\":\"Grid\"},{\"id\":\"4b9de3f5-555c-442e-83b8-bb0318d6f2cc\",\"type\":\"LinearAxis\"},{\"id\":\"e5428827-fb36-4c53-aa8c-c12338f39f3b\",\"type\":\"Grid\"},{\"id\":\"603c0550-845c-414d-a58d-5cccc8be5198\",\"type\":\"BoxAnnotation\"},{\"id\":\"4d4bbb7d-8434-4ee6-9425-ac3241f07247\",\"type\":\"Legend\"},{\"id\":\"57484a23-a5a3-4047-8ad5-009c069716f8\",\"type\":\"GlyphRenderer\"},{\"id\":\"5a149cf2-9e65-488a-b073-65a0b55167f5\",\"type\":\"GlyphRenderer\"},{\"id\":\"4319351a-3074-4c2f-aafe-0cb16f82fd8a\",\"type\":\"GlyphRenderer\"}],\"title\":{\"id\":\"4050c2b3-27c6-45f5-9304-a6b2be66d2dc\",\"type\":\"Title\"},\"toolbar\":{\"id\":\"c590b98e-bd7c-444f-853f-ac97e6a37318\",\"type\":\"Toolbar\"},\"x_range\":{\"id\":\"1f7f8d6c-bccb-45d9-852e-4d18d5c0157f\",\"type\":\"DataRange1d\"},\"x_scale\":{\"id\":\"f9f4ed28-8d1f-4ce3-b818-145ab3cc07f0\",\"type\":\"LinearScale\"},\"y_range\":{\"id\":\"c8419f76-23d2-4eb2-9c10-9eb08bfbd353\",\"type\":\"DataRange1d\"},\"y_scale\":{\"id\":\"7671b7a4-6965-4fc7-9c82-331da2aacef7\",\"type\":\"LinearScale\"}},\"id\":\"06e8d785-1d8d-4f11-96ea-a90b3723d66b\",\"subtype\":\"Figure\",\"type\":\"Plot\"},{\"attributes\":{\"source\":{\"id\":\"a20585dd-a86d-476f-a29a-7e0ab64cf067\",\"type\":\"ColumnDataSource\"}},\"id\":\"3183454f-87d8-48af-807f-cb97ca2505e8\",\"type\":\"CDSView\"},{\"attributes\":{},\"id\":\"fd74037a-cfbf-4346-9012-553972e1be5b\",\"type\":\"WheelZoomTool\"},{\"attributes\":{\"active_drag\":\"auto\",\"active_inspect\":\"auto\",\"active_scroll\":\"auto\",\"active_tap\":\"auto\",\"tools\":[{\"id\":\"c59a9377-bff1-4eb4-8e6b-a921b35e1a08\",\"type\":\"PanTool\"},{\"id\":\"fd74037a-cfbf-4346-9012-553972e1be5b\",\"type\":\"WheelZoomTool\"},{\"id\":\"4c8e57e4-b7c7-4099-ac55-b6a15f0847fe\",\"type\":\"BoxZoomTool\"},{\"id\":\"dd1909ad-50e5-45ce-952e-bb7039c9f8aa\",\"type\":\"SaveTool\"},{\"id\":\"4681ee7a-acbb-489b-957b-1fe4643b99ef\",\"type\":\"ResetTool\"},{\"id\":\"9bd9783c-6480-4bc9-9f79-3068d0925d93\",\"type\":\"HelpTool\"}]},\"id\":\"c590b98e-bd7c-444f-853f-ac97e6a37318\",\"type\":\"Toolbar\"}],\"root_ids\":[\"06e8d785-1d8d-4f11-96ea-a90b3723d66b\"]},\"title\":\"Bokeh Application\",\"version\":\"0.12.13\"}};\n",
       "  var render_items = [{\"docid\":\"077146ac-d75c-46ae-abba-b99adcb4a2dc\",\"elementid\":\"39020c13-8a39-437e-a8fd-a80e98411c3b\",\"modelid\":\"06e8d785-1d8d-4f11-96ea-a90b3723d66b\"}];\n",
       "  root.Bokeh.embed.embed_items_notebook(docs_json, render_items);\n",
       "\n",
       "  }\n",
       "  if (root.Bokeh !== undefined) {\n",
       "    embed_document(root);\n",
       "  } else {\n",
       "    var attempts = 0;\n",
       "    var timer = setInterval(function(root) {\n",
       "      if (root.Bokeh !== undefined) {\n",
       "        embed_document(root);\n",
       "        clearInterval(timer);\n",
       "      }\n",
       "      attempts++;\n",
       "      if (attempts > 100) {\n",
       "        console.log(\"Bokeh: ERROR: Unable to run BokehJS code because BokehJS library is missing\")\n",
       "        clearInterval(timer);\n",
       "      }\n",
       "    }, 10, root)\n",
       "  }\n",
       "})(window);"
      ],
      "application/vnd.bokehjs_exec.v0+json": ""
     },
     "metadata": {
      "application/vnd.bokehjs_exec.v0+json": {
       "id": "06e8d785-1d8d-4f11-96ea-a90b3723d66b"
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "output_notebook()\n",
    "p = figure(plot_width=950, plot_height=400)\n",
    "\n",
    "p.line(error_velocity['timestep'][:-10], error_velocity.dXB[:-10], line_width=2, color='blue', legend='dXB')\n",
    "p.line(error_velocity['timestep'][:-10], error_velocity.dYB[:-10], line_width=2, color='red', legend='dYB')\n",
    "p.line(error_velocity['timestep'][:-10], error_velocity.dZB[:-10], line_width=2, color='purple', legend='dZB')\n",
    "\n",
    "show(p)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Error in angular velocity (smallest angle) in radians (20 seconds) averaged across 10 random trajectories"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 94,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "\n",
       "    <div class=\"bk-root\">\n",
       "        <a href=\"https://bokeh.pydata.org\" target=\"_blank\" class=\"bk-logo bk-logo-small bk-logo-notebook\"></a>\n",
       "        <span id=\"8d811ea2-cef2-4e6c-8a91-3dadd8259880\">Loading BokehJS ...</span>\n",
       "    </div>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "application/javascript": [
       "\n",
       "(function(root) {\n",
       "  function now() {\n",
       "    return new Date();\n",
       "  }\n",
       "\n",
       "  var force = true;\n",
       "\n",
       "  if (typeof (root._bokeh_onload_callbacks) === \"undefined\" || force === true) {\n",
       "    root._bokeh_onload_callbacks = [];\n",
       "    root._bokeh_is_loading = undefined;\n",
       "  }\n",
       "\n",
       "  var JS_MIME_TYPE = 'application/javascript';\n",
       "  var HTML_MIME_TYPE = 'text/html';\n",
       "  var EXEC_MIME_TYPE = 'application/vnd.bokehjs_exec.v0+json';\n",
       "  var CLASS_NAME = 'output_bokeh rendered_html';\n",
       "\n",
       "  /**\n",
       "   * Render data to the DOM node\n",
       "   */\n",
       "  function render(props, node) {\n",
       "    var script = document.createElement(\"script\");\n",
       "    node.appendChild(script);\n",
       "  }\n",
       "\n",
       "  /**\n",
       "   * Handle when an output is cleared or removed\n",
       "   */\n",
       "  function handleClearOutput(event, handle) {\n",
       "    var cell = handle.cell;\n",
       "\n",
       "    var id = cell.output_area._bokeh_element_id;\n",
       "    var server_id = cell.output_area._bokeh_server_id;\n",
       "    // Clean up Bokeh references\n",
       "    if (id !== undefined) {\n",
       "      Bokeh.index[id].model.document.clear();\n",
       "      delete Bokeh.index[id];\n",
       "    }\n",
       "\n",
       "    if (server_id !== undefined) {\n",
       "      // Clean up Bokeh references\n",
       "      var cmd = \"from bokeh.io.state import curstate; print(curstate().uuid_to_server['\" + server_id + \"'].get_sessions()[0].document.roots[0]._id)\";\n",
       "      cell.notebook.kernel.execute(cmd, {\n",
       "        iopub: {\n",
       "          output: function(msg) {\n",
       "            var element_id = msg.content.text.trim();\n",
       "            Bokeh.index[element_id].model.document.clear();\n",
       "            delete Bokeh.index[element_id];\n",
       "          }\n",
       "        }\n",
       "      });\n",
       "      // Destroy server and session\n",
       "      var cmd = \"import bokeh.io.notebook as ion; ion.destroy_server('\" + server_id + \"')\";\n",
       "      cell.notebook.kernel.execute(cmd);\n",
       "    }\n",
       "  }\n",
       "\n",
       "  /**\n",
       "   * Handle when a new output is added\n",
       "   */\n",
       "  function handleAddOutput(event, handle) {\n",
       "    var output_area = handle.output_area;\n",
       "    var output = handle.output;\n",
       "\n",
       "    // limit handleAddOutput to display_data with EXEC_MIME_TYPE content only\n",
       "    if ((output.output_type != \"display_data\") || (!output.data.hasOwnProperty(EXEC_MIME_TYPE))) {\n",
       "      return\n",
       "    }\n",
       "\n",
       "    var toinsert = output_area.element.find(\".\" + CLASS_NAME.split(' ')[0]);\n",
       "\n",
       "    if (output.metadata[EXEC_MIME_TYPE][\"id\"] !== undefined) {\n",
       "      toinsert[0].firstChild.textContent = output.data[JS_MIME_TYPE];\n",
       "      // store reference to embed id on output_area\n",
       "      output_area._bokeh_element_id = output.metadata[EXEC_MIME_TYPE][\"id\"];\n",
       "    }\n",
       "    if (output.metadata[EXEC_MIME_TYPE][\"server_id\"] !== undefined) {\n",
       "      var bk_div = document.createElement(\"div\");\n",
       "      bk_div.innerHTML = output.data[HTML_MIME_TYPE];\n",
       "      var script_attrs = bk_div.children[0].attributes;\n",
       "      for (var i = 0; i < script_attrs.length; i++) {\n",
       "        toinsert[0].firstChild.setAttribute(script_attrs[i].name, script_attrs[i].value);\n",
       "      }\n",
       "      // store reference to server id on output_area\n",
       "      output_area._bokeh_server_id = output.metadata[EXEC_MIME_TYPE][\"server_id\"];\n",
       "    }\n",
       "  }\n",
       "\n",
       "  function register_renderer(events, OutputArea) {\n",
       "\n",
       "    function append_mime(data, metadata, element) {\n",
       "      // create a DOM node to render to\n",
       "      var toinsert = this.create_output_subarea(\n",
       "        metadata,\n",
       "        CLASS_NAME,\n",
       "        EXEC_MIME_TYPE\n",
       "      );\n",
       "      this.keyboard_manager.register_events(toinsert);\n",
       "      // Render to node\n",
       "      var props = {data: data, metadata: metadata[EXEC_MIME_TYPE]};\n",
       "      render(props, toinsert[0]);\n",
       "      element.append(toinsert);\n",
       "      return toinsert\n",
       "    }\n",
       "\n",
       "    /* Handle when an output is cleared or removed */\n",
       "    events.on('clear_output.CodeCell', handleClearOutput);\n",
       "    events.on('delete.Cell', handleClearOutput);\n",
       "\n",
       "    /* Handle when a new output is added */\n",
       "    events.on('output_added.OutputArea', handleAddOutput);\n",
       "\n",
       "    /**\n",
       "     * Register the mime type and append_mime function with output_area\n",
       "     */\n",
       "    OutputArea.prototype.register_mime_type(EXEC_MIME_TYPE, append_mime, {\n",
       "      /* Is output safe? */\n",
       "      safe: true,\n",
       "      /* Index of renderer in `output_area.display_order` */\n",
       "      index: 0\n",
       "    });\n",
       "  }\n",
       "\n",
       "  // register the mime type if in Jupyter Notebook environment and previously unregistered\n",
       "  if (root.Jupyter !== undefined) {\n",
       "    var events = require('base/js/events');\n",
       "    var OutputArea = require('notebook/js/outputarea').OutputArea;\n",
       "\n",
       "    if (OutputArea.prototype.mime_types().indexOf(EXEC_MIME_TYPE) == -1) {\n",
       "      register_renderer(events, OutputArea);\n",
       "    }\n",
       "  }\n",
       "\n",
       "  \n",
       "  if (typeof (root._bokeh_timeout) === \"undefined\" || force === true) {\n",
       "    root._bokeh_timeout = Date.now() + 5000;\n",
       "    root._bokeh_failed_load = false;\n",
       "  }\n",
       "\n",
       "  var NB_LOAD_WARNING = {'data': {'text/html':\n",
       "     \"<div style='background-color: #fdd'>\\n\"+\n",
       "     \"<p>\\n\"+\n",
       "     \"BokehJS does not appear to have successfully loaded. If loading BokehJS from CDN, this \\n\"+\n",
       "     \"may be due to a slow or bad network connection. Possible fixes:\\n\"+\n",
       "     \"</p>\\n\"+\n",
       "     \"<ul>\\n\"+\n",
       "     \"<li>re-rerun `output_notebook()` to attempt to load from CDN again, or</li>\\n\"+\n",
       "     \"<li>use INLINE resources instead, as so:</li>\\n\"+\n",
       "     \"</ul>\\n\"+\n",
       "     \"<code>\\n\"+\n",
       "     \"from bokeh.resources import INLINE\\n\"+\n",
       "     \"output_notebook(resources=INLINE)\\n\"+\n",
       "     \"</code>\\n\"+\n",
       "     \"</div>\"}};\n",
       "\n",
       "  function display_loaded() {\n",
       "    var el = document.getElementById(\"8d811ea2-cef2-4e6c-8a91-3dadd8259880\");\n",
       "    if (el != null) {\n",
       "      el.textContent = \"BokehJS is loading...\";\n",
       "    }\n",
       "    if (root.Bokeh !== undefined) {\n",
       "      if (el != null) {\n",
       "        el.textContent = \"BokehJS \" + root.Bokeh.version + \" successfully loaded.\";\n",
       "      }\n",
       "    } else if (Date.now() < root._bokeh_timeout) {\n",
       "      setTimeout(display_loaded, 100)\n",
       "    }\n",
       "  }\n",
       "\n",
       "\n",
       "  function run_callbacks() {\n",
       "    try {\n",
       "      root._bokeh_onload_callbacks.forEach(function(callback) { callback() });\n",
       "    }\n",
       "    finally {\n",
       "      delete root._bokeh_onload_callbacks\n",
       "    }\n",
       "    console.info(\"Bokeh: all callbacks have finished\");\n",
       "  }\n",
       "\n",
       "  function load_libs(js_urls, callback) {\n",
       "    root._bokeh_onload_callbacks.push(callback);\n",
       "    if (root._bokeh_is_loading > 0) {\n",
       "      console.log(\"Bokeh: BokehJS is being loaded, scheduling callback at\", now());\n",
       "      return null;\n",
       "    }\n",
       "    if (js_urls == null || js_urls.length === 0) {\n",
       "      run_callbacks();\n",
       "      return null;\n",
       "    }\n",
       "    console.log(\"Bokeh: BokehJS not loaded, scheduling load and callback at\", now());\n",
       "    root._bokeh_is_loading = js_urls.length;\n",
       "    for (var i = 0; i < js_urls.length; i++) {\n",
       "      var url = js_urls[i];\n",
       "      var s = document.createElement('script');\n",
       "      s.src = url;\n",
       "      s.async = false;\n",
       "      s.onreadystatechange = s.onload = function() {\n",
       "        root._bokeh_is_loading--;\n",
       "        if (root._bokeh_is_loading === 0) {\n",
       "          console.log(\"Bokeh: all BokehJS libraries loaded\");\n",
       "          run_callbacks()\n",
       "        }\n",
       "      };\n",
       "      s.onerror = function() {\n",
       "        console.warn(\"failed to load library \" + url);\n",
       "      };\n",
       "      console.log(\"Bokeh: injecting script tag for BokehJS library: \", url);\n",
       "      document.getElementsByTagName(\"head\")[0].appendChild(s);\n",
       "    }\n",
       "  };var element = document.getElementById(\"8d811ea2-cef2-4e6c-8a91-3dadd8259880\");\n",
       "  if (element == null) {\n",
       "    console.log(\"Bokeh: ERROR: autoload.js configured with elementid '8d811ea2-cef2-4e6c-8a91-3dadd8259880' but no matching script tag was found. \")\n",
       "    return false;\n",
       "  }\n",
       "\n",
       "  var js_urls = [\"https://cdn.pydata.org/bokeh/release/bokeh-0.12.13.min.js\", \"https://cdn.pydata.org/bokeh/release/bokeh-widgets-0.12.13.min.js\", \"https://cdn.pydata.org/bokeh/release/bokeh-tables-0.12.13.min.js\", \"https://cdn.pydata.org/bokeh/release/bokeh-gl-0.12.13.min.js\"];\n",
       "\n",
       "  var inline_js = [\n",
       "    function(Bokeh) {\n",
       "      Bokeh.set_log_level(\"info\");\n",
       "    },\n",
       "    \n",
       "    function(Bokeh) {\n",
       "      \n",
       "    },\n",
       "    function(Bokeh) {\n",
       "      console.log(\"Bokeh: injecting CSS: https://cdn.pydata.org/bokeh/release/bokeh-0.12.13.min.css\");\n",
       "      Bokeh.embed.inject_css(\"https://cdn.pydata.org/bokeh/release/bokeh-0.12.13.min.css\");\n",
       "      console.log(\"Bokeh: injecting CSS: https://cdn.pydata.org/bokeh/release/bokeh-widgets-0.12.13.min.css\");\n",
       "      Bokeh.embed.inject_css(\"https://cdn.pydata.org/bokeh/release/bokeh-widgets-0.12.13.min.css\");\n",
       "      console.log(\"Bokeh: injecting CSS: https://cdn.pydata.org/bokeh/release/bokeh-tables-0.12.13.min.css\");\n",
       "      Bokeh.embed.inject_css(\"https://cdn.pydata.org/bokeh/release/bokeh-tables-0.12.13.min.css\");\n",
       "    }\n",
       "  ];\n",
       "\n",
       "  function run_inline_js() {\n",
       "    \n",
       "    if ((root.Bokeh !== undefined) || (force === true)) {\n",
       "      for (var i = 0; i < inline_js.length; i++) {\n",
       "        inline_js[i].call(root, root.Bokeh);\n",
       "      }if (force === true) {\n",
       "        display_loaded();\n",
       "      }} else if (Date.now() < root._bokeh_timeout) {\n",
       "      setTimeout(run_inline_js, 100);\n",
       "    } else if (!root._bokeh_failed_load) {\n",
       "      console.log(\"Bokeh: BokehJS failed to load within specified timeout.\");\n",
       "      root._bokeh_failed_load = true;\n",
       "    } else if (force !== true) {\n",
       "      var cell = $(document.getElementById(\"8d811ea2-cef2-4e6c-8a91-3dadd8259880\")).parents('.cell').data().cell;\n",
       "      cell.output_area.append_execute_result(NB_LOAD_WARNING)\n",
       "    }\n",
       "\n",
       "  }\n",
       "\n",
       "  if (root._bokeh_is_loading === 0) {\n",
       "    console.log(\"Bokeh: BokehJS loaded, going straight to plotting\");\n",
       "    run_inline_js();\n",
       "  } else {\n",
       "    load_libs(js_urls, function() {\n",
       "      console.log(\"Bokeh: BokehJS plotting callback run at\", now());\n",
       "      run_inline_js();\n",
       "    });\n",
       "  }\n",
       "}(window));"
      ],
      "application/vnd.bokehjs_load.v0+json": "\n(function(root) {\n  function now() {\n    return new Date();\n  }\n\n  var force = true;\n\n  if (typeof (root._bokeh_onload_callbacks) === \"undefined\" || force === true) {\n    root._bokeh_onload_callbacks = [];\n    root._bokeh_is_loading = undefined;\n  }\n\n  \n\n  \n  if (typeof (root._bokeh_timeout) === \"undefined\" || force === true) {\n    root._bokeh_timeout = Date.now() + 5000;\n    root._bokeh_failed_load = false;\n  }\n\n  var NB_LOAD_WARNING = {'data': {'text/html':\n     \"<div style='background-color: #fdd'>\\n\"+\n     \"<p>\\n\"+\n     \"BokehJS does not appear to have successfully loaded. If loading BokehJS from CDN, this \\n\"+\n     \"may be due to a slow or bad network connection. Possible fixes:\\n\"+\n     \"</p>\\n\"+\n     \"<ul>\\n\"+\n     \"<li>re-rerun `output_notebook()` to attempt to load from CDN again, or</li>\\n\"+\n     \"<li>use INLINE resources instead, as so:</li>\\n\"+\n     \"</ul>\\n\"+\n     \"<code>\\n\"+\n     \"from bokeh.resources import INLINE\\n\"+\n     \"output_notebook(resources=INLINE)\\n\"+\n     \"</code>\\n\"+\n     \"</div>\"}};\n\n  function display_loaded() {\n    var el = document.getElementById(\"8d811ea2-cef2-4e6c-8a91-3dadd8259880\");\n    if (el != null) {\n      el.textContent = \"BokehJS is loading...\";\n    }\n    if (root.Bokeh !== undefined) {\n      if (el != null) {\n        el.textContent = \"BokehJS \" + root.Bokeh.version + \" successfully loaded.\";\n      }\n    } else if (Date.now() < root._bokeh_timeout) {\n      setTimeout(display_loaded, 100)\n    }\n  }\n\n\n  function run_callbacks() {\n    try {\n      root._bokeh_onload_callbacks.forEach(function(callback) { callback() });\n    }\n    finally {\n      delete root._bokeh_onload_callbacks\n    }\n    console.info(\"Bokeh: all callbacks have finished\");\n  }\n\n  function load_libs(js_urls, callback) {\n    root._bokeh_onload_callbacks.push(callback);\n    if (root._bokeh_is_loading > 0) {\n      console.log(\"Bokeh: BokehJS is being loaded, scheduling callback at\", now());\n      return null;\n    }\n    if (js_urls == null || js_urls.length === 0) {\n      run_callbacks();\n      return null;\n    }\n    console.log(\"Bokeh: BokehJS not loaded, scheduling load and callback at\", now());\n    root._bokeh_is_loading = js_urls.length;\n    for (var i = 0; i < js_urls.length; i++) {\n      var url = js_urls[i];\n      var s = document.createElement('script');\n      s.src = url;\n      s.async = false;\n      s.onreadystatechange = s.onload = function() {\n        root._bokeh_is_loading--;\n        if (root._bokeh_is_loading === 0) {\n          console.log(\"Bokeh: all BokehJS libraries loaded\");\n          run_callbacks()\n        }\n      };\n      s.onerror = function() {\n        console.warn(\"failed to load library \" + url);\n      };\n      console.log(\"Bokeh: injecting script tag for BokehJS library: \", url);\n      document.getElementsByTagName(\"head\")[0].appendChild(s);\n    }\n  };var element = document.getElementById(\"8d811ea2-cef2-4e6c-8a91-3dadd8259880\");\n  if (element == null) {\n    console.log(\"Bokeh: ERROR: autoload.js configured with elementid '8d811ea2-cef2-4e6c-8a91-3dadd8259880' but no matching script tag was found. \")\n    return false;\n  }\n\n  var js_urls = [\"https://cdn.pydata.org/bokeh/release/bokeh-0.12.13.min.js\", \"https://cdn.pydata.org/bokeh/release/bokeh-widgets-0.12.13.min.js\", \"https://cdn.pydata.org/bokeh/release/bokeh-tables-0.12.13.min.js\", \"https://cdn.pydata.org/bokeh/release/bokeh-gl-0.12.13.min.js\"];\n\n  var inline_js = [\n    function(Bokeh) {\n      Bokeh.set_log_level(\"info\");\n    },\n    \n    function(Bokeh) {\n      \n    },\n    function(Bokeh) {\n      console.log(\"Bokeh: injecting CSS: https://cdn.pydata.org/bokeh/release/bokeh-0.12.13.min.css\");\n      Bokeh.embed.inject_css(\"https://cdn.pydata.org/bokeh/release/bokeh-0.12.13.min.css\");\n      console.log(\"Bokeh: injecting CSS: https://cdn.pydata.org/bokeh/release/bokeh-widgets-0.12.13.min.css\");\n      Bokeh.embed.inject_css(\"https://cdn.pydata.org/bokeh/release/bokeh-widgets-0.12.13.min.css\");\n      console.log(\"Bokeh: injecting CSS: https://cdn.pydata.org/bokeh/release/bokeh-tables-0.12.13.min.css\");\n      Bokeh.embed.inject_css(\"https://cdn.pydata.org/bokeh/release/bokeh-tables-0.12.13.min.css\");\n    }\n  ];\n\n  function run_inline_js() {\n    \n    if ((root.Bokeh !== undefined) || (force === true)) {\n      for (var i = 0; i < inline_js.length; i++) {\n        inline_js[i].call(root, root.Bokeh);\n      }if (force === true) {\n        display_loaded();\n      }} else if (Date.now() < root._bokeh_timeout) {\n      setTimeout(run_inline_js, 100);\n    } else if (!root._bokeh_failed_load) {\n      console.log(\"Bokeh: BokehJS failed to load within specified timeout.\");\n      root._bokeh_failed_load = true;\n    } else if (force !== true) {\n      var cell = $(document.getElementById(\"8d811ea2-cef2-4e6c-8a91-3dadd8259880\")).parents('.cell').data().cell;\n      cell.output_area.append_execute_result(NB_LOAD_WARNING)\n    }\n\n  }\n\n  if (root._bokeh_is_loading === 0) {\n    console.log(\"Bokeh: BokehJS loaded, going straight to plotting\");\n    run_inline_js();\n  } else {\n    load_libs(js_urls, function() {\n      console.log(\"Bokeh: BokehJS plotting callback run at\", now());\n      run_inline_js();\n    });\n  }\n}(window));"
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "\n",
       "<div class=\"bk-root\">\n",
       "    <div class=\"bk-plotdiv\" id=\"77654181-68ea-4731-a24a-8dfe9416d0f4\"></div>\n",
       "</div>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "application/javascript": [
       "(function(root) {\n",
       "  function embed_document(root) {\n",
       "    \n",
       "  var docs_json = 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       "  var render_items = [{\"docid\":\"74dd3367-da7b-4a9d-ad61-5bcf7db82641\",\"elementid\":\"77654181-68ea-4731-a24a-8dfe9416d0f4\",\"modelid\":\"5a97ccc5-bbbd-422d-bff1-1a8fb63a802e\"}];\n",
       "  root.Bokeh.embed.embed_items_notebook(docs_json, render_items);\n",
       "\n",
       "  }\n",
       "  if (root.Bokeh !== undefined) {\n",
       "    embed_document(root);\n",
       "  } else {\n",
       "    var attempts = 0;\n",
       "    var timer = setInterval(function(root) {\n",
       "      if (root.Bokeh !== undefined) {\n",
       "        embed_document(root);\n",
       "        clearInterval(timer);\n",
       "      }\n",
       "      attempts++;\n",
       "      if (attempts > 100) {\n",
       "        console.log(\"Bokeh: ERROR: Unable to run BokehJS code because BokehJS library is missing\")\n",
       "        clearInterval(timer);\n",
       "      }\n",
       "    }, 10, root)\n",
       "  }\n",
       "})(window);"
      ],
      "application/vnd.bokehjs_exec.v0+json": ""
     },
     "metadata": {
      "application/vnd.bokehjs_exec.v0+json": {
       "id": "5a97ccc5-bbbd-422d-bff1-1a8fb63a802e"
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "output_notebook()\n",
    "p = figure(plot_width=950, plot_height=400)\n",
    "\n",
    "p.line(error_angular_velocity['timestep'][:-10], error_angular_velocity.dRoll[:-10], line_width=2, color='blue', legend='dRoll')\n",
    "p.line(error_angular_velocity['timestep'][:-10], error_angular_velocity.dPitch[:-10], line_width=2, color='red', legend='dPitch')\n",
    "p.line(error_angular_velocity['timestep'][:-10], error_angular_velocity.dYaw[:-10], line_width=2, color='purple', legend='dYaw')\n",
    "\n",
    "show(p)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Error in Position (smallest angle) in radians (20 seconds) averaged across 10 random trajectories"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 95,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "\n",
       "    <div class=\"bk-root\">\n",
       "        <a href=\"https://bokeh.pydata.org\" target=\"_blank\" class=\"bk-logo bk-logo-small bk-logo-notebook\"></a>\n",
       "        <span id=\"f4509364-d5a1-48a0-9e44-7ebc6bd404d4\">Loading BokehJS ...</span>\n",
       "    </div>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "application/javascript": [
       "\n",
       "(function(root) {\n",
       "  function now() {\n",
       "    return new Date();\n",
       "  }\n",
       "\n",
       "  var force = true;\n",
       "\n",
       "  if (typeof (root._bokeh_onload_callbacks) === \"undefined\" || force === true) {\n",
       "    root._bokeh_onload_callbacks = [];\n",
       "    root._bokeh_is_loading = undefined;\n",
       "  }\n",
       "\n",
       "  var JS_MIME_TYPE = 'application/javascript';\n",
       "  var HTML_MIME_TYPE = 'text/html';\n",
       "  var EXEC_MIME_TYPE = 'application/vnd.bokehjs_exec.v0+json';\n",
       "  var CLASS_NAME = 'output_bokeh rendered_html';\n",
       "\n",
       "  /**\n",
       "   * Render data to the DOM node\n",
       "   */\n",
       "  function render(props, node) {\n",
       "    var script = document.createElement(\"script\");\n",
       "    node.appendChild(script);\n",
       "  }\n",
       "\n",
       "  /**\n",
       "   * Handle when an output is cleared or removed\n",
       "   */\n",
       "  function handleClearOutput(event, handle) {\n",
       "    var cell = handle.cell;\n",
       "\n",
       "    var id = cell.output_area._bokeh_element_id;\n",
       "    var server_id = cell.output_area._bokeh_server_id;\n",
       "    // Clean up Bokeh references\n",
       "    if (id !== undefined) {\n",
       "      Bokeh.index[id].model.document.clear();\n",
       "      delete Bokeh.index[id];\n",
       "    }\n",
       "\n",
       "    if (server_id !== undefined) {\n",
       "      // Clean up Bokeh references\n",
       "      var cmd = \"from bokeh.io.state import curstate; print(curstate().uuid_to_server['\" + server_id + \"'].get_sessions()[0].document.roots[0]._id)\";\n",
       "      cell.notebook.kernel.execute(cmd, {\n",
       "        iopub: {\n",
       "          output: function(msg) {\n",
       "            var element_id = msg.content.text.trim();\n",
       "            Bokeh.index[element_id].model.document.clear();\n",
       "            delete Bokeh.index[element_id];\n",
       "          }\n",
       "        }\n",
       "      });\n",
       "      // Destroy server and session\n",
       "      var cmd = \"import bokeh.io.notebook as ion; ion.destroy_server('\" + server_id + \"')\";\n",
       "      cell.notebook.kernel.execute(cmd);\n",
       "    }\n",
       "  }\n",
       "\n",
       "  /**\n",
       "   * Handle when a new output is added\n",
       "   */\n",
       "  function handleAddOutput(event, handle) {\n",
       "    var output_area = handle.output_area;\n",
       "    var output = handle.output;\n",
       "\n",
       "    // limit handleAddOutput to display_data with EXEC_MIME_TYPE content only\n",
       "    if ((output.output_type != \"display_data\") || (!output.data.hasOwnProperty(EXEC_MIME_TYPE))) {\n",
       "      return\n",
       "    }\n",
       "\n",
       "    var toinsert = output_area.element.find(\".\" + CLASS_NAME.split(' ')[0]);\n",
       "\n",
       "    if (output.metadata[EXEC_MIME_TYPE][\"id\"] !== undefined) {\n",
       "      toinsert[0].firstChild.textContent = output.data[JS_MIME_TYPE];\n",
       "      // store reference to embed id on output_area\n",
       "      output_area._bokeh_element_id = output.metadata[EXEC_MIME_TYPE][\"id\"];\n",
       "    }\n",
       "    if (output.metadata[EXEC_MIME_TYPE][\"server_id\"] !== undefined) {\n",
       "      var bk_div = document.createElement(\"div\");\n",
       "      bk_div.innerHTML = output.data[HTML_MIME_TYPE];\n",
       "      var script_attrs = bk_div.children[0].attributes;\n",
       "      for (var i = 0; i < script_attrs.length; i++) {\n",
       "        toinsert[0].firstChild.setAttribute(script_attrs[i].name, script_attrs[i].value);\n",
       "      }\n",
       "      // store reference to server id on output_area\n",
       "      output_area._bokeh_server_id = output.metadata[EXEC_MIME_TYPE][\"server_id\"];\n",
       "    }\n",
       "  }\n",
       "\n",
       "  function register_renderer(events, OutputArea) {\n",
       "\n",
       "    function append_mime(data, metadata, element) {\n",
       "      // create a DOM node to render to\n",
       "      var toinsert = this.create_output_subarea(\n",
       "        metadata,\n",
       "        CLASS_NAME,\n",
       "        EXEC_MIME_TYPE\n",
       "      );\n",
       "      this.keyboard_manager.register_events(toinsert);\n",
       "      // Render to node\n",
       "      var props = {data: data, metadata: metadata[EXEC_MIME_TYPE]};\n",
       "      render(props, toinsert[0]);\n",
       "      element.append(toinsert);\n",
       "      return toinsert\n",
       "    }\n",
       "\n",
       "    /* Handle when an output is cleared or removed */\n",
       "    events.on('clear_output.CodeCell', handleClearOutput);\n",
       "    events.on('delete.Cell', handleClearOutput);\n",
       "\n",
       "    /* Handle when a new output is added */\n",
       "    events.on('output_added.OutputArea', handleAddOutput);\n",
       "\n",
       "    /**\n",
       "     * Register the mime type and append_mime function with output_area\n",
       "     */\n",
       "    OutputArea.prototype.register_mime_type(EXEC_MIME_TYPE, append_mime, {\n",
       "      /* Is output safe? */\n",
       "      safe: true,\n",
       "      /* Index of renderer in `output_area.display_order` */\n",
       "      index: 0\n",
       "    });\n",
       "  }\n",
       "\n",
       "  // register the mime type if in Jupyter Notebook environment and previously unregistered\n",
       "  if (root.Jupyter !== undefined) {\n",
       "    var events = require('base/js/events');\n",
       "    var OutputArea = require('notebook/js/outputarea').OutputArea;\n",
       "\n",
       "    if (OutputArea.prototype.mime_types().indexOf(EXEC_MIME_TYPE) == -1) {\n",
       "      register_renderer(events, OutputArea);\n",
       "    }\n",
       "  }\n",
       "\n",
       "  \n",
       "  if (typeof (root._bokeh_timeout) === \"undefined\" || force === true) {\n",
       "    root._bokeh_timeout = Date.now() + 5000;\n",
       "    root._bokeh_failed_load = false;\n",
       "  }\n",
       "\n",
       "  var NB_LOAD_WARNING = {'data': {'text/html':\n",
       "     \"<div style='background-color: #fdd'>\\n\"+\n",
       "     \"<p>\\n\"+\n",
       "     \"BokehJS does not appear to have successfully loaded. If loading BokehJS from CDN, this \\n\"+\n",
       "     \"may be due to a slow or bad network connection. Possible fixes:\\n\"+\n",
       "     \"</p>\\n\"+\n",
       "     \"<ul>\\n\"+\n",
       "     \"<li>re-rerun `output_notebook()` to attempt to load from CDN again, or</li>\\n\"+\n",
       "     \"<li>use INLINE resources instead, as so:</li>\\n\"+\n",
       "     \"</ul>\\n\"+\n",
       "     \"<code>\\n\"+\n",
       "     \"from bokeh.resources import INLINE\\n\"+\n",
       "     \"output_notebook(resources=INLINE)\\n\"+\n",
       "     \"</code>\\n\"+\n",
       "     \"</div>\"}};\n",
       "\n",
       "  function display_loaded() {\n",
       "    var el = document.getElementById(\"f4509364-d5a1-48a0-9e44-7ebc6bd404d4\");\n",
       "    if (el != null) {\n",
       "      el.textContent = \"BokehJS is loading...\";\n",
       "    }\n",
       "    if (root.Bokeh !== undefined) {\n",
       "      if (el != null) {\n",
       "        el.textContent = \"BokehJS \" + root.Bokeh.version + \" successfully loaded.\";\n",
       "      }\n",
       "    } else if (Date.now() < root._bokeh_timeout) {\n",
       "      setTimeout(display_loaded, 100)\n",
       "    }\n",
       "  }\n",
       "\n",
       "\n",
       "  function run_callbacks() {\n",
       "    try {\n",
       "      root._bokeh_onload_callbacks.forEach(function(callback) { callback() });\n",
       "    }\n",
       "    finally {\n",
       "      delete root._bokeh_onload_callbacks\n",
       "    }\n",
       "    console.info(\"Bokeh: all callbacks have finished\");\n",
       "  }\n",
       "\n",
       "  function load_libs(js_urls, callback) {\n",
       "    root._bokeh_onload_callbacks.push(callback);\n",
       "    if (root._bokeh_is_loading > 0) {\n",
       "      console.log(\"Bokeh: BokehJS is being loaded, scheduling callback at\", now());\n",
       "      return null;\n",
       "    }\n",
       "    if (js_urls == null || js_urls.length === 0) {\n",
       "      run_callbacks();\n",
       "      return null;\n",
       "    }\n",
       "    console.log(\"Bokeh: BokehJS not loaded, scheduling load and callback at\", now());\n",
       "    root._bokeh_is_loading = js_urls.length;\n",
       "    for (var i = 0; i < js_urls.length; i++) {\n",
       "      var url = js_urls[i];\n",
       "      var s = document.createElement('script');\n",
       "      s.src = url;\n",
       "      s.async = false;\n",
       "      s.onreadystatechange = s.onload = function() {\n",
       "        root._bokeh_is_loading--;\n",
       "        if (root._bokeh_is_loading === 0) {\n",
       "          console.log(\"Bokeh: all BokehJS libraries loaded\");\n",
       "          run_callbacks()\n",
       "        }\n",
       "      };\n",
       "      s.onerror = function() {\n",
       "        console.warn(\"failed to load library \" + url);\n",
       "      };\n",
       "      console.log(\"Bokeh: injecting script tag for BokehJS library: \", url);\n",
       "      document.getElementsByTagName(\"head\")[0].appendChild(s);\n",
       "    }\n",
       "  };var element = document.getElementById(\"f4509364-d5a1-48a0-9e44-7ebc6bd404d4\");\n",
       "  if (element == null) {\n",
       "    console.log(\"Bokeh: ERROR: autoload.js configured with elementid 'f4509364-d5a1-48a0-9e44-7ebc6bd404d4' but no matching script tag was found. \")\n",
       "    return false;\n",
       "  }\n",
       "\n",
       "  var js_urls = [\"https://cdn.pydata.org/bokeh/release/bokeh-0.12.13.min.js\", \"https://cdn.pydata.org/bokeh/release/bokeh-widgets-0.12.13.min.js\", \"https://cdn.pydata.org/bokeh/release/bokeh-tables-0.12.13.min.js\", \"https://cdn.pydata.org/bokeh/release/bokeh-gl-0.12.13.min.js\"];\n",
       "\n",
       "  var inline_js = [\n",
       "    function(Bokeh) {\n",
       "      Bokeh.set_log_level(\"info\");\n",
       "    },\n",
       "    \n",
       "    function(Bokeh) {\n",
       "      \n",
       "    },\n",
       "    function(Bokeh) {\n",
       "      console.log(\"Bokeh: injecting CSS: https://cdn.pydata.org/bokeh/release/bokeh-0.12.13.min.css\");\n",
       "      Bokeh.embed.inject_css(\"https://cdn.pydata.org/bokeh/release/bokeh-0.12.13.min.css\");\n",
       "      console.log(\"Bokeh: injecting CSS: https://cdn.pydata.org/bokeh/release/bokeh-widgets-0.12.13.min.css\");\n",
       "      Bokeh.embed.inject_css(\"https://cdn.pydata.org/bokeh/release/bokeh-widgets-0.12.13.min.css\");\n",
       "      console.log(\"Bokeh: injecting CSS: https://cdn.pydata.org/bokeh/release/bokeh-tables-0.12.13.min.css\");\n",
       "      Bokeh.embed.inject_css(\"https://cdn.pydata.org/bokeh/release/bokeh-tables-0.12.13.min.css\");\n",
       "    }\n",
       "  ];\n",
       "\n",
       "  function run_inline_js() {\n",
       "    \n",
       "    if ((root.Bokeh !== undefined) || (force === true)) {\n",
       "      for (var i = 0; i < inline_js.length; i++) {\n",
       "        inline_js[i].call(root, root.Bokeh);\n",
       "      }if (force === true) {\n",
       "        display_loaded();\n",
       "      }} else if (Date.now() < root._bokeh_timeout) {\n",
       "      setTimeout(run_inline_js, 100);\n",
       "    } else if (!root._bokeh_failed_load) {\n",
       "      console.log(\"Bokeh: BokehJS failed to load within specified timeout.\");\n",
       "      root._bokeh_failed_load = true;\n",
       "    } else if (force !== true) {\n",
       "      var cell = $(document.getElementById(\"f4509364-d5a1-48a0-9e44-7ebc6bd404d4\")).parents('.cell').data().cell;\n",
       "      cell.output_area.append_execute_result(NB_LOAD_WARNING)\n",
       "    }\n",
       "\n",
       "  }\n",
       "\n",
       "  if (root._bokeh_is_loading === 0) {\n",
       "    console.log(\"Bokeh: BokehJS loaded, going straight to plotting\");\n",
       "    run_inline_js();\n",
       "  } else {\n",
       "    load_libs(js_urls, function() {\n",
       "      console.log(\"Bokeh: BokehJS plotting callback run at\", now());\n",
       "      run_inline_js();\n",
       "    });\n",
       "  }\n",
       "}(window));"
      ],
      "application/vnd.bokehjs_load.v0+json": "\n(function(root) {\n  function now() {\n    return new Date();\n  }\n\n  var force = true;\n\n  if (typeof (root._bokeh_onload_callbacks) === \"undefined\" || force === true) {\n    root._bokeh_onload_callbacks = [];\n    root._bokeh_is_loading = undefined;\n  }\n\n  \n\n  \n  if (typeof (root._bokeh_timeout) === \"undefined\" || force === true) {\n    root._bokeh_timeout = Date.now() + 5000;\n    root._bokeh_failed_load = false;\n  }\n\n  var NB_LOAD_WARNING = {'data': {'text/html':\n     \"<div style='background-color: #fdd'>\\n\"+\n     \"<p>\\n\"+\n     \"BokehJS does not appear to have successfully loaded. If loading BokehJS from CDN, this \\n\"+\n     \"may be due to a slow or bad network connection. Possible fixes:\\n\"+\n     \"</p>\\n\"+\n     \"<ul>\\n\"+\n     \"<li>re-rerun `output_notebook()` to attempt to load from CDN again, or</li>\\n\"+\n     \"<li>use INLINE resources instead, as so:</li>\\n\"+\n     \"</ul>\\n\"+\n     \"<code>\\n\"+\n     \"from bokeh.resources import INLINE\\n\"+\n     \"output_notebook(resources=INLINE)\\n\"+\n     \"</code>\\n\"+\n     \"</div>\"}};\n\n  function display_loaded() {\n    var el = document.getElementById(\"f4509364-d5a1-48a0-9e44-7ebc6bd404d4\");\n    if (el != null) {\n      el.textContent = \"BokehJS is loading...\";\n    }\n    if (root.Bokeh !== undefined) {\n      if (el != null) {\n        el.textContent = \"BokehJS \" + root.Bokeh.version + \" successfully loaded.\";\n      }\n    } else if (Date.now() < root._bokeh_timeout) {\n      setTimeout(display_loaded, 100)\n    }\n  }\n\n\n  function run_callbacks() {\n    try {\n      root._bokeh_onload_callbacks.forEach(function(callback) { callback() });\n    }\n    finally {\n      delete root._bokeh_onload_callbacks\n    }\n    console.info(\"Bokeh: all callbacks have finished\");\n  }\n\n  function load_libs(js_urls, callback) {\n    root._bokeh_onload_callbacks.push(callback);\n    if (root._bokeh_is_loading > 0) {\n      console.log(\"Bokeh: BokehJS is being loaded, scheduling callback at\", now());\n      return null;\n    }\n    if (js_urls == null || js_urls.length === 0) {\n      run_callbacks();\n      return null;\n    }\n    console.log(\"Bokeh: BokehJS not loaded, scheduling load and callback at\", now());\n    root._bokeh_is_loading = js_urls.length;\n    for (var i = 0; i < js_urls.length; i++) {\n      var url = js_urls[i];\n      var s = document.createElement('script');\n      s.src = url;\n      s.async = false;\n      s.onreadystatechange = s.onload = function() {\n        root._bokeh_is_loading--;\n        if (root._bokeh_is_loading === 0) {\n          console.log(\"Bokeh: all BokehJS libraries loaded\");\n          run_callbacks()\n        }\n      };\n      s.onerror = function() {\n        console.warn(\"failed to load library \" + url);\n      };\n      console.log(\"Bokeh: injecting script tag for BokehJS library: \", url);\n      document.getElementsByTagName(\"head\")[0].appendChild(s);\n    }\n  };var element = document.getElementById(\"f4509364-d5a1-48a0-9e44-7ebc6bd404d4\");\n  if (element == null) {\n    console.log(\"Bokeh: ERROR: autoload.js configured with elementid 'f4509364-d5a1-48a0-9e44-7ebc6bd404d4' but no matching script tag was found. \")\n    return false;\n  }\n\n  var js_urls = [\"https://cdn.pydata.org/bokeh/release/bokeh-0.12.13.min.js\", \"https://cdn.pydata.org/bokeh/release/bokeh-widgets-0.12.13.min.js\", \"https://cdn.pydata.org/bokeh/release/bokeh-tables-0.12.13.min.js\", \"https://cdn.pydata.org/bokeh/release/bokeh-gl-0.12.13.min.js\"];\n\n  var inline_js = [\n    function(Bokeh) {\n      Bokeh.set_log_level(\"info\");\n    },\n    \n    function(Bokeh) {\n      \n    },\n    function(Bokeh) {\n      console.log(\"Bokeh: injecting CSS: https://cdn.pydata.org/bokeh/release/bokeh-0.12.13.min.css\");\n      Bokeh.embed.inject_css(\"https://cdn.pydata.org/bokeh/release/bokeh-0.12.13.min.css\");\n      console.log(\"Bokeh: injecting CSS: https://cdn.pydata.org/bokeh/release/bokeh-widgets-0.12.13.min.css\");\n      Bokeh.embed.inject_css(\"https://cdn.pydata.org/bokeh/release/bokeh-widgets-0.12.13.min.css\");\n      console.log(\"Bokeh: injecting CSS: https://cdn.pydata.org/bokeh/release/bokeh-tables-0.12.13.min.css\");\n      Bokeh.embed.inject_css(\"https://cdn.pydata.org/bokeh/release/bokeh-tables-0.12.13.min.css\");\n    }\n  ];\n\n  function run_inline_js() {\n    \n    if ((root.Bokeh !== undefined) || (force === true)) {\n      for (var i = 0; i < inline_js.length; i++) {\n        inline_js[i].call(root, root.Bokeh);\n      }if (force === true) {\n        display_loaded();\n      }} else if (Date.now() < root._bokeh_timeout) {\n      setTimeout(run_inline_js, 100);\n    } else if (!root._bokeh_failed_load) {\n      console.log(\"Bokeh: BokehJS failed to load within specified timeout.\");\n      root._bokeh_failed_load = true;\n    } else if (force !== true) {\n      var cell = $(document.getElementById(\"f4509364-d5a1-48a0-9e44-7ebc6bd404d4\")).parents('.cell').data().cell;\n      cell.output_area.append_execute_result(NB_LOAD_WARNING)\n    }\n\n  }\n\n  if (root._bokeh_is_loading === 0) {\n    console.log(\"Bokeh: BokehJS loaded, going straight to plotting\");\n    run_inline_js();\n  } else {\n    load_libs(js_urls, function() {\n      console.log(\"Bokeh: BokehJS plotting callback run at\", now());\n      run_inline_js();\n    });\n  }\n}(window));"
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "\n",
       "<div class=\"bk-root\">\n",
       "    <div class=\"bk-plotdiv\" id=\"fac5d651-5e14-4eb4-aa20-c67683df2c74\"></div>\n",
       "</div>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "application/javascript": [
       "(function(root) {\n",
       "  function embed_document(root) {\n",
       "    \n",
       "  var docs_json = 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Application\",\"version\":\"0.12.13\"}};\n",
       "  var render_items = [{\"docid\":\"67a1b6cd-6fa8-4cd1-9c16-93ecee204505\",\"elementid\":\"fac5d651-5e14-4eb4-aa20-c67683df2c74\",\"modelid\":\"b54b6b83-3fd3-48fb-8f4a-ff451d7f8984\"}];\n",
       "  root.Bokeh.embed.embed_items_notebook(docs_json, render_items);\n",
       "\n",
       "  }\n",
       "  if (root.Bokeh !== undefined) {\n",
       "    embed_document(root);\n",
       "  } else {\n",
       "    var attempts = 0;\n",
       "    var timer = setInterval(function(root) {\n",
       "      if (root.Bokeh !== undefined) {\n",
       "        embed_document(root);\n",
       "        clearInterval(timer);\n",
       "      }\n",
       "      attempts++;\n",
       "      if (attempts > 100) {\n",
       "        console.log(\"Bokeh: ERROR: Unable to run BokehJS code because BokehJS library is missing\")\n",
       "        clearInterval(timer);\n",
       "      }\n",
       "    }, 10, root)\n",
       "  }\n",
       "})(window);"
      ],
      "application/vnd.bokehjs_exec.v0+json": ""
     },
     "metadata": {
      "application/vnd.bokehjs_exec.v0+json": {
       "id": "b54b6b83-3fd3-48fb-8f4a-ff451d7f8984"
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "output_notebook()\n",
    "p = figure(plot_width=950, plot_height=400)\n",
    "\n",
    "p.line(error_pos['timestep'][:-10], error_pos.x[:-10], line_width=2, color='blue', legend='x')\n",
    "p.line(error_pos['timestep'][:-10], error_pos.y[:-10], line_width=2, color='red', legend='y')\n",
    "p.line(error_pos['timestep'][:-10], error_pos.z[:-10], line_width=2, color='purple', legend='z')\n",
    "\n",
    "show(p)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Error in Orientation (smallest angle) in radians (20 seconds) averaged across 10 random trajectories"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 96,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "\n",
       "    <div class=\"bk-root\">\n",
       "        <a href=\"https://bokeh.pydata.org\" target=\"_blank\" class=\"bk-logo bk-logo-small bk-logo-notebook\"></a>\n",
       "        <span id=\"e3953d39-1cd4-4e34-93bf-2ad6d2916a5c\">Loading BokehJS ...</span>\n",
       "    </div>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "application/javascript": [
       "\n",
       "(function(root) {\n",
       "  function now() {\n",
       "    return new Date();\n",
       "  }\n",
       "\n",
       "  var force = true;\n",
       "\n",
       "  if (typeof (root._bokeh_onload_callbacks) === \"undefined\" || force === true) {\n",
       "    root._bokeh_onload_callbacks = [];\n",
       "    root._bokeh_is_loading = undefined;\n",
       "  }\n",
       "\n",
       "  var JS_MIME_TYPE = 'application/javascript';\n",
       "  var HTML_MIME_TYPE = 'text/html';\n",
       "  var EXEC_MIME_TYPE = 'application/vnd.bokehjs_exec.v0+json';\n",
       "  var CLASS_NAME = 'output_bokeh rendered_html';\n",
       "\n",
       "  /**\n",
       "   * Render data to the DOM node\n",
       "   */\n",
       "  function render(props, node) {\n",
       "    var script = document.createElement(\"script\");\n",
       "    node.appendChild(script);\n",
       "  }\n",
       "\n",
       "  /**\n",
       "   * Handle when an output is cleared or removed\n",
       "   */\n",
       "  function handleClearOutput(event, handle) {\n",
       "    var cell = handle.cell;\n",
       "\n",
       "    var id = cell.output_area._bokeh_element_id;\n",
       "    var server_id = cell.output_area._bokeh_server_id;\n",
       "    // Clean up Bokeh references\n",
       "    if (id !== undefined) {\n",
       "      Bokeh.index[id].model.document.clear();\n",
       "      delete Bokeh.index[id];\n",
       "    }\n",
       "\n",
       "    if (server_id !== undefined) {\n",
       "      // Clean up Bokeh references\n",
       "      var cmd = \"from bokeh.io.state import curstate; print(curstate().uuid_to_server['\" + server_id + \"'].get_sessions()[0].document.roots[0]._id)\";\n",
       "      cell.notebook.kernel.execute(cmd, {\n",
       "        iopub: {\n",
       "          output: function(msg) {\n",
       "            var element_id = msg.content.text.trim();\n",
       "            Bokeh.index[element_id].model.document.clear();\n",
       "            delete Bokeh.index[element_id];\n",
       "          }\n",
       "        }\n",
       "      });\n",
       "      // Destroy server and session\n",
       "      var cmd = \"import bokeh.io.notebook as ion; ion.destroy_server('\" + server_id + \"')\";\n",
       "      cell.notebook.kernel.execute(cmd);\n",
       "    }\n",
       "  }\n",
       "\n",
       "  /**\n",
       "   * Handle when a new output is added\n",
       "   */\n",
       "  function handleAddOutput(event, handle) {\n",
       "    var output_area = handle.output_area;\n",
       "    var output = handle.output;\n",
       "\n",
       "    // limit handleAddOutput to display_data with EXEC_MIME_TYPE content only\n",
       "    if ((output.output_type != \"display_data\") || (!output.data.hasOwnProperty(EXEC_MIME_TYPE))) {\n",
       "      return\n",
       "    }\n",
       "\n",
       "    var toinsert = output_area.element.find(\".\" + CLASS_NAME.split(' ')[0]);\n",
       "\n",
       "    if (output.metadata[EXEC_MIME_TYPE][\"id\"] !== undefined) {\n",
       "      toinsert[0].firstChild.textContent = output.data[JS_MIME_TYPE];\n",
       "      // store reference to embed id on output_area\n",
       "      output_area._bokeh_element_id = output.metadata[EXEC_MIME_TYPE][\"id\"];\n",
       "    }\n",
       "    if (output.metadata[EXEC_MIME_TYPE][\"server_id\"] !== undefined) {\n",
       "      var bk_div = document.createElement(\"div\");\n",
       "      bk_div.innerHTML = output.data[HTML_MIME_TYPE];\n",
       "      var script_attrs = bk_div.children[0].attributes;\n",
       "      for (var i = 0; i < script_attrs.length; i++) {\n",
       "        toinsert[0].firstChild.setAttribute(script_attrs[i].name, script_attrs[i].value);\n",
       "      }\n",
       "      // store reference to server id on output_area\n",
       "      output_area._bokeh_server_id = output.metadata[EXEC_MIME_TYPE][\"server_id\"];\n",
       "    }\n",
       "  }\n",
       "\n",
       "  function register_renderer(events, OutputArea) {\n",
       "\n",
       "    function append_mime(data, metadata, element) {\n",
       "      // create a DOM node to render to\n",
       "      var toinsert = this.create_output_subarea(\n",
       "        metadata,\n",
       "        CLASS_NAME,\n",
       "        EXEC_MIME_TYPE\n",
       "      );\n",
       "      this.keyboard_manager.register_events(toinsert);\n",
       "      // Render to node\n",
       "      var props = {data: data, metadata: metadata[EXEC_MIME_TYPE]};\n",
       "      render(props, toinsert[0]);\n",
       "      element.append(toinsert);\n",
       "      return toinsert\n",
       "    }\n",
       "\n",
       "    /* Handle when an output is cleared or removed */\n",
       "    events.on('clear_output.CodeCell', handleClearOutput);\n",
       "    events.on('delete.Cell', handleClearOutput);\n",
       "\n",
       "    /* Handle when a new output is added */\n",
       "    events.on('output_added.OutputArea', handleAddOutput);\n",
       "\n",
       "    /**\n",
       "     * Register the mime type and append_mime function with output_area\n",
       "     */\n",
       "    OutputArea.prototype.register_mime_type(EXEC_MIME_TYPE, append_mime, {\n",
       "      /* Is output safe? */\n",
       "      safe: true,\n",
       "      /* Index of renderer in `output_area.display_order` */\n",
       "      index: 0\n",
       "    });\n",
       "  }\n",
       "\n",
       "  // register the mime type if in Jupyter Notebook environment and previously unregistered\n",
       "  if (root.Jupyter !== undefined) {\n",
       "    var events = require('base/js/events');\n",
       "    var OutputArea = require('notebook/js/outputarea').OutputArea;\n",
       "\n",
       "    if (OutputArea.prototype.mime_types().indexOf(EXEC_MIME_TYPE) == -1) {\n",
       "      register_renderer(events, OutputArea);\n",
       "    }\n",
       "  }\n",
       "\n",
       "  \n",
       "  if (typeof (root._bokeh_timeout) === \"undefined\" || force === true) {\n",
       "    root._bokeh_timeout = Date.now() + 5000;\n",
       "    root._bokeh_failed_load = false;\n",
       "  }\n",
       "\n",
       "  var NB_LOAD_WARNING = {'data': {'text/html':\n",
       "     \"<div style='background-color: #fdd'>\\n\"+\n",
       "     \"<p>\\n\"+\n",
       "     \"BokehJS does not appear to have successfully loaded. If loading BokehJS from CDN, this \\n\"+\n",
       "     \"may be due to a slow or bad network connection. Possible fixes:\\n\"+\n",
       "     \"</p>\\n\"+\n",
       "     \"<ul>\\n\"+\n",
       "     \"<li>re-rerun `output_notebook()` to attempt to load from CDN again, or</li>\\n\"+\n",
       "     \"<li>use INLINE resources instead, as so:</li>\\n\"+\n",
       "     \"</ul>\\n\"+\n",
       "     \"<code>\\n\"+\n",
       "     \"from bokeh.resources import INLINE\\n\"+\n",
       "     \"output_notebook(resources=INLINE)\\n\"+\n",
       "     \"</code>\\n\"+\n",
       "     \"</div>\"}};\n",
       "\n",
       "  function display_loaded() {\n",
       "    var el = document.getElementById(\"e3953d39-1cd4-4e34-93bf-2ad6d2916a5c\");\n",
       "    if (el != null) {\n",
       "      el.textContent = \"BokehJS is loading...\";\n",
       "    }\n",
       "    if (root.Bokeh !== undefined) {\n",
       "      if (el != null) {\n",
       "        el.textContent = \"BokehJS \" + root.Bokeh.version + \" successfully loaded.\";\n",
       "      }\n",
       "    } else if (Date.now() < root._bokeh_timeout) {\n",
       "      setTimeout(display_loaded, 100)\n",
       "    }\n",
       "  }\n",
       "\n",
       "\n",
       "  function run_callbacks() {\n",
       "    try {\n",
       "      root._bokeh_onload_callbacks.forEach(function(callback) { callback() });\n",
       "    }\n",
       "    finally {\n",
       "      delete root._bokeh_onload_callbacks\n",
       "    }\n",
       "    console.info(\"Bokeh: all callbacks have finished\");\n",
       "  }\n",
       "\n",
       "  function load_libs(js_urls, callback) {\n",
       "    root._bokeh_onload_callbacks.push(callback);\n",
       "    if (root._bokeh_is_loading > 0) {\n",
       "      console.log(\"Bokeh: BokehJS is being loaded, scheduling callback at\", now());\n",
       "      return null;\n",
       "    }\n",
       "    if (js_urls == null || js_urls.length === 0) {\n",
       "      run_callbacks();\n",
       "      return null;\n",
       "    }\n",
       "    console.log(\"Bokeh: BokehJS not loaded, scheduling load and callback at\", now());\n",
       "    root._bokeh_is_loading = js_urls.length;\n",
       "    for (var i = 0; i < js_urls.length; i++) {\n",
       "      var url = js_urls[i];\n",
       "      var s = document.createElement('script');\n",
       "      s.src = url;\n",
       "      s.async = false;\n",
       "      s.onreadystatechange = s.onload = function() {\n",
       "        root._bokeh_is_loading--;\n",
       "        if (root._bokeh_is_loading === 0) {\n",
       "          console.log(\"Bokeh: all BokehJS libraries loaded\");\n",
       "          run_callbacks()\n",
       "        }\n",
       "      };\n",
       "      s.onerror = function() {\n",
       "        console.warn(\"failed to load library \" + url);\n",
       "      };\n",
       "      console.log(\"Bokeh: injecting script tag for BokehJS library: \", url);\n",
       "      document.getElementsByTagName(\"head\")[0].appendChild(s);\n",
       "    }\n",
       "  };var element = document.getElementById(\"e3953d39-1cd4-4e34-93bf-2ad6d2916a5c\");\n",
       "  if (element == null) {\n",
       "    console.log(\"Bokeh: ERROR: autoload.js configured with elementid 'e3953d39-1cd4-4e34-93bf-2ad6d2916a5c' but no matching script tag was found. \")\n",
       "    return false;\n",
       "  }\n",
       "\n",
       "  var js_urls = [\"https://cdn.pydata.org/bokeh/release/bokeh-0.12.13.min.js\", \"https://cdn.pydata.org/bokeh/release/bokeh-widgets-0.12.13.min.js\", \"https://cdn.pydata.org/bokeh/release/bokeh-tables-0.12.13.min.js\", \"https://cdn.pydata.org/bokeh/release/bokeh-gl-0.12.13.min.js\"];\n",
       "\n",
       "  var inline_js = [\n",
       "    function(Bokeh) {\n",
       "      Bokeh.set_log_level(\"info\");\n",
       "    },\n",
       "    \n",
       "    function(Bokeh) {\n",
       "      \n",
       "    },\n",
       "    function(Bokeh) {\n",
       "      console.log(\"Bokeh: injecting CSS: https://cdn.pydata.org/bokeh/release/bokeh-0.12.13.min.css\");\n",
       "      Bokeh.embed.inject_css(\"https://cdn.pydata.org/bokeh/release/bokeh-0.12.13.min.css\");\n",
       "      console.log(\"Bokeh: injecting CSS: https://cdn.pydata.org/bokeh/release/bokeh-widgets-0.12.13.min.css\");\n",
       "      Bokeh.embed.inject_css(\"https://cdn.pydata.org/bokeh/release/bokeh-widgets-0.12.13.min.css\");\n",
       "      console.log(\"Bokeh: injecting CSS: https://cdn.pydata.org/bokeh/release/bokeh-tables-0.12.13.min.css\");\n",
       "      Bokeh.embed.inject_css(\"https://cdn.pydata.org/bokeh/release/bokeh-tables-0.12.13.min.css\");\n",
       "    }\n",
       "  ];\n",
       "\n",
       "  function run_inline_js() {\n",
       "    \n",
       "    if ((root.Bokeh !== undefined) || (force === true)) {\n",
       "      for (var i = 0; i < inline_js.length; i++) {\n",
       "        inline_js[i].call(root, root.Bokeh);\n",
       "      }if (force === true) {\n",
       "        display_loaded();\n",
       "      }} else if (Date.now() < root._bokeh_timeout) {\n",
       "      setTimeout(run_inline_js, 100);\n",
       "    } else if (!root._bokeh_failed_load) {\n",
       "      console.log(\"Bokeh: BokehJS failed to load within specified timeout.\");\n",
       "      root._bokeh_failed_load = true;\n",
       "    } else if (force !== true) {\n",
       "      var cell = $(document.getElementById(\"e3953d39-1cd4-4e34-93bf-2ad6d2916a5c\")).parents('.cell').data().cell;\n",
       "      cell.output_area.append_execute_result(NB_LOAD_WARNING)\n",
       "    }\n",
       "\n",
       "  }\n",
       "\n",
       "  if (root._bokeh_is_loading === 0) {\n",
       "    console.log(\"Bokeh: BokehJS loaded, going straight to plotting\");\n",
       "    run_inline_js();\n",
       "  } else {\n",
       "    load_libs(js_urls, function() {\n",
       "      console.log(\"Bokeh: BokehJS plotting callback run at\", now());\n",
       "      run_inline_js();\n",
       "    });\n",
       "  }\n",
       "}(window));"
      ],
      "application/vnd.bokehjs_load.v0+json": "\n(function(root) {\n  function now() {\n    return new Date();\n  }\n\n  var force = true;\n\n  if (typeof (root._bokeh_onload_callbacks) === \"undefined\" || force === true) {\n    root._bokeh_onload_callbacks = [];\n    root._bokeh_is_loading = undefined;\n  }\n\n  \n\n  \n  if (typeof (root._bokeh_timeout) === \"undefined\" || force === true) {\n    root._bokeh_timeout = Date.now() + 5000;\n    root._bokeh_failed_load = false;\n  }\n\n  var NB_LOAD_WARNING = {'data': {'text/html':\n     \"<div style='background-color: #fdd'>\\n\"+\n     \"<p>\\n\"+\n     \"BokehJS does not appear to have successfully loaded. If loading BokehJS from CDN, this \\n\"+\n     \"may be due to a slow or bad network connection. Possible fixes:\\n\"+\n     \"</p>\\n\"+\n     \"<ul>\\n\"+\n     \"<li>re-rerun `output_notebook()` to attempt to load from CDN again, or</li>\\n\"+\n     \"<li>use INLINE resources instead, as so:</li>\\n\"+\n     \"</ul>\\n\"+\n     \"<code>\\n\"+\n     \"from bokeh.resources import INLINE\\n\"+\n     \"output_notebook(resources=INLINE)\\n\"+\n     \"</code>\\n\"+\n     \"</div>\"}};\n\n  function display_loaded() {\n    var el = document.getElementById(\"e3953d39-1cd4-4e34-93bf-2ad6d2916a5c\");\n    if (el != null) {\n      el.textContent = \"BokehJS is loading...\";\n    }\n    if (root.Bokeh !== undefined) {\n      if (el != null) {\n        el.textContent = \"BokehJS \" + root.Bokeh.version + \" successfully loaded.\";\n      }\n    } else if (Date.now() < root._bokeh_timeout) {\n      setTimeout(display_loaded, 100)\n    }\n  }\n\n\n  function run_callbacks() {\n    try {\n      root._bokeh_onload_callbacks.forEach(function(callback) { callback() });\n    }\n    finally {\n      delete root._bokeh_onload_callbacks\n    }\n    console.info(\"Bokeh: all callbacks have finished\");\n  }\n\n  function load_libs(js_urls, callback) {\n    root._bokeh_onload_callbacks.push(callback);\n    if (root._bokeh_is_loading > 0) {\n      console.log(\"Bokeh: BokehJS is being loaded, scheduling callback at\", now());\n      return null;\n    }\n    if (js_urls == null || js_urls.length === 0) {\n      run_callbacks();\n      return null;\n    }\n    console.log(\"Bokeh: BokehJS not loaded, scheduling load and callback at\", now());\n    root._bokeh_is_loading = js_urls.length;\n    for (var i = 0; i < js_urls.length; i++) {\n      var url = js_urls[i];\n      var s = document.createElement('script');\n      s.src = url;\n      s.async = false;\n      s.onreadystatechange = s.onload = function() {\n        root._bokeh_is_loading--;\n        if (root._bokeh_is_loading === 0) {\n          console.log(\"Bokeh: all BokehJS libraries loaded\");\n          run_callbacks()\n        }\n      };\n      s.onerror = function() {\n        console.warn(\"failed to load library \" + url);\n      };\n      console.log(\"Bokeh: injecting script tag for BokehJS library: \", url);\n      document.getElementsByTagName(\"head\")[0].appendChild(s);\n    }\n  };var element = document.getElementById(\"e3953d39-1cd4-4e34-93bf-2ad6d2916a5c\");\n  if (element == null) {\n    console.log(\"Bokeh: ERROR: autoload.js configured with elementid 'e3953d39-1cd4-4e34-93bf-2ad6d2916a5c' but no matching script tag was found. \")\n    return false;\n  }\n\n  var js_urls = [\"https://cdn.pydata.org/bokeh/release/bokeh-0.12.13.min.js\", \"https://cdn.pydata.org/bokeh/release/bokeh-widgets-0.12.13.min.js\", \"https://cdn.pydata.org/bokeh/release/bokeh-tables-0.12.13.min.js\", \"https://cdn.pydata.org/bokeh/release/bokeh-gl-0.12.13.min.js\"];\n\n  var inline_js = [\n    function(Bokeh) {\n      Bokeh.set_log_level(\"info\");\n    },\n    \n    function(Bokeh) {\n      \n    },\n    function(Bokeh) {\n      console.log(\"Bokeh: injecting CSS: https://cdn.pydata.org/bokeh/release/bokeh-0.12.13.min.css\");\n      Bokeh.embed.inject_css(\"https://cdn.pydata.org/bokeh/release/bokeh-0.12.13.min.css\");\n      console.log(\"Bokeh: injecting CSS: https://cdn.pydata.org/bokeh/release/bokeh-widgets-0.12.13.min.css\");\n      Bokeh.embed.inject_css(\"https://cdn.pydata.org/bokeh/release/bokeh-widgets-0.12.13.min.css\");\n      console.log(\"Bokeh: injecting CSS: https://cdn.pydata.org/bokeh/release/bokeh-tables-0.12.13.min.css\");\n      Bokeh.embed.inject_css(\"https://cdn.pydata.org/bokeh/release/bokeh-tables-0.12.13.min.css\");\n    }\n  ];\n\n  function run_inline_js() {\n    \n    if ((root.Bokeh !== undefined) || (force === true)) {\n      for (var i = 0; i < inline_js.length; i++) {\n        inline_js[i].call(root, root.Bokeh);\n      }if (force === true) {\n        display_loaded();\n      }} else if (Date.now() < root._bokeh_timeout) {\n      setTimeout(run_inline_js, 100);\n    } else if (!root._bokeh_failed_load) {\n      console.log(\"Bokeh: BokehJS failed to load within specified timeout.\");\n      root._bokeh_failed_load = true;\n    } else if (force !== true) {\n      var cell = $(document.getElementById(\"e3953d39-1cd4-4e34-93bf-2ad6d2916a5c\")).parents('.cell').data().cell;\n      cell.output_area.append_execute_result(NB_LOAD_WARNING)\n    }\n\n  }\n\n  if (root._bokeh_is_loading === 0) {\n    console.log(\"Bokeh: BokehJS loaded, going straight to plotting\");\n    run_inline_js();\n  } else {\n    load_libs(js_urls, function() {\n      console.log(\"Bokeh: BokehJS plotting callback run at\", now());\n      run_inline_js();\n    });\n  }\n}(window));"
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "\n",
       "<div class=\"bk-root\">\n",
       "    <div class=\"bk-plotdiv\" id=\"24b947e4-a1fa-4139-b8ed-092ad1a29e7b\"></div>\n",
       "</div>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "application/javascript": [
       "(function(root) {\n",
       "  function embed_document(root) {\n",
       "    \n",
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       "  var render_items = [{\"docid\":\"fa90f4f5-731a-47c0-ad88-65c96394ee9a\",\"elementid\":\"24b947e4-a1fa-4139-b8ed-092ad1a29e7b\",\"modelid\":\"e5999736-08d4-43ba-9514-c51f708ba059\"}];\n",
       "  root.Bokeh.embed.embed_items_notebook(docs_json, render_items);\n",
       "\n",
       "  }\n",
       "  if (root.Bokeh !== undefined) {\n",
       "    embed_document(root);\n",
       "  } else {\n",
       "    var attempts = 0;\n",
       "    var timer = setInterval(function(root) {\n",
       "      if (root.Bokeh !== undefined) {\n",
       "        embed_document(root);\n",
       "        clearInterval(timer);\n",
       "      }\n",
       "      attempts++;\n",
       "      if (attempts > 100) {\n",
       "        console.log(\"Bokeh: ERROR: Unable to run BokehJS code because BokehJS library is missing\")\n",
       "        clearInterval(timer);\n",
       "      }\n",
       "    }, 10, root)\n",
       "  }\n",
       "})(window);"
      ],
      "application/vnd.bokehjs_exec.v0+json": ""
     },
     "metadata": {
      "application/vnd.bokehjs_exec.v0+json": {
       "id": "e5999736-08d4-43ba-9514-c51f708ba059"
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "output_notebook()\n",
    "p = figure(plot_width=950, plot_height=400)\n",
    "\n",
    "p.line(error_orientation['timestep'][:-10], error_orientation.roll[:-10], line_width=2, color='blue', legend='roll')\n",
    "p.line(error_orientation['timestep'][:-10], error_orientation.pitch[:-10], line_width=2, color='red', legend='pitch')\n",
    "p.line(error_orientation['timestep'][:-10], error_orientation.yaw[:-10], line_width=2, color='purple', legend='yaw')\n",
    "\n",
    "show(p)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### GBT error variance (multistep)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 100,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "x              0.888438\n",
       "y              0.066446\n",
       "z              0.039534\n",
       "timestep    3333.250000\n",
       "dtype: float64"
      ]
     },
     "execution_count": 100,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.std(error_pos) ** 2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 101,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "roll           0.005443\n",
       "pitch          0.005115\n",
       "yaw            0.008805\n",
       "timestep    3333.250000\n",
       "dtype: float64"
      ]
     },
     "execution_count": 101,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.std(error_orientation) ** 2"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### MLP error variance (multistep)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 107,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "x              0.035295\n",
       "y              0.011301\n",
       "z              0.226235\n",
       "timestep    3333.250000\n",
       "dtype: float64"
      ]
     },
     "execution_count": 107,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.std(error_pos) ** 2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 108,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "roll           0.004998\n",
       "pitch          0.004999\n",
       "yaw            0.017678\n",
       "timestep    3333.250000\n",
       "dtype: float64"
      ]
     },
     "execution_count": 108,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.std(error_orientation) ** 2"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### MLP has lower variance than GBT in multistep predictions despite having higher RMSE on test dataset"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Model Verification\n",
    "\n",
    "obtained model is used in a simulated environment, and controlled manually (actions taken at each time step is displayed)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<img src='images/demo3.gif'>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Model successfully captures multirotor dynamics!!"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Conclusion\n",
    "\n",
    "#### 1. MLP has higher RMSE on test dataset, but has lower variance on multistep ahead predictions.\n",
    "#### 2. MLP is 20x times faster than GBT per prediction.\n",
    "#### 3. MLP successfully captures multirotor dynamics including non-linear effects like inertia.\n",
    "#### 4. A better model was obtained by decoupling multirotor actions (allowing only one action to be selected at any timestep)\n",
    "#### 5. MLP can do reliable multistep ahead predictions "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "joblib.dump(gradient, '../models/gradient-m.model')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 136,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "['../models/nn-m.model']"
      ]
     },
     "execution_count": 136,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "joblib.dump(mlp, '../models/nn-m.model')"
   ]
  }
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