examples/interactive_quadrotor_ext.ipynb

{
 "cells": [
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Python Interactive Example: TinyMPC on Quadrotor (Extended Version)\n",
    "In this demonstration, we showcase an interactive Python workflow using TinyMPC. You can generate C++ code and engage with it seamlessly within the Python environment. This example guides you through the entire workflow, beginning with the quadrotor's nonlinear dynamics. The process closely mirrors the steps taken for deploying MPC on the Crazyflie.\n",
    "\n",
    "If any issues arise, restart the kernel."
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Load necessary packages, make sure to install `tinympc` ([README.md](../README.md))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [],
   "source": [
    "import tinympc\n",
    "import math\n",
    "%matplotlib inline\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Quadrotor Dynamics\n",
    "Build the quadrotor nonlinear dynamics and linearize around the hovering state using `autograd`. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [],
   "source": [
    "import autograd.numpy as np\n",
    "import autograd.numpy as sqrt\n",
    "from autograd.numpy.linalg import norm\n",
    "from autograd.numpy.linalg import inv\n",
    "from autograd import jacobian\n",
    "from autograd.test_util import check_grads\n",
    "np.set_printoptions(precision=3, suppress=True)\n",
    "\n",
    "# autograd does not work with np.block\n",
    "\n",
    "#Quaternion stuff, check `Planning with Attitude` paper for more details\n",
    "def hat(v):\n",
    "    return np.array([[0, -v[2], v[1]],\n",
    "                     [v[2], 0, -v[0]],\n",
    "                     [-v[1], v[0], 0.0]])\n",
    "\n",
    "def L(q):\n",
    "    s = q[0]\n",
    "    v = q[1:4]\n",
    "    up = np.hstack([s, -v])\n",
    "    down = np.hstack([v.reshape(3,1), s*np.eye(3) + hat(v)])\n",
    "    L = np.vstack([up,down])\n",
    "    return L\n",
    "\n",
    "T = np.diag([1.0, -1, -1, -1])\n",
    "H = np.vstack([np.zeros((1,3)), np.eye(3)])\n",
    "\n",
    "def qtoQ(q):\n",
    "    return H.T @ T @ L(q) @ T @ L(q) @ H\n",
    "\n",
    "def G(q):\n",
    "    return L(q) @ H\n",
    "\n",
    "def rptoq(phi):\n",
    "    return (1./sqrt(1+phi.T @ phi)) * np.hstack([1, phi])\n",
    "\n",
    "def qtorp(q):\n",
    "    return q[1:4]/q[0]\n",
    "\n",
    "def E(q):\n",
    "    up = np.hstack([np.eye(3), np.zeros((3,3)), np.zeros((3,6))])\n",
    "    mid = np.hstack([np.zeros((4,3)), G(q), np.zeros((4,6))])\n",
    "    down = np.hstack([np.zeros((6,3)), np.zeros((6,3)), np.eye(6)])\n",
    "    E = np.vstack([up, mid, down])\n",
    "    return E\n",
    "\n",
    "# Quadrotor parameters\n",
    "mass = 0.035  # mass\n",
    "J = np.array([[1.66e-5, 0.83e-6, 0.72e-6], [0.83e-6, 1.66e-5, 1.8e-6], [0.72e-6, 1.8e-6, 2.93e-5]])  # inertia\n",
    "g = 9.81  # gravity\n",
    "# thrustToTorque = 0.005964552\n",
    "thrustToTorque = 0.0008  # thrust to torque ratio\n",
    "el = 0.046/1.414213562  # arm length\n",
    "scale = 65535  # PWM scale\n",
    "kt = 2.245365e-6*scale # thrust coefficient, u is PWM in range [0...1], 0 is no thrust, 1 is max thrust\n",
    "km = kt*thrustToTorque # moment coefficient\n",
    "\n",
    "freq = 50.0 # >>>>>>>> CONTROL FREQUENCY <<<<<<<<<<\n",
    "h = 1/freq #50 Hz \n",
    "\n",
    "Nx1 = 13        # number of states (quaternion)\n",
    "Nx = 12         # number of states (linearized): x, y, z, Rodriguez 3-parameters (p, q, r), vx, vy, vz, wx, wy, wz\n",
    "Nu = 4          # number of controls (motor pwm signals, 0-1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[0. 0. 0. 1. 0. 0. 0. 0. 0. 0. 0. 0. 0.] [0.583 0.583 0.583 0.583]\n",
      "A = \n",
      " [[ 1.     0.     0.     0.     0.004  0.     0.02   0.     0.     0.\n",
      "   0.     0.   ]\n",
      " [ 0.     1.     0.    -0.004  0.     0.     0.     0.02   0.    -0.\n",
      "   0.     0.   ]\n",
      " [ 0.     0.     1.     0.     0.     0.     0.     0.     0.02   0.\n",
      "   0.     0.   ]\n",
      " [ 0.     0.     0.     1.     0.     0.     0.     0.     0.     0.01\n",
      "   0.     0.   ]\n",
      " [ 0.     0.     0.     0.     1.     0.     0.     0.     0.     0.\n",
      "   0.01   0.   ]\n",
      " [ 0.     0.     0.     0.     0.     1.     0.     0.     0.     0.\n",
      "   0.     0.01 ]\n",
      " [ 0.     0.     0.     0.     0.392  0.     1.     0.     0.     0.\n",
      "   0.002  0.   ]\n",
      " [ 0.     0.     0.    -0.392  0.     0.     0.     1.     0.    -0.002\n",
      "   0.     0.   ]\n",
      " [ 0.     0.     0.     0.     0.     0.     0.     0.     1.     0.\n",
      "   0.     0.   ]\n",
      " [ 0.     0.     0.     0.     0.     0.     0.     0.     0.     1.\n",
      "   0.     0.   ]\n",
      " [ 0.     0.     0.     0.     0.     0.     0.     0.     0.     0.\n",
      "   1.     0.   ]\n",
      " [ 0.     0.     0.     0.     0.     0.     0.     0.     0.     0.\n",
      "   0.     1.   ]]\n",
      "B = \n",
      " [[-0.     0.     0.    -0.   ]\n",
      " [ 0.     0.    -0.    -0.   ]\n",
      " [ 0.001  0.001  0.001  0.001]\n",
      " [-0.028 -0.03   0.028  0.03 ]\n",
      " [-0.028  0.03   0.028 -0.031]\n",
      " [ 0.002 -0.001 -0.003  0.002]\n",
      " [-0.004  0.004  0.004 -0.004]\n",
      " [ 0.004  0.004 -0.004 -0.004]\n",
      " [ 0.084  0.084  0.084  0.084]\n",
      " [-5.507 -6.065  5.513  6.059]\n",
      " [-5.534  6.086  5.551 -6.103]\n",
      " [ 0.395 -0.144 -0.557  0.306]]\n"
     ]
    }
   ],
   "source": [
    "# Quadrotor dynamics -- single rigid body dynamics\n",
    "def quad_dynamics(x, u):\n",
    "    r = x[0:3]  # position\n",
    "    q = x[3:7]/norm(x[3:7])  # normalize quaternion\n",
    "    v = x[7:10]  # linear velocity\n",
    "    omg = x[10:13]  # angular velocity\n",
    "    Q = qtoQ(q)  # quaternion to rotation matrix\n",
    "\n",
    "    dr = v\n",
    "    dq = 0.5*L(q)@H@omg\n",
    "    dv = np.array([0, 0, -g]) + (1/mass)*Q@np.array([[0, 0, 0, 0], [0, 0, 0, 0], [kt, kt, kt, kt]])@u\n",
    "    domg = inv(J)@(-hat(omg)@J@omg + np.array([[-el*kt, -el*kt, el*kt, el*kt], [-el*kt, el*kt, el*kt, -el*kt], [-km, km, -km, km]])@u)\n",
    "    \n",
    "    return np.hstack([dr, dq, dv, domg])\n",
    "\n",
    "# RK4 integration with zero-order hold on u\n",
    "def quad_dynamics_rk4(x, u):\n",
    "    f1 = quad_dynamics(x, u)\n",
    "    f2 = quad_dynamics(x + 0.5*h*f1, u)\n",
    "    f3 = quad_dynamics(x + 0.5*h*f2, u)\n",
    "    f4 = quad_dynamics(x + h*f3, u)\n",
    "    xn = x + (h/6.0)*(f1 + 2*f2 + 2*f3 + f4)\n",
    "    xnormalized = xn[3:7]/norm(xn[3:7])  # normalize quaternion\n",
    "    return np.hstack([xn[0:3], xnormalized, xn[7:13]])\n",
    "\n",
    "# Linearize the dynamics around x0, u0\n",
    "A_jac = jacobian(quad_dynamics_rk4, 0)  # jacobian wrt x\n",
    "B_jac = jacobian(quad_dynamics_rk4, 1)  # jacobian wrt u\n",
    "\n",
    "# Hovering state and control input\n",
    "rg = np.array([0.0, 0, 0.0])\n",
    "qg = np.array([1.0, 0, 0, 0])\n",
    "vg = np.zeros(3)\n",
    "omgg = np.zeros(3)\n",
    "x0 = np.hstack([rg, qg, vg, omgg])\n",
    "u0 = (mass*g/kt/4)*np.ones(4)  # ~each motor thrust to compensate for gravity\n",
    "print(x0, u0)\n",
    "\n",
    "check_grads(quad_dynamics_rk4, modes=['rev'], order=2)(x0, u0)\n",
    "\n",
    "Anp1 = A_jac(x0, u0)  # jacobian of the dynamics wrt x at x0, u0\n",
    "Bnp1 = B_jac(x0, u0)  # jacobian of the dynamics wrt u at x0, u0\n",
    "\n",
    "# `Planning with Attitude` trick, attitude Jacobians\n",
    "Anp = E(qg).T @ Anp1 @ E(qg) \n",
    "Bnp = E(qg).T @ Bnp1\n",
    "print(\"A = \\n\", Anp)\n",
    "print(\"B = \\n\", Bnp)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
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",
      "text/plain": [
       "<Figure size 640x480 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# function to visualize the trajectory\n",
    "def visualize_trajectory(x_all):\n",
    "    # Set up the figure and axis for plotting\n",
    "    fig, ax = plt.subplots(2, 1)\n",
    "\n",
    "    # Plot the trajectory\n",
    "    x_all = np.array(x_all)\n",
    "    nsteps = len(x_all)\n",
    "    steps = np.arange(nsteps)\n",
    "    ax[0].plot(steps, x_all[:, 0], label=\"x\", linewidth=2)\n",
    "    ax[0].plot(steps, x_all[:, 1], label=\"y\", linewidth=2)\n",
    "    ax[0].plot(steps, x_all[:, 2], label=\"z\", linewidth=2)\n",
    "    ax[0].legend()\n",
    "    ax[0].title.set_text(\"Position\")\n",
    "\n",
    "    ax[1].plot(steps, x_all[:, 3], label=\"q0\", linewidth=2)\n",
    "    ax[1].plot(steps, x_all[:, 4], label=\"q1\", linewidth=2)\n",
    "    ax[1].plot(steps, x_all[:, 5], label=\"q2\", linewidth=2)\n",
    "    ax[1].plot(steps, x_all[:, 6], label=\"q3\", linewidth=2)\n",
    "    ax[1].legend()\n",
    "    ax[1].title.set_text(\"Attitude\")\n",
    "    plt.show()\n",
    "\n",
    "x_all = []\n",
    "# simulate the dynamics with the zero controller\n",
    "x = 1*x0\n",
    "for i in range(300):\n",
    "    x = quad_dynamics_rk4(x, u0)\n",
    "    x_all.append(x)\n",
    "\n",
    "visualize_trajectory(x_all)"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## LQR Controller\n",
    "\n",
    "Let's run LQR on the linearized model"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "K = \n",
      " [[-0.222  0.213  0.4   -0.631 -0.717 -1.266 -0.133  0.124  0.232 -0.046\n",
      "  -0.059 -0.342]\n",
      " [ 0.213  0.188  0.4   -0.48   0.687  1.292  0.127  0.104  0.232 -0.026\n",
      "   0.056  0.345]\n",
      " [ 0.182 -0.197  0.4    0.512  0.418 -1.352  0.098 -0.11   0.232  0.028\n",
      "   0.015 -0.351]\n",
      " [-0.174 -0.204  0.4    0.6   -0.388  1.326 -0.093 -0.118  0.232  0.043\n",
      "  -0.013  0.348]]\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Choose Q and R matrices based on Bryson's rule \n",
    "max_dev_x = np.array([0.1, 0.1, 0.1,  0.5, 0.5, 0.03,  0.5, 0.5, 0.5,  0.7, 0.7, 0.2])\n",
    "max_dev_u = np.array([0.5, 0.5, 0.5, 0.5])/6\n",
    "Q = np.diag(1./max_dev_x**2)\n",
    "R = np.diag(1./max_dev_u**2)\n",
    "# print(\"Q = \\n\", Q)\n",
    "# print(\"R = \\n\", R)\n",
    "\n",
    "# Riccati recursion on the linearized dynamics\n",
    "P = Q\n",
    "for i in range(100):\n",
    "    P = Q + Anp.T @ P @ Anp - Anp.T @ P @ Bnp @ inv(R + Bnp.T @ P @ Bnp) @ Bnp.T @ P @ Anp\n",
    "    # print(P)\n",
    "    K = inv(R + Bnp.T @ P @ Bnp) @ Bnp.T @ P @ Anp\n",
    "print(\"K = \\n\", K)\n",
    "\n",
    "# Drive the system from initial state to the hovering state using the LQR controller:\n",
    "# LQR controller, input is 13x1 state vector\n",
    "def lqr_controller(x):\n",
    "    q = x[3:7]\n",
    "    phi = qtorp(L(qg).T @ q)\n",
    "    delta_x = np.hstack([x[0:3]-rg, phi, x[7:10]-vg, x[10:13]-omgg])\n",
    "    return -K @ delta_x + u0\n",
    "\n",
    "x = 1*x0\n",
    "x[0:3] = rg + 1*np.random.randn(3)/3  # disturbed initial position\n",
    "NSIM = 100\n",
    "x_all = []\n",
    "# simulate the dynamics with the LQR controller\n",
    "for i in range(NSIM):\n",
    "    u = lqr_controller(x)\n",
    "    x = quad_dynamics_rk4(x, u)\n",
    "    x_all.append(x)\n",
    "\n",
    "visualize_trajectory(x_all)"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Code Generation\n",
    "\n",
    "We are done with the dynamics and LQR controller. Now, let's define the class and compile original TinyMPC code to get a generic shared/dynamic library\n",
    "\n",
    "**PLEASE CHANGE `tinympc_python_dir` TO YOUR ABSOLUTE PATH**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "True"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "prob = tinympc.TinyMPC()\n",
    "\n",
    "tinympc_python_dir = \"/home/khai/SSD/Code/tinympc-python\"  # Your absolute path to the tinympc-python directory\n",
    "\n",
    "tinympc_dir = tinympc_python_dir + \"/tinympc/TinyMPC\"  # Path to the TinyMPC directory (C code)\n",
    "prob.compile_lib(tinympc_dir)  # Compile the library (or use the binary provided)"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Load the generic shared/dynamic library. **You may want to change the extension of the library based on your OS -- Linux: .so, Mac: .dylib, Windows: .dll**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [],
   "source": [
    "os_ext = \".so\"  # CHANGE THIS BASED ON YOUR OS\n",
    "lib_dir = tinympc_dir + \"/build/src/tinympc/libtinympcShared\" + os_ext  # Path to the compiled library\n",
    "prob.load_lib(lib_dir)  # Load the library"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Here we setup problem data and settings for TinyMPC"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "True"
      ]
     },
     "execution_count": 28,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "n = 12  # number of states == Nx\n",
    "m = 4   # number of inputs == Nu\n",
    "N = 10  # horizon length\n",
    "\n",
    "A = Anp.transpose().reshape((n * n)).tolist() # col-major order list\n",
    "B = Bnp.transpose().reshape((n * m)).tolist() # col-major order list\n",
    "Q = (1./max_dev_x**2).tolist()  # diagonal of state cost\n",
    "R = (1./max_dev_u**2).tolist()  # diagonal of input cost\n",
    "rho = 0.1  # ADMM penalty parameter\n",
    "\n",
    "x_min = [-1000.0] * n * N           # state constraints \n",
    "x_max = [1000.] * n * N             # state constraints\n",
    "u_min = [-u0[0]] * m * (N - 1)      # input constraints\n",
    "u_max = [1.0-u0[0]] * m * (N - 1)   # input constraints\n",
    "\n",
    "abs_pri_tol = 1.0e-3    # absolute primal tolerance\n",
    "abs_dual_tol = 1.0e-3   # absolute dual tolerance\n",
    "max_iter = 100          # maximum number of iterations\n",
    "check_termination = 1   # whether to check termination and period\n",
    "\n",
    "# Setup problem data\n",
    "prob.setup(n, m, N, A, B, Q, R, x_min, x_max, u_min, u_max, rho, abs_pri_tol, abs_dual_tol, max_iter, check_termination)"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "After define the problem, we generate the tailored code with above data. \n",
    "\n",
    "**Here we compile it for interactive Python script but you can use it directly for your applications/systems**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "True"
      ]
     },
     "execution_count": 29,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "output_dir = tinympc_python_dir + \"/generated_code\"  # Path to the generated code\n",
    "prob.tiny_codegen(tinympc_dir, output_dir)  \n",
    "# You may want to check if Kinf in generated_code follows the same pattern as previous K in LQR, otherwise something is wrong\n",
    "prob.compile_lib(output_dir)"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Interactive MPC"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Run the interactive MPC example which calls the generated code, use nonlinear dynamics for simulation\n",
    "\n",
    "Since this works with pointers, underlying data is persistent in each kernel session (something like deepcopy/shallowcopy or pass by reference/value). If you want to run from the original setup, you may need to change data back or \n",
    "restart kernel."
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Quadrotor Hovering"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[0. 0. 0. 1. 0. 0. 0. 0. 0. 0. 0. 0. 0.]\n",
      "=== START INTERACTIVE MPC ===\n",
      "[0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]\n",
      "[0.19459684193134308, 0.200664222240448, 0.2054303139448166, 0.20073944330215454, 0.1836681067943573, 0.18463972210884094, 0.18463177978992462, 0.184676855802536, 0.16979557275772095, 0.16933602094650269, 0.16824862360954285, 0.16933012008666992, 0.15560322999954224, 0.15474194288253784, 0.1535884588956833, 0.15471895039081573, 0.14182233810424805, 0.14085160195827484, 0.13988111913204193, 0.14082540571689606, 0.12864673137664795, 0.12765264511108398, 0.12690098583698273, 0.127628356218338, 0.11611733585596085, 0.11512859910726547, 0.1145758330821991, 0.11510764807462692, 0.10423079878091812, 0.1032613143324852, 0.10287695378065109, 0.10324373841285706, 0.09297068417072296, 0.09203172475099564, 0.09178794175386429, 0.09201744198799133]\n",
      "[0.778 0.784 0.789 0.784]\n",
      "[2.617277197913806e-07, -2.6423364047508876e-07, 0.0006738887303432466, 0.00030072443189739707, 0.0002978913112451288, -2.51371029462466e-05, 5.234596886106335e-05, -5.284630704944095e-05, 0.06738885729153161, 0.06014374768737385, 0.05957941050441446, -0.005027432335051963]\n",
      "[0.1835586428642273, 0.18465059995651245, 0.18476490676403046, 0.18469145894050598, 0.16983550786972046, 0.1693475842475891, 0.16823607683181763, 0.1693417727947235, 0.1556694209575653, 0.1547534018754959, 0.15355302393436432, 0.1547289788722992, 0.1418818235397339, 0.1408628523349762, 0.13985446095466614, 0.14083510637283325, 0.12869256734848022, 0.12766404449939728, 0.12688899040222168, 0.127638578414917, 0.1161501333117485, 0.11514049768447876, 0.11457709223031998, 0.11511877179145813, 0.10425373166799545, 0.1032739207148552, 0.10288794338703156, 0.10325600951910019, 0.09298774600028992, 0.09204526990652084, 0.09180443733930588, 0.09203081578016281, 0.08233045786619186, 0.08143500983715057, 0.08131454139947891, 0.08142384141683578]\n",
      "[0.767 0.768 0.768 0.768]\n",
      "[3.900361768498752e-06, -3.939393952194259e-06, 0.0026419344065672255, 0.0009365821371302064, 0.0009258642644799193, -7.78249049507855e-05, 0.00036556502694668, -0.00036940693341568624, 0.12941557646303087, 0.06702738493126606, 0.06601540734978939, -0.005509937284363699]\n",
      "[0.16974323987960815, 0.16935758292675018, 0.16835689544677734, 0.16935598850250244, 0.15571428835391998, 0.15476462244987488, 0.15353995561599731, 0.15474030375480652, 0.14194853603839874, 0.14087429642677307, 0.1398223638534546, 0.1408451497554779, 0.1287509649991989, 0.12767557799816132, 0.12686680257320404, 0.12764862179756165, 0.11619431525468826, 0.11515240371227264, 0.11456967145204544, 0.11512967944145203, 0.10428499430418015, 0.10328662395477295, 0.10289336740970612, 0.103268101811409, 0.09300980716943741, 0.0920589417219162, 0.09181860089302063, 0.09204418957233429, 0.08234898746013641, 0.08144988864660263, 0.08133174479007721, 0.08143840730190277, 0.07227859646081924, 0.07143963873386383, 0.07142238318920135, 0.07143132388591766]\n",
      "[0.753 0.753 0.752 0.753]\n",
      "[1.6979581073068983e-05, -1.71679661530631e-05, 0.005799336011518097, 0.0015685667598989352, 0.001547660535930383, -0.00012938251676426936, 0.0009948063357783788, -0.0010067813374501906, 0.1863243206940432, 0.05936928889221575, 0.05834334879988325, -0.004800967603913734]\n",
      "[0.1556398868560791, 0.15477442741394043, 0.15364867448806763, 0.15475399792194366, 0.14199797809123993, 0.14088553190231323, 0.13980993628501892, 0.14085634052753448, 0.12881846725940704, 0.12768720090389252, 0.12683838605880737, 0.1276588886976242, 0.1162523403763771, 0.1151643693447113, 0.11455167829990387, 0.11514029651880264, 0.10432853549718857, 0.10329923033714294, 0.10288991034030914, 0.103279709815979, 0.09304037690162659, 0.0920724868774414, 0.09182750433683395, 0.09205719828605652, 0.08237084746360779, 0.08146461099386215, 0.08134859800338745, 0.08145289123058319, 0.07229847460985184, 0.07145576179027557, 0.07144032418727875, 0.07144714891910553, 0.06279793381690979, 0.062026068568229675, 0.0620933473110199, 0.06202039122581482]\n",
      "[0.739 0.738 0.737 0.738]\n",
      "[4.547840899518756e-05, -4.602877980177995e-05, 0.010046128676237612, 0.002106752930903994, 0.002076553811506753, -0.00017258399495204686, 0.0018988251607782484, -0.0019238443459287137, 0.23835462350642378, 0.048267263675253434, 0.0474346036024859, -0.0038385995899319213]\n",
      "[0.14193665981292725, 0.1408957540988922, 0.13991035521030426, 0.14086978137493134, 0.12887147068977356, 0.12769877910614014, 0.12682664394378662, 0.1276702582836151, 0.11632076650857925, 0.11517646163702011, 0.1145261898636818, 0.11515101790428162, 0.10438667237758636, 0.10331187397241592, 0.1028752252459526, 0.10329104959964752, 0.09308379143476486, 0.09208592772483826, 0.09182721376419067, 0.09206976741552353, 0.0824013203382492, 0.08147910982370377, 0.08136028796434402, 0.0814669206738472, 0.07232055813074112, 0.07147160172462463, 0.0714593231678009, 0.07146278023719788, 0.06281930208206177, 0.062043413519859314, 0.06211186945438385, 0.06203740835189819, 0.05387118458747864, 0.053174614906311035, 0.05330914258956909, 0.05317135155200958]\n",
      "[0.725 0.724 0.723 0.724]\n",
      "[9.429477602342277e-05, -9.550917295641613e-05, 0.015287089687158244, 0.0025328011978386312, 0.002495559345567671, -0.0002062131175223799, 0.003016819535138753, -0.0030588006249767383, 0.28574116153903906, 0.03694127664726704, 0.036365844673799955, -0.002886763603190635]\n",
      "[0.12881799042224884, 0.12770976126194, 0.12692292034626007, 0.12768401205539703, 0.1163763478398323, 0.11518875509500504, 0.11451538652181625, 0.11516295373439789, 0.10445606708526611, 0.10332470387220383, 0.10285194963216782, 0.10330252349376678, 0.09314248710870743, 0.09209934622049332, 0.09181489795446396, 0.09208189696073532, 0.08244514465332031, 0.08149345964193344, 0.0813622698187828, 0.08148040622472763, 0.07235151529312134, 0.07148705422878265, 0.07147304713726044, 0.07147781550884247, 0.06284213066101074, 0.06206029653549194, 0.06213246285915375, 0.06205405294895172, 0.05389438569545746, 0.05319306254386902, 0.05332799255847931, 0.053189486265182495, 0.04548104107379913, 0.04486547410488129, 0.04505138099193573, 0.04486443102359772]\n",
      "[0.712 0.711 0.71  0.711]\n",
      "[0.0001671046229371036, -0.00016935035597108705, 0.021431638032681007, 0.002849224828308256, 0.0028075101929361046, -0.00023074086380645475, 0.004289023931685481, -0.004350554608342068, 0.3287134053557953, 0.026342125604493373, 0.02602384300351729, -0.002018813875657359]\n",
      "[0.11632625013589859, 0.1152006983757019, 0.11461088061332703, 0.11517730355262756, 0.10451311618089676, 0.10333780199289322, 0.10284207761287689, 0.10331521928310394, 0.0932127982378006, 0.09211300313472748, 0.09179303795099258, 0.09209419786930084, 0.08250456303358078, 0.08150769770145416, 0.08135136216878891, 0.08149339258670807, 0.07239598035812378, 0.07150225341320038, 0.07147638499736786, 0.07149213552474976, 0.06287379562854767, 0.06207661330699921, 0.062147364020347595, 0.06206996738910675, 0.05391809344291687, 0.053210824728012085, 0.053349465131759644, 0.05320701003074646, 0.045506060123443604, 0.04488486051559448, 0.04507023096084595, 0.04488343000411987, 0.03760990500450134, 0.03707893192768097, 0.03730182349681854, 0.03707978129386902]\n",
      "[0.7   0.699 0.698 0.699]\n",
      "[0.0002664473826760142, -0.00027013033029668404, 0.02839372674471736, 0.0030646874280527404, 0.0030209521729940127, -0.00024709694401679397, 0.005661962208665831, -0.0057443269176299955, 0.36749526859893156, 0.016749113011983043, 0.016664303509018277, -0.001252999633596318]\n",
      "[0.10446292161941528, 0.10335075855255127, 0.10293929278850555, 0.10333044826984406, 0.09327052533626556, 0.09212706238031387, 0.09178417176008224, 0.09210778772830963, 0.08257574588060379, 0.08152222633361816, 0.0813303142786026, 0.08150657266378403, 0.07245636731386185, 0.07151734828948975, 0.07146625220775604, 0.07150599360466003, 0.06291916966438293, 0.06209258735179901, 0.06215140223503113, 0.0620851069688797, 0.053950801491737366, 0.05322791635990143, 0.0533650666475296, 0.053223684430122375, 0.04553098976612091, 0.04490336775779724, 0.04509216547012329, 0.044901683926582336, 0.03763672709465027, 0.03709903359413147, 0.03732043504714966, 0.037099480628967285, 0.03023993968963623, 0.029795169830322266, 0.030042320489883423, 0.029797717928886414]\n",
      "[0.688 0.687 0.686 0.687]\n",
      "[0.00039386530165825905, -0.00039940531213586146, 0.036091728776615574, 0.00318960027746503, 0.00314602141962562, -0.00025631032721717837, 0.007089455565272333, -0.007192794407361854, 0.4023048150403946, 0.008232427859750882, 0.008349517192756178, -0.0005908375404053147]\n",
      "[0.09321765601634979, 0.09214100986719131, 0.09188494086265564, 0.09212400764226913, 0.08263343572616577, 0.0815371721982956, 0.08132237195968628, 0.08152108639478683, 0.07252826541662216, 0.07153268158435822, 0.07144546508789062, 0.07151997089385986, 0.06298057734966278, 0.06210845708847046, 0.06214138865470886, 0.06209971010684967, 0.053997233510017395, 0.053244560956954956, 0.0533691942691803, 0.05323950946331024, 0.04556471109390259, 0.044921115040779114, 0.0451078861951828, 0.044918984174728394, 0.03766287863254547, 0.03711812198162079, 0.037342414259910583, 0.03711828589439392, 0.030268386006355286, 0.02981582283973694, 0.030060499906539917, 0.029817849397659302, 0.02335311472415924, 0.022994622588157654, 0.023254677653312683, 0.022998571395874023]\n",
      "[0.677 0.675 0.675 0.675]\n",
      "[0.0005500485015073093, -0.0005578584285580983, 0.04444831799493158, 0.003234707589820742, 0.0031931357893685824, -0.0002593972853623771, 0.008532431608228728, -0.008655935702170221, 0.43335406221636735, 0.0007884000889157583, 0.0010734841931978583, -2.822228894891921e-05]\n",
      "[0.08257618546485901, 0.08155208081007004, 0.08142776042222977, 0.08153833448886871, 0.07258545607328415, 0.07154849171638489, 0.07143835723400116, 0.0715353935956955, 0.06305308640003204, 0.06212463974952698, 0.062120482325553894, 0.06211447715759277, 0.054059550166130066, 0.05326111614704132, 0.053358882665634155, 0.053254738450050354, 0.045612260699272156, 0.04493832588195801, 0.0451117604970932, 0.044935375452041626, 0.037697672843933105, 0.03713636100292206, 0.03735792636871338, 0.03713609278202057, 0.03029574453830719, 0.029835328459739685, 0.03008224070072174, 0.02983708679676056, 0.023383110761642456, 0.023015707731246948, 0.023272469639778137, 0.02301912009716034, 0.016931578516960144, 0.0166579931974411, 0.01692134141921997, 0.016663148999214172]\n",
      "[0.666 0.665 0.665 0.665]\n",
      "[0.0007349720510793872, -0.0007454407473951245, 0.0533903465555208, 0.0032105496893991676, 0.003172500796826566, -0.00025732157654933076, 0.009958385704439809, -0.010100493990665536, 0.46084881524706556, -0.005620145354114067, -0.005200298270662749, 0.0004412703237413161]\n",
      "[0.07252266258001328, 0.07156424224376678, 0.07154896855354309, 0.07155361771583557, 0.06310941278934479, 0.06214118003845215, 0.06211411952972412, 0.06213071942329407, 0.05413252115249634, 0.05327795445919037, 0.05333751440048218, 0.053270190954208374, 0.04567541182041168, 0.044955477118492126, 0.04510076344013214, 0.04495115578174591, 0.037746235728263855, 0.03715407848358154, 0.037361159920692444, 0.037152886390686035, 0.030331581830978394, 0.0298539400100708, 0.030097171664237976, 0.029855266213417053, 0.023411527276039124, 0.023035496473312378, 0.023293718695640564, 0.023038581013679504, 0.016962751746177673, 0.01667925715446472, 0.01693861186504364, 0.016683831810951233, 0.010957285761833191, 0.010766148567199707, 0.011024564504623413, 0.010772168636322021]\n",
      "[0.656 0.655 0.655 0.655]\n",
      "[0.0009480210691992728, -0.0009615001998483958, 0.06284871966880216, 0.003127212538789387, 0.0030938779449793076, -0.0002509778648844125, 0.011340744689820556, -0.011499327605365955, 0.4849885710591337, -0.01104696162842584, -0.010524143375737902, 0.0008250472503840587]\n",
      "[0.06304046511650085, 0.06215755641460419, 0.062230050563812256, 0.06214979290962219, 0.05418768525123596, 0.053295135498046875, 0.053331658244132996, 0.053287073969841, 0.04574871063232422, 0.04497283697128296, 0.045078665018081665, 0.044967085123062134, 0.037810057401657104, 0.0371716171503067, 0.03734925389289856, 0.037169069051742554, 0.03038102388381958, 0.02987198531627655, 0.03009955585002899, 0.029872357845306396, 0.023448318243026733, 0.0230543315410614, 0.02330794930458069, 0.023056939244270325, 0.016992121934890747, 0.016699254512786865, 0.016959264874458313, 0.016703441739082336, 0.010989457368850708, 0.010787531733512878, 0.01104135811328888, 0.010793030261993408, 0.0054124146699905396, 0.005300357937812805, 0.005547121167182922, 0.005307123064994812]\n",
      "[0.646 0.645 0.646 0.645]\n",
      "[0.001188102885172548, -0.0012048972410742785, 0.0727582684817096, 0.002994189191675621, 0.0029664568733896797, -0.00024118435459550332, 0.012658217293975371, -0.012830742350606343, 0.5059664250827615, -0.015556917994094902, -0.014960106143341097, 0.0011309950744911247]\n",
      "[0.054112523794174194, 0.053312137722969055, 0.05345289409160614, 0.053306952118873596, 0.04580274224281311, 0.04499056935310364, 0.04507334530353546, 0.04498462378978729, 0.03788366913795471, 0.037189409136772156, 0.037326380610466, 0.0371854305267334, 0.030445531010627747, 0.029889896512031555, 0.030086681246757507, 0.029888823628425598, 0.02349846065044403, 0.023072615265846252, 0.023309379816055298, 0.023074209690093994, 0.017029717564582825, 0.016718238592147827, 0.016972616314888, 0.016721919178962708, 0.011019542813301086, 0.010807514190673828, 0.01106126606464386, 0.010812640190124512, 0.005445241928100586, 0.005321681499481201, 0.005563363432884216, 0.005327895283699036, 0.0002791881561279297, 0.00024214386940002441, 0.0004717409610748291, 0.00024944543838500977]\n",
      "[0.637 0.637 0.637 0.637]\n",
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      "[0.58 0.58 0.58 0.58]\n",
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      "[0.58 0.58 0.58 0.58]\n",
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      "[-0.002593815326690674, -0.0026442259550094604, -0.0026042312383651733, -0.002643883228302002, -0.0021879971027374268, -0.0023571401834487915, -0.002442076802253723, -0.002360105514526367, -0.001948326826095581, -0.0020856261253356934, -0.0021477043628692627, -0.0020884722471237183, -0.0017490983009338379, -0.0018284022808074951, -0.0018452554941177368, -0.0018298327922821045, -0.0015567243099212646, -0.001585051417350769, -0.0015662461519241333, -0.0015850067138671875, -0.0013639479875564575, -0.001355290412902832, -0.0013157427310943604, -0.0013541579246520996, -0.0011710375547409058, -0.0011390745639801025, -0.0010915696620941162, -0.0011373013257980347, -0.0009808242321014404, -0.0009360909461975098, -0.0008896738290786743, -0.0009341984987258911, -0.0007965415716171265, -0.0007460564374923706, -0.0007055699825286865, -0.000744059681892395]\n",
      "[0.581 0.581 0.581 0.581]\n",
      "[0.01328678571456354, -0.013296101718769297, 0.5124589023923954, 0.00013867048858545554, 0.00014137293987295687, -1.7939312436123216e-05, -0.0004920687771283755, 0.00046589535870548645, -0.01120834004081566, -0.0005039621391190439, -0.00047768471871389496, 6.714565954656265e-05]\n",
      "[-0.0023054033517837524, -0.0023526400327682495, -0.002315536141395569, -0.0023523420095443726, -0.0019157826900482178, -0.002081245183944702, -0.002168506383895874, -0.002084195613861084, -0.0016915202140808105, -0.0018250048160552979, -0.001889243721961975, -0.0018278658390045166, -0.0015070289373397827, -0.0015825778245925903, -0.0016016364097595215, -0.0015840232372283936, -0.0013289004564285278, -0.0013535469770431519, -0.0013369321823120117, -0.0013534724712371826, -0.001149877905845642, -0.0011376291513442993, -0.0011002123355865479, -0.0011365413665771484, -0.0009702891111373901, -0.0009348392486572266, -0.0008894652128219604, -0.0009331405162811279, -0.0007928460836410522, -0.0007448345422744751, -0.0007005035877227783, -0.0007428228855133057, -0.0006210207939147949, -0.0005673319101333618, -0.0005288124084472656, -0.0005653798580169678]\n",
      "[0.581 0.581 0.581 0.581]\n",
      "100\n"
     ]
    },
    {
     "data": {
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",
      "text/plain": [
       "<Figure size 640x480 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "x_all = []  # List of all stored states\n",
    "\n",
    "def mpc_tasks():\n",
    "    solver = tinympc.TinyMPC()\n",
    "    solver.setup(n, m, N, A, B, Q, R, x_min, x_max, u_min, u_max, rho, abs_pri_tol, abs_dual_tol, max_iter, check_termination)\n",
    "    solver.load_lib(output_dir + \"/build/tinympc/libtinympcShared\" + os_ext)  # Load the library\n",
    "    \n",
    "    # This function is similar in firmware\n",
    "    def mpc_controller(x):\n",
    "        # input is 13d state vector\n",
    "        q = x[3:7]\n",
    "        phi = qtorp(L(qg).T @ q)\n",
    "        delta_x = np.hstack([x[0:3]-rg, phi, x[7:10]-vg, x[10:13]-omgg]) # 12d state vector\n",
    "        noise = np.random.normal(0, 0.01, (n,))*0\n",
    "        delta_x_noise = (delta_x + noise).reshape(n).tolist()\n",
    "        print(delta_x_noise)\n",
    "\n",
    "        # 1. Set initial state from measurement    \n",
    "        solver.set_x0(delta_x_noise, 0)  # Set initial state to C code\n",
    "\n",
    "        # 2. Set the reference state if needed\n",
    "        # At step 200, set x = 1\n",
    "        # if (i == 200):\n",
    "        #     solver.set_xref(delta_xref_next, 0)  # Set the reference state to C code\n",
    "\n",
    "        # 3. Solve the problem\n",
    "        solver.solve(0)  # Call the solve in C code\n",
    "\n",
    "        # 4. Get the control input\n",
    "        solver.get_u(uhrz, 0)  # Get the control input from C code\n",
    "        print(uhrz)\n",
    "\n",
    "        return np.array(uhrz[0:4]) + u0\n",
    "    \n",
    "    x = 1*x0  # initial state\n",
    "    # x[0:3] = rg + np.random.randn(3)  # initial position\n",
    "    print(x0)\n",
    "    xhrz = [0.0] * n * N  # List of states in horizon\n",
    "    uhrz = [0.0] * m * (N - 1)  # List of control inputs in horizon\n",
    "\n",
    "    print(\"=== START INTERACTIVE MPC ===\")\n",
    "\n",
    "    NSIM = 100\n",
    "    for i in range(NSIM):\n",
    "        # Get the control input\n",
    "        u_current = mpc_controller(x)\n",
    "        print(u_current)\n",
    "        \n",
    "        # Simulate the dynamics\n",
    "        x = quad_dynamics_rk4(x, u_current)\n",
    "\n",
    "        x = x.reshape(n+1).tolist()\n",
    "        x_all.append(x)\n",
    "\n",
    "    print(len(x_all))\n",
    "\n",
    "mpc_tasks()\n",
    "visualize_trajectory(x_all)"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Quadrotor Tracking\n",
    "\n",
    "Quadroter hovering task is done. Let's try trajectory tracking! Remember that the original reference is a 13-state trajectory. Since we linearized about hovering, the correct reference for MPC is a 12-state trajectory, relative to the hovering state. Let's do a figure-8.\n",
    "We don't use input reference for now."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Generate reference trajectory\n",
    "Tfinal = 10.0\n",
    "Nt = int(Tfinal/h)+1\n",
    "Xref = np.array([[1*math.cos(t)*math.sin(t), 1*math.cos(t), 0.5, 1., 0.0, 0.0, 0, 0, 0, 0, 0, 0, 0] for t in np.linspace(-math.pi/2, 3*math.pi/2, Nt)])\n",
    "xref = [np.zeros(n) for i in range(Nt)]\n",
    "\n",
    "for k in range(Nt):\n",
    "    x_ = Xref[k]\n",
    "    q_ = x_[3:7]\n",
    "    phi_ = qtorp(L(qg).T @ q_)\n",
    "    xref[k] = np.hstack([x_[0:3]-rg, phi_, x_[7:10]-vg, x_[10:13]-omgg])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "=== START INTERACTIVE MPC ===\n",
      "491\n"
     ]
    },
    {
     "data": {
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",
      "text/plain": [
       "<Figure size 640x480 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "x_all = []  # List of all stored states\n",
    "\n",
    "def mpc_tasks():\n",
    "    solver = tinympc.TinyMPC()\n",
    "    solver.setup(n, m, N, A, B, Q, R, x_min, x_max, u_min, u_max, rho, abs_pri_tol, abs_dual_tol, max_iter, check_termination)\n",
    "    solver.load_lib(output_dir + \"/build/tinympc/libtinympcShared\" + os_ext)  # Load the library\n",
    "    \n",
    "    # This function is similar in firmware\n",
    "    def mpc_controller(x, xref):\n",
    "        # input is 13d state vector\n",
    "        q = x[3:7]\n",
    "        phi = qtorp(L(qg).T @ q)\n",
    "        delta_x = np.hstack([x[0:3]-rg, phi, x[7:10]-vg, x[10:13]-omgg]) # 12d state vector\n",
    "        noise = np.random.normal(0, 0.01, (n,))*0\n",
    "        delta_x_noise = (delta_x + noise).reshape(n).tolist()\n",
    "\n",
    "        # 1. Set initial state from measurement    \n",
    "        solver.set_x0(delta_x_noise, 0)  # Set initial state to C code\n",
    "\n",
    "        # 2. Set the reference state if needed\n",
    "        xref_ = np.array(xref).reshape(n*N).tolist()  # col-major order list\n",
    "        # print(xref_)\n",
    "        solver.set_xref(xref_, 0)  # Set the reference state to C code\n",
    "\n",
    "        # 3. Solve the problem\n",
    "        solver.solve(0)  # Call the solve in C code\n",
    "\n",
    "        # 4. Get the control input\n",
    "        solver.get_u(uhrz, 0)  # Get the control input from C code\n",
    "\n",
    "        return np.array(uhrz[0:4]) + u0\n",
    "    \n",
    "    x = Xref[0]  # initial state\n",
    "    x[0:3] = Xref[0,0:3] + np.random.randn(3)/10  # initial position\n",
    "    xhrz = [0.0] * n * N  # List of states in horizon\n",
    "    uhrz = [0.0] * m * (N - 1)  # List of control inputs in horizon\n",
    "\n",
    "    print(\"=== START INTERACTIVE MPC ===\")\n",
    "\n",
    "    NSIM = Nt - N\n",
    "    for i in range(NSIM):\n",
    "        # Get the control input\n",
    "        u_current = mpc_controller(x, xref[i:i+N])\n",
    "        \n",
    "        # Simulate the dynamics\n",
    "        x = quad_dynamics_rk4(x, u_current)\n",
    "\n",
    "        x = x.reshape(n+1).tolist()\n",
    "        x_all.append(x)\n",
    "\n",
    "    print(len(x_all))\n",
    "\n",
    "mpc_tasks()\n",
    "visualize_trajectory(x_all)"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The actual trajectory is slower than the reference because we only gave it position trajectory to track (dynamically infeasible), you can also provide velocity trajectory via finite difference from the positions."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# visualize xy trajectory\n",
    "x_all = np.array(x_all)\n",
    "plt.scatter(x_all[0, 0], x_all[0, 1], label=\"xy\", marker=\"o\", linewidth=5)\n",
    "plt.scatter(x_all[-1, 0], x_all[-1, 1], label=\"xy\", marker=\"x\", linewidth=5)\n",
    "plt.plot(x_all[:, 0], x_all[:, 1], label=\"xy\", linewidth=2)\n",
    "plt.plot(Xref[1:Nt - N, 0], Xref[1:Nt - N, 1], label=\"xy\", linewidth=2, linestyle='dashed', color='red')\n",
    "plt.legend([\"start\", \"end\", \"real\", \"ref\"])\n",
    "plt.xlabel(\"x\")\n",
    "plt.ylabel(\"y\")\n",
    "plt.title(\"xy trajectory\")\n",
    "plt.show()"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Deployment"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "OK, everything works well. Let's see how to use the generated code for deployment. We can export the reference to C code for future use."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Export a vector of vectors to C header\n",
    "def export_vec_of_vec_to_c(filename, var_type, var_name, data):\n",
    "    size = len(data)*len(data[0])\n",
    "    declare = var_type + \" \" + var_name + \"[\" + str(size) + \"]\"\n",
    "    def_ = declare + \" = {\\n\"\n",
    "    for i in range(len(data)):\n",
    "        def_ = def_ + \"  \"\n",
    "        for j in range(len(data[0])):\n",
    "            def_ = def_ + str(data[i][j])\n",
    "            if j < len(data[0]) - 1:\n",
    "                def_ = def_ + \",\"\n",
    "        if i < len(data) - 1:\n",
    "            def_ = def_ + \",\\n\"\n",
    "    def_ = def_ + \"};\\n\"\n",
    "\n",
    "    with open(filename + \".hpp\", \"a\") as f:\n",
    "        f.write(def_)\n",
    "\n",
    "export_vec_of_vec_to_c(\"ref_fig8\", \"tinytype\", \"Xref_data\", xref)"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Post testing the MPC procedure with the generated code, the next step involves deploying it for your specific applications/systems.\n",
    "The workflow for deployment is tailored to your specific needs, and we aim to provide clear guidance.\n",
    "\n",
    "Your `tiny_main` may look like this\n",
    "\n",
    "```C\n",
    "#include \"ref_fig8.hpp\"\n",
    "\n",
    "int main()\n",
    "{\n",
    "    int exitflag = 1;\n",
    "    TinyWorkspace* work = tiny_data_solver.work;\n",
    "    tiny_data_solver.work->Xref = tiny_MatrixNxNh::Zero();\n",
    "    tiny_data_solver.work->Uref = tiny_MatrixNuNhm1::Zero();\n",
    "    tiny_data_solver.settings->max_iter = 150;\n",
    "    tiny_data_solver.settings->en_input_bound = 1;\n",
    "    tiny_data_solver.settings->en_state_bound = 1;\n",
    "\n",
    "    // Map data from trajectory_data\n",
    "    Matrix<tinytype, NSTATES, NTOTAL> Xref_total = Eigen::Map<Matrix<tinytype, NSTATES, NTOTAL>>(Xref_data);\n",
    "    work.Xref = Xref_total.block<NSTATES, NHORIZON>(0, 0);\n",
    "\n",
    "    tiny_VectorNx x0, x1; // current and next simulation states\n",
    "    x0 = work.Xref.col(0);  // Initial state\n",
    "\n",
    "    int i = 0;\n",
    "    for (int k = 0; k < 300; ++k)\n",
    "    {\n",
    "        printf(\"tracking error at step %2d: %.4f\\n\", k, (x0 - work->Xref.col(1)).norm());\n",
    "\n",
    "        // 1. Update measurement (use your API to get measurement)\n",
    "        work->x.col(0) = x0;\n",
    "\n",
    "        // 2. Update reference (if needed)\n",
    "        work.Xref = Xref_total.block<NSTATES, NHORIZON>(0, k);\n",
    "\n",
    "        // 3. Reset dual variables (if needed)\n",
    "        // work->y = tiny_MatrixNuNhm1::Zero();\n",
    "        // work->g = tiny_MatrixNxNh::Zero();\n",
    "\n",
    "        // 4. Solve MPC problem\n",
    "        exitflag = tiny_solve(&tiny_data_solver);\n",
    "\n",
    "        // if (exitflag == 0)\n",
    "        // \tprintf(\"HOORAY! Solved with no error!\\n\");\n",
    "        // else\n",
    "        // \tprintf(\"OOPS! Something went wrong!\\n\");\n",
    "        // \t// break;\n",
    "\n",
    "        std::cout << work->iter << std::endl;\n",
    "        std::cout << work->u.col(0).transpose().format(CleanFmt) << std::endl;\n",
    "\n",
    "        // 5. Simulate forward/or use API to send control signal to your real system\n",
    "        // work->u.col(0) = -tiny_data_solver.cache->Kinf * (x0 - work->Xref.col(0));  // if use LQR only\n",
    "        x1 = work->Adyn * x0 + work->Bdyn * work->u.col(0);\n",
    "        x0 = x1;\n",
    "        // std::cout << x0.transpose().format(CleanFmt) << std::endl;\n",
    "    }\n",
    "}\n",
    "```"
   ]
  }
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