Self-Driving Car Engineer Nanodegree Program

MPC is an advanced control method that rely on a dynamic model of the process to control, that unlike PID control, has the advantage of being capable to predict or anticipate future events, and take actions accordingly. MPC uses a cost function to calculate the optimum control moves.

The MPC consist in the following:

• The vehicle model: which consists in the set of equations that describe the movement of the vehicle. This equations take the following parameters: -- x, y coordinates, that are captured referenced to the map, and are converted to be referenced to the vehicle by using rotation and translation techniques. -- Orientation psi -- Velocity v -- Cross-track error CTE, that is obtained by using the polynomial fit obtain from the current trajectory points of the vehicle in the simulator. -- Orientation error epsi, also obtained from the polynomial fit.
• Actuator constraints. The consists in the limits of the values of the model that control the movement of the vehicle. In this project, steering angle (with a range of [-25, 25]) and acceleration (between [-1,1]) are used.
• Trajectory constraints. Consists on the number of steps N to be executed in a time dt.

For each iteration of the process, the program receives information about the state of the car in coordinates referenced to the map in the simulator, that are later converted to vehicle referenced coordinates.

Then, a polynomial is obtained from the current trajectory points returned from the simulator. This polynomial is useful to calculate CTE and epsi. Later, the parameters are feed into the model, that returns the actuators response that determine the optimum moves for the vehicle, and a set of points that predict the future trajectory.

At first, I tried N = 50 and dt = 10. In this case, the vehicle model didn't show too much movement, even generating a future trajectory backwards!

Then, I tries N = 20 and dt = 1. This mde the vehicle to go very slowly (even when the reference velocity was set to 70). The vehicle completely stopped before the first curve.

I chose for the final parameters N = 10 and dt = 0.1. This enabled the vehicle to complete a lap at 70 MPH. To do this, was also required to assign weights to the costs of the CTE, EPSI and the actuators.

static const double CTE_COST_WEIGHT                 = 20000;
static const double EPSI_COST_WEIGHT                = 20000;
static const double SPEED_COST_WEIGHT               = 100;
static const double ACTUATOR_COST_WEIGHT            = 1;
static const double STEER_CHANGE_COST_WEIGHT        = 200;
static const double ACCELERATION_CHANGE_COST_WEIGHT = 200;

As described before, the waypoints obtained from the simulator are preprocessed so they are in the vehicle reference system, instead of the global map reference. This is done by rotating and translating the point, as described here.

The equations of the model has been altered so they take in account the latency, given that the actuators actions are going to happen after 100 ms.

const double speedFactor = v *  - delta / LF_VALUE * LATENCY_SECONDS;
const double predX       = 0.0  + v * LATENCY_SECONDS;
const double predY       = 0.0;
const double predPsi     = 0.0  + speedFactor;
const double predV       = v    + a * LATENCY_SECONDS;
const double predCte     = cte  + v * sin(epsi) * LATENCY_SECONDS;
const double predEpsi    = epsi + speedFactor;

A video of the final run can be found here:

• 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
  • 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: 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.

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

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.

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)

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

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.

• 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.

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./