/CarND-MPC-Project

CarND Term 2 Model Predictive Control (MPC) Project

Primary LanguageC++MIT LicenseMIT

CarND-Controls-MPC

Self-Driving Car Engineer Nanodegree Program

Objective

The main objective of this project is to implement a model predictive controller (MPC) to drive a vehicle around the track.

In the simulator, the reference trajectory is show as a YELLOW line and the predicted path is in GREEN.

1. The Vehicle Model

We constructing the kinematic model of the vehicle where we neglect all dynamical effects such as inertia, friction and torque. Vehicle model is given by the following equation:

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

where, x ,y are position of the vehicle in global co-ordinate system psi is heading direction of the vehicle v velocity cte cross track error epsi orientation error

2. Timestep Length and Elapsed Duration (N & dt)

The product of the timestep length N and elapsed duration dt is called as Prediction Horizon T. The number of timesteps in the horizon is denoted by timestep length and time elapses between each actuation is denoted by Elapsed Duration.

The value of N and dt will greatly affect the performance of my system.

  • In case of large number of way points(N), Contoller tends to estimate N successive way points for each step. This will slow down my overall process.
  • I think calculating the vehicle position between 50 to 500 milliseconds is resonable.

I have tried the following combinations of N and dt.

N dt
20 0.1
15 0.1
10 0.1
10 0.2
10 0.05

From the above experimentation, N as 10 and dt as 0.1 works well.

3. Polynomial Fitting and MPC Preprocessing

The waypoints provided by the simulator are transformed to the car coordinate system in main.cpp file.

// Create a vectorxD space for way_points 
          Eigen::VectorXd waypoints_x(ptsx.size());
          Eigen::VectorXd waypoints_y(ptsy.size());
          
          // Transform the points to the vehicle's orientation
          for (int i = 0; i < ptsx.size(); i++) {
            double x = ptsx[i] - px;
            double y = ptsy[i] - py;
            waypoints_x[i] = x * cos(-psi) - y * sin(-psi);
            waypoints_y[i] = x * sin(-psi) + y * cos(-psi);
          }

The a third order polynomial is fitted to the transformed waypoints. The coefficients of the above polynomial is used to calculate the cte and epsi which is used in solver function as well.

4. Model Predictive Control with Latency

We calculate the future position of the car by 100 millisecond, assuming there were no changes in the velocity or in the steer angle. We ,then , send the future position of the car as the initial state to componsate for the 100ms latency.

Dependencies

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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