/CarND-MPC-Project

Implementation of MCP (Model-Predictive-Control ) in C++ to race around the lake track.

Primary LanguageC++

CarND-Controls-MPC

Self-Driving Car Engineer Nanodegree Program

A Model Predictive controller are generally intended to represent the behavior of complex dynamical systems. In this case it was generated to be able to control a car for Udacity simulator. The Number of steps = 10 and the time step is 0.1 (100 milliseconds) this means that MCP was planning 1 second into the future. With this configuration, I got 90 MPH as max speed. Using 1.5 seconds or higher planning time I got almost the 100MPH but it crashes in some points. And a lower planning time (for instance 0.5 seconds), it didn’t performed well predictions even in straight. For the 0.1 as time step duration it got me a good result (not too spare neither too short). That is why I elected those values. For the polynomial equations was shifted to (0,0) and its heading direction was rotated to zero degrees, in other words the fitter polynomial was in most of the cases horizontal where if it was vertical it would return higher coefficient values.
This is the result of the implementation:

  • IMAGE ALT TEXT HERE

The yellow line is being drawn in the simulator represent the fitted polynomial line between the waypoints (it is the reference path). The green line shows each of the connected steps from the MPC output.

  • State values:
  • X ,y , psi, v , cte, epsi *Actuators
  • Delta, a
  • Update equation
fg[1 + x_start + t] = x1 - (x0 + v0 * CppAD::cos(psi0) * dt);
fg[1 + y_start + t] = y1 - (y0 + v0 * CppAD::sin(psi0) * dt);
fg[1 + psi_start + t] = psi1 - (psi0 - v0 * delta0 / Lf * dt);
fg[1 + v_start + t] = v1 - (v0 + a0 * dt);
fg[1 + cte_start + t] = cte1 - ((f0 - y0) + (v0 * CppAD::sin(epsi0) * dt));
fg[1 + epsi_start + t] = epsi1 - ((psi0 - psides0) - v0 * delta0 / Lf * dt);
  • The cost function:the constants where were manually tuned like the number of steps and the duration of each step.
/ ------------Cost function----------------------
	// The part of the cost based on the reference state.
    for (int t = 0; t < N; t++) {
      fg[0] += 1500*CppAD::pow(vars[cte_start + t] - ref_cte, 2);
      fg[0] += 1500*CppAD::pow(vars[epsi_start + t] - ref_epsi, 2);
      fg[0] += CppAD::pow(vars[v_start + t] - ref_v, 2);
	}
	// Minimize the use of actuators.
	for (int t = 0; t < N - 1; t++) {
      fg[0] += 10*CppAD::pow(vars[delta_start + t], 2);
      fg[0] += 10*CppAD::pow(vars[a_start + t], 2);
    }
	// Minimize the value gap between sequential actuations.
    for (int t = 0; t < N - 2; t++) {
      fg[0] += 250*CppAD::pow(vars[delta_start + t + 1] - vars[delta_start + t], 2);
      fg[0] += 10*CppAD::pow(vars[a_start + t + 1] - vars[a_start + t], 2);
  • These are the equations to estimate the measuarements to get a low latency..
  double delay_t = .1;
  const double Lf = 2.67;

  //factor in delay
  double delay_x = v*delay_t;
  double delay_y = 0;
  double delay_psi = -v*steer_value / Lf * delay_t;
  double delay_v = v + throttle_value*delay_t;
  double delay_cte = cte + v*sin(epsi)*delay_t;
  double delay_epsi = epsi-v*steer_value /Lf * delay_t;
  
  Eigen::VectorXd state(6);
  state << delay_x, delay_y, delay_psi, delay_v, delay_cte, delay_epsi;

When the angle of the car is 0 (it was centered), then the calculations against 0 are: sin(0) = 0 and cos(0) = 1. This means that the delay_x = vdelay_tCos(0) is equal to v * delay_t, the delay_y = v * delay_tsin(0) is equal 0 (for all this I used the update equation as base). For delay_v, it is only a vague idea about it, because the throttle is not equal to acceleration and the factor for MPH is diferent than m/s^2 (v + throttle_valuedelay_t ) . For the For delay_psi, delay_v , delay_cte and delay_epsi; they are using the same logic for the mcp update equation. For instance:

  • fg[1 + psi_start + t] = psi1 - (psi0 - v0 * delta0 / Lf * dt);
  • delay_psi = -v*steer_value / Lf * delay_t;

Dependencies

  • cmake >= 3.5
  • All OSes: click here for installation instructions
  • make >= 4.1
  • gcc/g++ >= 5.4
  • 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.

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./