MPC Project

In this project Model predictive control (MPC) is used to drive the car around the track, there's a 100 millisecond latency between actuations commands on top of the connection latency.

The goals / steps of this project are the following:

• Step 1: converting the map's coordinate system to the car's coordinate system for easier CTE and Epsi calculation
• Step 2: fitting a 3rd order polynomial to the converted x and y coordinates
• Step 3: using coefficients to predict car's state (px,py,psi, v) at t+dt (considering latency)
• Step 4: feeding states to the model to solve and optimize the costs and thereby calculate the state and actuator values at t+1
• Step 5: adjusting throttle & steering values based on predictions

Vehicle Model

Actuator Constraints

Vehicle can't have steering angle of 90 degrees, such conditions can be fixed by setting a lower and upper bound for actuators:

Prediction Horizon

The prediction horizon is the duration over which future predictions are made.

N dt are the hyperparameters to tune for each model predictive controller. The general guidelines is to have N as large as possible, while dt should be as small as possible.

I tested my model with dt= 0.01 and N=5, which was not enough input for the model to control the vehicle. I then increased dt to 0.05 and N to 10 which significanlty improved my model.

For dealing with latency, I used coefficients to predict car's state (px,py,psi, v) at t+dt (dt=0.05) before passing it to the model.

Optimizing cost

Model's goal is to minimize errors:

• cte: distance of vehicle from trajectory
• epsi: difference of vehicle orientation and trajectory

This model also considers additional costs to penalize vehicle:

• for not maintaining the reference velocity (75mph)
• control-input magnitude & change rate as well as th3e differences from the next control-input state

However I added more weights to some of the costs to add more penalty to the model for a smoother driving:

Here are the cte, v & steering_angle diagrams that I collected for 1000 iterations, as depicted below majority of cte-values are around 0 which shows model is trying to stay in track & valocity is maintaining 50mph, steering-angle-values are very similar to cte-values and it's to stay around 0 to avoid sharp changes:

CTE	Velocity	Steering Anlge

---

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
    • Some Mac users have experienced the following error:

    Listening to port 4567
    Connected!!!
    mpc(4561,0x7ffff1eed3c0) malloc: *** error for object 0x7f911e007600: incorrect checksum for freed object
    - object was probably modified after being freed.
    *** set a breakpoint in malloc_error_break to debug
    

    This error has been resolved by updrading ipopt with brew upgrade ipopt --with-openblas per this forum post.
  • 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.
    • Then call install_ipopt.sh with the source directory as the first argument, ex: sudo 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.