CarND-Controls-MPC

Self-Driving Car Engineer Nanodegree Program

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Project Description

The vehicle model used by this project is a non-linear kinamatic bicycle model. It does not take into consideration dynamic factor such inertia, drag etc. The vehicle state is represented by its position (px, py), heading direction psi, its speed v, its cross track error cte, and heading angle differential epsi. The actuation is represented by steering angle delta and throttle a.

The following equation is used to update the vehicle state from timestep t to t+1:

      x(t+1) = x(t) + v(t) * cos(psi(t)) * dt;
      y(t+1) = y(t) + v(t) * sin(psi(t)) * dt);
      psi(t+1) = psi(t) + v(t) * delta(t) / Lf * dt;
      v(t+1) = v(t) + a(t) * dt;
      cte(t+1) = f(t) - y(t) + v(t) * sin(epsi(t)) * dt;
      epsi(t+1) = psi(t) - psides(t) + v(t) * delta(t) / Lf * dt;

where dt is the time step, Lf is obtained by measuring the radius formed by running the vehicle in the simulator around in a circle with a constant steering angle and velocity on a flat terrain. f(t) is x(t) calculated to the fitted polynomial, psides(t) is the heading differential based on the fitted polynomial.

Polynomial Fitting

The waypoints which describes the tracks in front of the vehicle is first transformed from map coordinates to the vehicle coordinates via the following code in main.cpp:

          // transform waypoints to car local coord
          int size = ptsx.size();
          Eigen::VectorXd ptsx_car = Eigen::VectorXd(size);
          Eigen::VectorXd ptsy_car = Eigen::VectorXd(size);
          for(int i=0; i < size; i++) {
            ptsx_car[i] = (ptsx[i] - px) * cos(-psi) - (ptsy[i] - py) * sin(-psi);
            ptsy_car[i] = (ptsx[i] - px) * sin(-psi) + (ptsy[i] - py) * cos(-psi);
          }

The waypoints (the yellow line) is then fitted to a polynomial to the third order. The coefficients of the polynomial is passed to FG_eval to set up cost function and constraints. These were then used to an ipopt solver to give us the solution on actuation (steering and throttle) and predicted vehicle positions ahead. These predicted positions (px, py) are passed back to the car simulator for visual display (the green line).

N * dt dictates how far ahead does the model look in order to make prediction on steering angle and throttle calculations. Given that we need to account for 100ms of actuation latency, the value of dt probably should be close to 0.1. And looking ahead 15 to 20 steps seem to provide reasonable result in testing.

Latency in actuation is accounted for by predicting the vehicle state ahead by 0.1s (100ms) before feeding it to the solver. Latency related code is in the function: MPC::GetState()

Screenshots of MPC in action:

Dependencies

• cmake >= 3.5
• All OSes: click here for installation instructions
• make >= 4.1
  • 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.
• Fortran Compiler
  • Mac: brew install gcc (might not be required)
  • Linux: sudo apt-get install gfortran. Additionall you have also have to install gcc and g++, sudo apt-get install gcc g++. Look in this Dockerfile for more info.
• Ipopt
  • Mac: brew install ipopt
    • Some Mac users have experienced the following error:

    Listening to port 4567
    Connected!!!
    mpc(4561,0x7ffff1eed3c0) malloc: *** error for object 0x7f911e007600: incorrect checksum for freed object
    - object was probably modified after being freed.
    *** set a breakpoint in malloc_error_break to debug
    

    This error has been resolved by updrading ipopt with brew upgrade ipopt --with-openblas per this forum post.
  • Linux
    • You will need a version of Ipopt 3.12.1 or higher. The version available through apt-get is 3.11.x. If you can get that version to work great but if not there's a script install_ipopt.sh that will install Ipopt. You just need to download the source from the Ipopt releases page or the Github releases page.
    • Then call install_ipopt.sh with the source directory as the first argument, ex: sudo bash install_ipopt.sh Ipopt-3.12.1.
  • Windows: TODO. If you can use the Linux subsystem and follow the Linux instructions.
• CppAD
  • Mac: brew install cppad
  • Linux sudo apt-get install cppad or equivalent.
  • Windows: TODO. If you can use the Linux subsystem and follow the Linux 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.

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./