aaronleesmith / CarND-MPC-Project

CarND Term 2 Model Predictive Control (MPC) Project

CarND-Controls-MPC

Self-Driving Car Engineer Nanodegree Program

---

Student responses and implementation details.

The model

Student describes their model in detail. This includes the state, actuators and update equations.

The model is based on 6 variables:

• x
• y
• velocity
• orientation
• cross-track error
• orientation error

And there are two actuators:

• delta: the steering angle actuator.
• alpha: the acceleration actuator.

The model take the car's current velocity, x, y, and orientation and implements model predictive control.

At a high level, it converts the waypoint and vehicle positions into the car's coordinate system, then calculates the error between the car's location and the waypoints. This error is then used to fit a third order polynomial.

These coefficients are evaluated in order to calculate a scalar cross-track error (how far the car is off the best line) and an orientation error.

This information is fed into a non-linear problem solver with certain contraints.

The constraints I have tweaked are:

• The model considers the cte * 2 as part of the cost. This means the car will try and get back to the line a bit more when cost is considered.
• The steering angle is heavily weighted in the cost function (250x). Basically we want to discourage very strong turn angles, which tend to throw the car into a wobbly state and then off the road.

The other constraints are basic and can be found in the code.

Timestep Length and Elapsed Duration (N & dt)

Student discusses the reasoning behind the chosen N (timestep length) and dt (elapsed duration between timesteps) values. Additionally the student details the previous values tried.

I chose N = 15 and dt = 0.05. There is a tradeoff between the number of points to look ahead and the time between deach point. If dt is too large, the car could make rapid changes as new inputs come in. If N is too large (and dt is not very small) the polynomial fitting the waypoint path most likely will not be representative of the path the car should follow in the immediate future.

I tried values of N=20 and dt=.1, but found it was looking too far ahead and causing errors in the polynomial fit.

Polynomial Fitting and MPC Preprocessing

A polynomial is fitted to waypoints. If the student preprocesses waypoints, the vehicle state, and/or actuators prior to the MPC procedure it is described.

The only processing I do to the waypoints is convert them into coordiantes in the car's local coordinate space. This is done using a simple transformation matrix.

Model Predictive Control with Latency

The student implements Model Predictive Control that handles a 100 millisecond latency. Student provides details on how they deal with latency.

There are two ways I deal with the latency problem.

1. I project out where the car's expected x and y will be at latency seconds forward. This is a very rough estimation, and it is done by multiplying the car's x and y coordinates by the velocity times latency in the car's coordinate space.

2. I take an average of the next two actuator commands generated by the MPC solver instead of using the first one only. This has an effect of smoothing the actuator commands and potentially reducing jitter that might be caused by the lag.

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
  • 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./