CarND-Controls-MPC

Self-Driving Car Engineer Nanodegree Program

Introduction

A Model Predictive Controller (MPC) was implemented on a vechilce within a simulator successfully navigating it through a track. MPC’s can anticipate a vehicle’s position in the future and can take actions accordingly to improve their trajectory which make it advantagous over other types of controllers.

Model

In order to predict a vehicles future position an MPC uses a vehicles current state. This includes it’s current position, it’s heading and it’s speed. State. The Actuators, which are variables that control and move the vehicle, included the steering wheel angle with values between -25 degrees and 25 degrees update equations and the throttle which accelerated the vehicle and had values between -1 and 1. In addition the distance from the front of the vehicle to its center of gravity was used to determine turn rate. This is important as the larger a vehicle the slower it’s turn rate is. The difference between the ideal path line and the current vehicles position was considered the cross track error (CTE). The orientation error of the vehicle was considered as the EPSI.

The MPC gets the trajectory from the simulator as an array of waypoints called ptsx and ptsy in the world map. The CTE and the EPSI are then transformed in the vehicle coordinate space (the vehicle is at 0,0). Following this a 3rd order polynomial is calculated and predicts N states of the vehicle in space and time with a time delay between calculations of dt. The polynomial function at point x = 0 will be equal to the CTE and the EPSI will be the negative arctan of the first derivative at the same point. The MPC then predicts the vehicles state, and corresponding actuator vectors with the Interior Point Optimizer. The cost function in the class FG_eval begining with fg[0] = 0 is used to predict the preceding optimal states and actuators with the polynomial being completed on line 104 in MPC.cpp.

For driving within the simulator the model is sufficient but as does not account for variables experienced during actual driving such as variable road surface friction, wind etc.

Parameters

The elapsed duration (dt) to wait before running the model was 0.2 and was probably limited by the lower menory of the virtual machine I was using. With dt = 0.2 the car wobbles a bit to begin with but then stays very close to the ideal path line. With the dt = .1 the vehicle wobbles violently at the start, improves but never maintains stable trajectory.

The number of future timesteps (N) chosen was 15. With N = 15 the car stayed on almost exactly on the ideal path line. An N = 20 also had a great trajectory but the vehicle seemed to slow more around curves than was needed. An N = 10 had a slightly more inaccurate trajectory but it’s speed was quicker around corners.

A delay of 100 m/s between sensing and processing the model is present to simulate more realistic conidtions outside the simulator. An equal latency value of 100 m/s is added to the model to change the vehicles state in time and place to accomodate the delay as is shown below. The Y state will be zero as the vehicle will move along the same plane.

      double latency = 0.1;
      double Lf = 2.67;

      // position after latency
      psi = v * (-steer_value) / Lf * latency;
      px = v * latency;
      //py = v*sin(psi) * latency; // will be zero 
      v = v + throttle_value * latency;
      cte = cte + v * sin(epsi) * latency;
      epsi = epsi + v * (-steer_value) / Lf * latency;

      Eigen::VectorXd state(6);
      state << px, 0, psi, v, cte, epsi;

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.
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
- If challenges to installation are encountered (install script fails). Please review this thread for tips on installing 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

Clone this repo.
Make a build directory: mkdir build && cd build
Compile: cmake .. && make
Run it: ./mpc.

Tips

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.
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.
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./

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esolty/CarND-MPC-Project