CarND-Controls-MPC

Self-Driving Car Engineer Nanodegree Program

This implemintation is based on the quiz implementation in [1]

Model Description

1. The state vector is represented by the variables:

• cte, epsi the cross track error. Ideally, both of these errors would be 0 - which indicate that there would be no difference from the actual vehicle position and heading to the desired position and heading.
• x, y Vehicle coordinates
• psi Vehicle bearing
• v Vehicle velocity

2. The vehicle is considered to have two actuators only for simplicity
4. Model initialization

''' fg[1 + x_start] = vars[x_start]; fg[1 + y_start] = vars[y_start]; fg[1 + psi_start] = vars[psi_start]; fg[1 + v_start] = vars[v_start]; fg[1 + cte_start] = vars[cte_start]; fg[1 + epsi_start] = vars[epsi_start]; ''' 5. Model equation

''' x_[t] = x[t-1] + v[t-1] * cos(psi[t-1]) * dt y_[t] = y[t-1] + v[t-1] * sin(psi[t-1]) * dt psi_[t] = psi[t-1] + v[t-1] / Lf * delta[t-1] * dt v_[t] = v[t-1] + a[t-1] * dt cte[t] = f(x[t-1]) - y[t-1] + v[t-1] * sin(epsi[t-1]) * dt epsi[t] = psi[t] - psides[t-1] + v[t-1] * delta[t-1] / Lf * dt '''

Prediction horizon N*dt:

The product of N and dt gives us the prediction horizon T which helps the model foresee the road further. Choosing a high value of the number of time steps in the future can lead to more computation as well as unstable driving. I have tested values between 10 and 30 and I found that starting with N bigger than 18 the car drives erratically before sharp turns. I have also considered values between 0. -0.4 for dt which describes how much time lapse between actuations and found than a value of 0.2 was the best for making the can as stable as possible. a lower dt value results in delayed response to the road condition, while a high value made the car drive erratically.

Polynomial Fitting and MPC Preprocessing

The polynomial is fitted with a 3-degree polynomial . ''' auto coeffs = polyfit(ptsx, ptsy, 3); ''' Where pstx and psty contain the vehicle position py and py. Therefore the position was transformed into the vehicle coordinate to improve the accuracy of the polynomial fit.

Model Predictive Control with Latency

One major advantage for using MPC over Pid is that it can deal with latency much more effectively. Carefully choosing the prediction horizon value help the system plan in the future and reduce the latency. The initial values and weights for the steering, throttle, and speed are chosen to lower the latency. the steering and throttle weights were chosen to be small and weak on the velocity.

[1] https://github.com/udacity/CarND-MPC-Quizzes/blob/master/mpc_to_line/solution/MPC.cpp

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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
  • 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./