Self-Driving Car Engineer Nanodegree Program

Project objective is to develop Model Predictive Controller which help steer a car effectively on target trajectory in a simulator. The simulator provides stream of values for the car containing the position, speed, heading direction & waypoints (reference trajectory, in Global Coordinate System).

This was complex project to understand, I had to take help from many forum artciles, too many people to thank to get over hurdles during project.

The vehicle model used in this project is a kinematic bicycle model. It does not take into account inertia, friction and torque. The model is non-linear as it accounts for changes in heading direction. The model is centred around following key parameters:

• x,y denote the 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 gravity of the vehicle and the front wheels

• Mathematical computations are performed in the vehicle coordinate system. Waypoints which are in Global Coordinate System are transfomed in vehicle coordinates, further a third order polynomial is then fitted to the waypoints.
• For every state value, Trajectory for N time steps is re-computed which mimimize cost function.
• Cost Function: Main objective - to minimize our cross track, heading, and velocity errors. A further enhancement is to constrain erratic control inputs. For example, if we're making a turn, we'd like the turn to be smooth, not sharp. Additionally, the vehicle velocity should not change too radically. This can be achieved by Minimizing change-rate & Minimizing the value gap between sequential actuations.
• To cover variable speed, I took help from forums to further improvise, by playing with Cost Minimization functions, I was able to achieve decent results.
• T - Perdiction Horizon is the duration over which the future predictions are made. T is product of N times dt, where N is the number of time steps and dt is the how much time elapse between actuations. There are some general guidelines. T should be as large as possible, while dt should be as small as possible, hence create trade-offs. Short prediction horizons lead to more responsive controlers, but are less accurate. Larger values of dt result in less frequent actuations, which makes it harder to accurately approximate a continuous reference trajectory. This is sometimes called "discretization error". A good approach to setting N, dt, and T is to first determine a reasonable range for T and then tune dt and N appropriately, keeping the effect of each in mind. After trial and error, N=12 and dt=0.05 gave desired results.

An additional complication of this project consists in taking delayed actuations into account. A delay of 100ms is introduced before the actuations are sent back to the simulator. Delays could lead to erractic behavior of the car and car may possibly go off the target trajectory.

In contrast to PID, MPC can factor Delay/Latency in pipeline by constraining the controls to the values of the previous iteration for the duration of the latency. Thus the optimal trajectory is computed starting from the time after the latency period.

https://youtu.be/jMRdCmgn0K4

• 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./