CarND-Controls-MPC

Model Predictive Control is an optimization problem. Our objective is to minimize the cost function subject to certain constraints. In this project our high level objective is that the self driving car should complete the lap in finite time and in a safe manner. These requirements drive our cost function to penalize following behavior of the car:

• Drifiting away from the center of the lane (cross track error).
• Having an undesired orientation (error in heading).
• Stopping in between the lap.
• Maximum use of actuators (steer and throttle).
• Extreme changes in actuator values.

The cost function defined above is subject to the following constraints:

• Car should follow laws of physics i.e. Kinematic equations of motion.
  • px = px + v * cos(psi) * dt
  • py = py + v * sin(psi) * dt
  • psi = psi + v * delta * dt / Lf
  • cte = f(x) - y position of the car
  • epsi = psi - atan(f'(x))
• Steering value is always between [-25 deg, +25 deg].
• Throttle is always between [-1, +1].
• The state variables can take any real value between the min, max values stored by a double data type.

Other important thing to address is the handling of latency between generating actuator commands and actually implementing those commands. Any real vehicle would be impacted by latency. The way I handled latency was I updated the px, py position of the car given by the simulator using the same kinematic equations but replacing the time step with latency before solving the cost function for control inputs. I am assuming that the orientation of the car would remain the same during the latency period.

• px = px + v * cos(psi) * latency
• py = py + v * sin(psi) * latency

Tuning:

• N = 10 and dt = 0.11.
• Before chosing the above values I tried N = 25 and dt = 0.05. But then I realized that we had latency and dt>=latency. Also larger values of N with small dt values were slowing down the computations.
• With large dt greater than latency and large N the model predictions would get inaccurate.

Further Improvements:

• Implementing a fast way to compute the shortest distance from car's position to the polynomial fit to the way points.
• Implementing a better vehicle model.
• Accounting for "traffic" in the cost function.

Video: https://youtu.be/4X451IdAby4

Dependencies

• 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.

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./