CarND-Controls-MPC

Self-Driving Car Engineer Nanodegree Program

Model

I implemented a cost function that took into account crosstrack error, orientation error, velocity error, steering error, throttle error, sequential steering error, and sequential throttle error. Of these I weighted the value gap between sequential actuations the most heavily, and also manually tuned the rest of the cost function to penalize use of actuators and cross track error. My model takes a series of waypoints in world space, transforms them to vehicle space, and then uses them to fit a third order polynomial, to the predicted path. This is then used to calculate the crosstrack error and orientation error of the vehicle and these state variables are passed to the solver to convert the polynomial into predicted actuations for the vehicle.

Timestep Length and Elapsed Duration

For the timestep I wanted the vehicle to be able to predict between 1 to 1.5 seconds into the future. The value T of the overall time horizon is calculated by the product N * dt or the number of timesteps times the duration of each timestep. I began by setting the timestep to 100 milliseconds to match the estimated latency of the vehicle and set the number of timesteps N to 15. These values worked ok, but ultimately the vehicle wasn't responsive enough and was too slow to react with such a large dt. I tried going to the opposite extreme and setting N=150 and dt=0.01 but this fine a timestep made the vehicle too quick to respond and it would often end up going off the road because it was constantly updating and trying to correct the vehicle towards the waypoints. Eventually I settled right in the middle with N=25 and dt=0.05 and this seemed to give the best responsiveness without being over reactive.

Polynomial Fitting

In order to fit a polynomial to the waypoints, I converted the points from world space to vehicle space. This can be seen in main.cpp lines 101-108.

Model Predictive Control with Latency

In order to control for latency I preprocessed the state of the vehicle to predict the state 100 milliseconds into the future and then pass this predicted state to the MPC solver. This produced actuations that corresponded with the next predicted state and allowed the car to drive at higher speeds while remaining fairly close to the reference waypoints. With this approach I was able to get the car to drive safely around the track at up to 60mph. Higher speeds are possible, but would probably require having a better dynamics model and further tuning the cost function to control the use of actuators and maintain the best possible crosstrack error.

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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 == 0.14, but the master branch will probably work just fine
  • Follow the instructions in the uWebSockets README to get setup for your platform. You can download the zip of the appropriate version from the releases page. Here's a link to the v0.14 zip.
  • If you have MacOS and have Homebrew installed you can just run the ./install-mac.sh script to install this.
• Ipopt
  • Mac: brew install ipopt --with-openblas
  • 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.

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./