CarND-Controls-MPC

Self-Driving Car Engineer Nanodegree Program

Write-up

The Model

Student describes their model in detail. This includes the state, actuators and update equations.

In this project I used kinematic bicycle model for implementing Model Predictive Controller.

The state of the model consists of:

x, y - coordinates of the vehicle;
psi - vehicle orientation;
v - velocity;
delta - steering value;
throttle - acceleration value;
cte - cross track error;
epsi - orientation error.

Delta and throttle act as actuators. Steering angle varies between -25 and 25 degrees. Throttle may be between -1 and 1. Negative values are used as break. The goal on each step is to compute these values for the next tick.

The following constraints are used in this model:

x_t+1=x_t+v_t∗cos(ψ_t)∗dt

y_t+1=y_t+v_t∗sin(ψ_t)∗dt

ψ_t+1=ψ_t+v_t/L_f∗δ_t∗dt

v_t+1=vt_t+at∗dt

cte_t+1=f(x_t)−yt_t+(v_t∗sin(eψ_t)∗dt)

eψ_t+1=ψ_t−ψdes_t+(v_t/L_f∗δ_t∗dt)

Timestep Length and Elapsed Duration (N & dt)

Student discusses the reasoning behind the chosen N (timestep length) and dt (elapsed duration between timesteps) values. Additionally the student details the previous values tried.

While I tried to choose dt as small as possible, choosing dt smaller than 100ms (which is the latency between actuation commands) makes no sence. Because of some time gap between sending command and receiving next data I found that dt=150ms works better.

N=10 means that controller predictes values for the next 1 second. This can be considered enough. I didn't find any improvement from larger values.

Polynomial Fitting and MPC Preprocessing

A polynomial is fitted to waypoints.

I used algorithm from lections to fit polynomial. As suggested in lections polynomial with order=3 is enough for most of the roads.

If the student preprocesses waypoints, the vehicle state, and/or actuators prior to the MPC procedure it is described.

On each step simulator sends coordinates relative to the global map. But model computations are much simpler in car coordinate system. So I transformed them in main.cpp:78.

I also tranfromed speed sent by simulator from MPH to m/s for proper using it in model.

Model Predictive Control with Latency

The student implements Model Predictive Control that handles a 100 millisecond latency. Student provides details on how they deal with latency.

In order to take into account the latency I added state prediction as the first step in my controller. I used constraints described above for state prediction.

Video

Please find below video of the simulation at a speed of 70 mph.

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

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./

villytiger/CarND-MPC-Project