CarND-Controls-MPC

Self-Driving Car Engineer Nanodegree Program

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Compile

This project could be compile build and run well on Linux(ubuntu) by following instructions provided.

The Model

(If MathJax is not supported, please read PDF version to see these equations clearly). For the car with a state vector S = $(x, y, \psi, v)$. The kinematic model can be expressed as following equations:

$$ x_t = x_{t-1} + v_{t-1} * \cos(\psi_{t-1}) * dt $$

$$ y_t = y_{t-1} + v_{t-1} * \sin(\psi_{t-1}) * dt $$

$$\psi_t = \psi_{t-1} + \frac{v_{t-1}}{L_f} * \delta * dt$$

$$v_t = v_{t-1} + a_{t-1} * dt$$

where $(x, y)$ is the coordinate of the car, $\psi$ is the heading angle, and $v$ is the velocity. $a$ is the throttle acceleration and $\delta$ is the steering angle that need to be calculated to optimize.

The cross-trace error and orientation error update could be expressed below:

$$cte_t = cte_{t-1} + v_t * sin(e\psi_{t-1}) * dt$$

$$e\psi_t = e\psi_{t-1} + \frac{v_{t-1}}{L_f} * \delta * dt$$

Line 103 - 109 in MPC.cpp reflects the model update in the code.

Timestep Length and Elapsed Duration

Time horizon T = N * dt here N is 10 and dt is 0.1. Other combinations have been tried were proven that easy to cause the car behavior wierd. A length of 100ms time step is also consistent with latency. We need a small dt to provide a good resolution in calculation regards of accuracy, large values of dt will cause discretization error. However if the dt is too small, the computational time would be large and it might cause asynchronous error. 1 sec for the Time horizon looks good considering about the car's speed - environment change beyond it doesnot make the prediction any sense.

Polynomial Fitting and MPC Preprocessing

From line 99 - 120 in main.cpp, I preprocessed waypoints to vehicle's cordinate system also with state vector, then used the provide utils to fitting the polynomial.

Model Predictive Control with Latency

Since the timestep and latency is consistent, which is 100ms, we are able to use previous step's actuations to apply to current step. In the init state it takes the original actuations, after that it will takes previous step.(MPC.cpp : Line 96-97)

Simulation

Simulation looks well, car can run and run over laps within the track.

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Dependencies

• cmake >= 3.5

• All OSes: click here for installation instructions

• make >= 4.1(mac, linux), 3.81(Windows)

  • Linux: make is installed by default on most Linux distros
  • Mac: install Xcode command line tools to get make
  • Windows: Click here for installation instructions

• gcc/g++ >= 5.4

  • Linux: gcc / g++ is installed by default on most Linux distros
  • Mac: same deal as make - [install Xcode command line tools]((https://developer.apple.com/xcode/features/)
  • Windows: recommend using MinGW

• uWebSockets

  • Run either install-mac.sh or install-ubuntu.sh.
  • If you install from source, checkout to commit e94b6e1, i.e.

    git clone https://github.com/uWebSockets/uWebSockets
    cd uWebSockets
    git checkout e94b6e1
    

    Some function signatures have changed in v0.14.x. See this PR for more details.

• Ipopt and CppAD: Please refer to this document for installation instructions.

• Eigen. This is already part of the repo so you shouldn't have to worry about it.

• Simulator. You can download these from the releases tab.

• Not a dependency but read the DATA.md for a description of the data sent back from the simulator.

Basic Build Instructions

1. Clone this repo.
2. Make a build directory: mkdir build && cd build
3. Compile: cmake .. && make
4. Run it: ./mpc.

Tips

1. It's recommended to test the MPC on basic examples to see if your implementation behaves as desired. One possible example is the vehicle starting offset of a straight line (reference). If the MPC implementation is correct, after some number of timesteps (not too many) it should find and track the reference line.
2. The lake_track_waypoints.csv file has the waypoints of the lake track. You could use this to fit polynomials and points and see of how well your model tracks curve. NOTE: This file might be not completely in sync with the simulator so your solution should NOT depend on it.
3. For visualization this C++ matplotlib wrapper could be helpful.)
4. Tips for setting up your environment are available here
5. VM Latency: Some students have reported differences in behavior using VM's ostensibly a result of latency. Please let us know if issues arise as a result of a VM environment.

Editor Settings

We've purposefully kept editor configuration files out of this repo in order to keep it as simple and environment agnostic as possible. However, we recommend using the following settings:

• indent using spaces
• set tab width to 2 spaces (keeps the matrices in source code aligned)

Code Style

Please (do your best to) stick to Google's C++ style guide.

Project Instructions and Rubric

Note: regardless of the changes you make, your project must be buildable using cmake and make!

More information is only accessible by people who are already enrolled in Term 2 of CarND. If you are enrolled, see the project page for instructions and the project rubric.

Hints!

• You don't have to follow this directory structure, but if you do, your work will span all of the .cpp files here. Keep an eye out for TODOs.

Call for IDE Profiles Pull Requests

Help your fellow students!

We decided to create Makefiles with cmake to keep this project as platform agnostic as possible. Similarly, we omitted IDE profiles in order to we ensure that students don't feel pressured to use one IDE or another.

However! I'd love to help people get up and running with their IDEs of choice. If you've created a profile for an IDE that you think other students would appreciate, we'd love to have you add the requisite profile files and instructions to ide_profiles/. For example if you wanted to add a VS Code profile, you'd add:

• /ide_profiles/vscode/.vscode
• /ide_profiles/vscode/README.md

The README should explain what the profile does, how to take advantage of it, and how to install it.

Frankly, I've never been involved in a project with multiple IDE profiles before. I believe the best way to handle this would be to keep them out of the repo root to avoid clutter. My expectation is that most profiles will include instructions to copy files to a new location to get picked up by the IDE, but that's just a guess.

One last note here: regardless of the IDE used, every submitted project must still be compilable with cmake and make./

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