CarND-Controls-MPC

Self-Driving Car Engineer Nanodegree Program

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Dependencies

• cmake >= 3.5
  • All OSes: click here for installation instructions
  • Used version: 3.8.2
• 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
  • Used version: 0.6.2 Beta
• 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.
  • Windows: Refer to the section "Windows Install Instructions" here
• 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: Refer to the structure here
• CppAD
  • Mac: brew install cppad
  • Linux sudo apt-get install cppad or equivalent.
  • Windows: Refer to the structure here
• 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 OR
4. Build the project "mpc.vcxproj" using Visual Studio 17 (should work normally using cmake .. && make but it did on Windows using the original files in the project directory. I used the files here after asking on forum)
5. Open the simulator in autonomous mode
6. Run mpc.exe

Model

• Exactly as in MPC quiz
• State: state vector consists of the following:
  • Position x
  • Position y
  • Orientation angle psi
  • Velocity v
  • Cross-Track Error cte
  • Orientation Error epsi
• Actuators: simulator accepts only the following actuators:
  • Steering angle delta
  • Throttle, modeled by acceleration a
• Update equations:

  * x_[t+1] = x[t] + v[t] * cos(psi[t]) * dt
  * y_[t+1] = y[t] + v[t] * sin(psi[t]) * dt
  * psi_[t+1] = psi[t] + v[t] / Lf * delta[t] * dt
  * v_[t+1] = v[t] + a[t] * dt
  * cte[t+1] = f(x[t]) - y[t] + v[t] * sin(epsi[t]) * dt
  * epsi[t+1] = psi[t] - psides[t] + v[t] * delta[t] / Lf * dt

• Where dt is a tuned parameter representing the time between current and next prediction
• Where Lf is length from front to CoG that has a similar radius
• Where f(x(t)) is the predicted y value according to the trajectory fitting polynomial
• Where psides is the atan of the differential of f(x(t)) with respect to x

Parammeters Tuning

• N (timestep length): was set to 10 according to the helper video
  • Having a larger N is better to predict more points but it consumes longer time for computing actuators (number of parameters to optimize is proportional to N)
  • But having a larger N may also make the outcomes unpredictable because the optimizer may override controls that decrease cost in the near future to decrease cost in the far future
  • Other experimented value: 25 (like in MPC quiz)
• dt (elapsed duration between timesteps): was set to 0.1 according to the helper video
  • Having a small dt is better to predict for more recent times but it increases computations
  • Having a large dt is worse because it makes the systen slower
  • Other experimented value: 0.05 (like in MPC quiz)
• So, we predict 1s into the future

Polynomial Fitting

• We have 6 way points given by the simulator, we fit a 3rd order polynomial as done in the helper video and in all discussions

Preprocessing

• Preprocessing is done to convert from map coordinates to vehicle coordinates. This is done on 2 steps: Translate to car coordinate system then rotate to the car's orientation

x = ptsx[i] - px;
x = ptsx[i] - px;
ptsx[i] = (x * cos(psi) + y * sin(psi));
ptsy[i] = (-x * sin(psi) + y * cos(psi));

• Consequently, x, y, and psi are always 0 in the state vector passed to MPC solver

Adding Latency

• To account for 100ms latency between prediction and applying of controls, the idea in main.cpp is to provide the model with predicted outputs after 100ms

Did it work?

• Honestly on my machine it did not work. I posted this on forum, applied all the known solutions to me but nothing worked. I also got some code on Github from students that completed the project and also did not work on my laptop. I think my laptop may be the reason because it is extremely slow.

Notes

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.