CarND-Controls-MPC

Self-Driving Car Engineer Nanodegree Program

The Vehicle Model

The vehicle model used in this project is a kinematic bicycle model. It neglects all dynamical effects such as inertia, friction and torque. the following equations ared used in the model

x,y : position of the car psi : the heading direction v : its velocity cte : the cross-track error epsi : the orientation error. Lf : is the distance between the center of mass of the vehicle and the front wheels and affects the maneuverability.

  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

Timestep Length and Elapsed Duration (N & dt)

The time T=N dt defines the prediction horizon. Short prediction horizons lead to more responsive controlers, but are less accurate and can suffer from instabilities when chosen too short. Long prediction horizons generally lead to smoother controls. For a given prediction horizon shorter time steps dt imply more accurate controls but also require a larger NMPC problem to be solved, thus increasing latency.

N : 15 , dt : 0.05. I choose 0.05 as dt because I would like to have more responsive controller. I found that N > 15 may make my car flips over when the speed is >50.

Polynomial Fitting and MPC Preprocessing

All computations are performed in the vehicle coordinate system. The coordinates of waypoints in vehicle coordinates are obtained by first shifting the origin to the current poistion of the vehicle and a subsequet 2D rotation to align the x-axis with the heading direction. Therby the waypoints are obtained in the frame of the vehicle. A third order polynomial is then fitted to the waypoints. The transformation between coordinate systems is implemented as below functions double x = xvals[i]-px; double y = yvals[i]-py; xvals[i] = x * cos(0-psi) - y * sin(0-psi); yvals[i] = x * sin(0-psi) + y * cos(0-psi); Note that the initial position of the car and heading direction are always zero in this frame. Thus the state of the car in the vehicle cordinate system is

      state << 0, 0, 0, v, cte, epsi;

Model Predictive Control with Latency

An additional complication of this project consists in taking delayed actuations into account. After the solution of the NMPC problem a delay of 100ms is introduced before the actuations are sent back to the simulator. I still keep the delay of 100ms, but the controller would be more responsive if I make the delay as 50ms. however, the car will tend to drive out of lane if I use 200ms as the delay. more delay may introduce bigger steering angle and make the car drive out of lane in the end.

I predict the state of the vehicle 100 ms in the future before passing the state vector to the solver. the implementation is from line 166 - 177 in main.cpp.

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

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

Tips

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.
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.
For visualization this C++ matplotlib wrapper could be helpful.)
Tips for setting up your environment are available here
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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louietsai / CarND-MPC-Project