/CarND-Model-Predictive-Control-Project-P10

Primary LanguageC++MIT LicenseMIT

CarND-Controls-MPC

Self-Driving Car Engineer Nanodegree Program

Implementation

1. The Model

There are six states contained in the model: State [x,y,ψ,v,cte,eψ]

  • x: vehicle's x position
  • y: vehicle's y position
  • ψ: vehicle's orientation angle
  • v: vehicle's velocity
  • cte: cross-track error
  • eψ: orientation angle error (epsi)

There are two actuators used for the vehicle control: Actuator [δ, a]

  • δ: steering angle
  • a: throttle/acceleration

The following update equation was used to model the vehicle dynamics: model update equation

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

Define N and dt:

MPC attempts to approximate a continuous reference trajectory by means of discrete paths between actuations.

  • N: number of timesteps the model predicts / number of variables optimized by the MPC
  • dt: time period between each timestep. Larger values of dt result in less frequent actuations, which makes it harder to accurately approximate a continuous reference trajectory.

N&dt tuning:

Started with (N, dt) = (10, 0.5). The vehicle was too slow to react on turning. It leads the vehicle off the track.

Decreasing dt to 0.2. Shorter time period leaded to quicker react. It became better on turning.

Decreasing dt to 0.1. Much better on following the track.

Noticed the end predicted path will reach the edge of road when the vehicle was on turning. Try to increase the number of timesteps to make a longer 3rd-order polynomial fitting. N = 15. Vehicle keeps moving closely along the centre of the lane. At last, I choose N=15, dt = 0.1.

However, it was noticed that the turning speed on N=15 was slower then the one on N=10. So, there is no doubt that further improvements can be made with parameter tuning.

3. Polynomial Fitting and MPC Preprocessing

A 3rd order polynomial is fitted to waypoints. Before the polynomial fitting, in order to simplify the calculation, we made a coordinate transform to vehicle's coordinate.

Then the calculated polynomial coeffs were used for calculating cte and epsi.

4. Model Predictive Control with Latency

The latency is the delay between the control and the real situation. The faster the vehicle is moving, the worse the influence from latency. Considering latency into the model can help minimise the influence. Given the provided experience the vehicle control latency is around 100ms. We use vehicle kinematic model to calculate/predict the state 100ms ahead, and then feed the predicted stats into MPC solver.

The predicted stated is calculated as follows:

// Initial states.
const double x0 = 0;
const double y0 = 0;
const double psi0 = 0;
const double cte0 = coeffs[0];
const double epsi0 = -atan(coeffs[1]);

// Predicted states with Latency taken into account.
double x_delay = x0 + ( v * cos(psi0) * delay );
double y_delay = y0 + ( v * sin(psi0) * delay );
double psi_delay = psi0 - ( v * delta * delay / mpc.Lf );
double v_delay = v + a * delay;
double cte_delay = cte0 + ( v * sin(epsi0) * delay );
double epsi_delay = epsi0 - ( v * atan(coeffs[1]) * delay / mpc.Lf );

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./

How to write a README

A well written README file can enhance your project and portfolio. Develop your abilities to create professional README files by completing this free course.

Error

When install ipopt on Mac:

make[2]: dynamiclib: No such file or directory
make[2]: [libpord.dylib] Error 1 (ignored)
echo libpord.dylib
libpord.dylib
if [ "./PORD/lib/" != "" ] ; then \
	  cp ./PORD/lib//libpord.dylib lib/libpord.dylib; \
	fi;
cp: ./PORD/lib//libpord.dylib: No such file or directory
make[1]: *** [lib/libpord.dylib] Error 1
make: *** [c] Error 2

Solution:

udacity/CarND-MPC-Project#22