amit-jain / carnd-mpc-project

CarND Term 2 Model Predictive Control (MPC) Project

CarND-Controls-MPC

Self-Driving Car Engineer Nanodegree Program

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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.

Implementation

Model

The state consists of the following:

• x, y co-ordinates of the vehicle
• psi - the current angle of the vehicle
• v - the current speed of the vehicle
• cte - the calculated cross track error of the vechicle
• epis - the error calculated for the psi

A 3-degree polynomial were fitted to the waypoints sent from the server which were used to calculate the cte and epsi.

The actuators are the steering angle and the throttle.

The constraints were defined on following for minimizing the ot function:

• cte
• epsi
• velocity

Constraints on the steering:

• steering angle
• throttle

Constraints in difference of the below steering actuators sequentially

• steering angles
• throttle

There was no special handling done to handle latency but the assumption is that adding a constraint for the differences in steering actuators soothes the values and keeps sequential values closer thus accounting for some latency.

Checking timesteps & interval between timesteps

The following values are the ones which were arrived at after some trial and error and work for the respective reference velocities. The N & the dt parameters (the timestamp length and the duration between timesteps) are constant for all. These values worked best for all the velocities tried. Increasing the timesteps (N) parameter made the model less sensitive at higher velocities and caused the vehicle to veer out of the track on sharp turns. Decreasing the duration between timesteps (dt) parameter caused the vehicle to be over-sensitive and caused the vehicle to veer off courser at the start itself.

Finalized values

Reference Velocity 80

size_t N = 6
double dt = 0.1
double cte_cost_coeff = 10.0
double psi_cost_coeff = 10.0
double v_cost_coeff = 1.0
double delta_cost_coeff = 20000.0
double throttle_cost_coeff = 3.0
double delta_change_cost_coeff = 100.0
double throttle_change_cost_coeff = 3.0  

Reference Velocity 60

size_t N = 6
double dt = 0.1
double cte_cost_coeff = 5.0
double psi_cost_coeff = 5.0
double v_cost_coeff = 1.0
double delta_cost_coeff = 5000.0
double throttle_cost_coeff = 3.0
double delta_change_cost_coeff = 100.0
double throttle_change_cost_coeff = 3.0  

Reference Velocity 40

size_t N = 6
double dt = 0.1
double cte_cost_coeff = 5.0
double psi_cost_coeff = 5.0
double v_cost_coeff = 1.0
double delta_cost_coeff = 2000.0
double throttle_cost_coeff = 3.0
double delta_change_cost_coeff = 100.0
double throttle_change_cost_coeff = 3.0  

Project Video