CarND-Controls-MPC

Self-Driving Car Engineer Nanodegree Program

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OBJECTIVE

This project is to use Model Predictive Control (MPC) to drive a car in the Udacity simulator. The simulator provides reference waypoints and we use MPC to compute steering and throttle commands to drive the car. The solution must be robust to 100ms latency to simulate real-world user and actuator delays. In this project, the MPC optimize the actuators (steering and throttle), simulate the vehicle trajactory, and minimize the cost like cross-track error. A max speed of 80 MPH is achieved in this project.

MODEL

• Kinematic Model A kinematic model is implemented to control the vehicle around the track. Kinematic models are simplifications of dynamic models that ignore tire forces, gravity, and mass. This simplification reduces the accuracy of the models, but it also makes them more tractable. The kinematic model includes the vehicle's x and y coordinates, orientation angle (psi), and velocity, as well as the cross-track error and psi error (epsi). Actuator outputs are acceleration and delta (steering angle). The model combines the state and actuations from the previous timestep to calculate the state for the current timestep.

  • States:

    • x: cars x position
    • y: cars y position
    • ψ (psi): vehicle's angle in radians from the x-direction (radians)
    • ν: vehicle's velocity
    • cte: cross track error
    • eψ : orientation error

  • Actuator values

    • δ (delta): steering angle
    • a : acceleration (including throttle and break)

  • The kinematic model can predict the state on the next time step by taking into account the current state and actuators:

• Timestep Length and Elapsed Duration (N & dt)

  • N = 10
  • dt = 0.10 s // tested with 0.3, 0.12, 0.1, 0.08s

  The prediction horizon T is the duration over which future predictions are made. T is the product of N and dt, T = N * dt. T is usually a few seconds, at most. Beyond that horizon, the environment will change enough that it won't make sense to predict any further into the future. N and dt are parameters to be tuned for each model predictive controller. However, there are some general guidelines: T should be as large as possible, while dt should be as small as possible. These guidelines create tradeoffs.

  These following dt has been tested 0.3, 0.12, 0.1, 0.08, and I found that the dt should be closer to the latency in order to make the MPC work. So, dt = 0.10 was selected.

  The goal of Model Predictive Control is to optimize the control inputs: [δ,a]. An optimizer will tune these inputs until a low cost vector of control inputs is found.

• Polynomial Fitting and MPC Preprocessing

  Since the reference waypoints are given in the map global coordinates, they were converted into the car's coordinate and then a 3rd order polynomial is fitted to waypoints. Actual state of the vehicle was "shifted" into the future by 100 ms latency. It helps to reduce negative effects of the latency and increase stability of the controller. The cost function parameters were tuned by try-and-error method.

• Model Predictive Control with Latency

  The latency was introduced to simulate real delay of a human driver or physical actuators in case of a self driving car. The original kinematic equations depend upon the actuations from the previous timestep, but with a delay of 100ms (which happens to be the timestep interval) the actuations are applied another timestep later, so the equations have been altered to account for this.

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Dependencies

• cmake >= 3.5

• All OSes: click here for installation instructions

• make >= 4.1(mac, linux), 3.81(Windows)

  • 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.

• Ipopt and CppAD: Please refer to this document for installation 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.)
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./

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