Self-Driving Car Engineer Nanodegree Program
The MPC model state is:
x - x position of the car. 0 with car being the origin
y - y position of the car. 0 with car being the origin
psi - the current yaw of the car. 0 at time 0 with car being the origin
v - the velocity of the car in m/s
cte - the cross track error, shortest distance from car to the planned path. Achieved by evaluating the reference path polynomial and evaluating at point of vehicle.
epsi - error in our yaw from desired yaw. Essentially the difference of the reference path tangential gradient vs current yaw.
The actuators:
delta - the steering angle, restricted between +-25 degrees.
a - acceleration, between -1 and 1.
update equations:
It appeared when N is too high the algorithm would lag significantly. When N is too low it'd be wildly off road.
When dt is too low then N would need to be very high just to optimize for 1-2 seconds into the future. When dt is too high it'd optimize for the vehicle to turn too early.
A balance is required so N*dt is sufficient time into the future.
Range of N experimented with: 5 - 40 Range of dt experimented with: 0.025 - 0.5
Settled on N=10, dt=0.2
The simulator provided a set of path points forward in the form of vector ptsx & ptsx. These points were global positioning points. The simulator also provided the car's location globally.
Since it's easier to measure cross track error and psi error from the perspective of the vehicle's front direction, being the X axis, we calculate these points with respect to the car's location and rotate from global position to coordinates where the car is the centre.
//use negative psi to rotate the point towards 0, 0 being the direct front of the car
float s = sin(-psi);
float c = cos(-psi);
for(std::size_t i = 0; i < ptsx.size(); i++){
double tempx = ptsx[i] - px;
double tempy = ptsy[i] - py;
ptsx[i] = tempx * c - tempy * s;
ptsy[i] = tempx * s + tempy * c;
}
Once I could visualize the desired path in the simulator I fitted a 3rd degree polynomial to the points.
Eigen::VectorXd eigenX = Eigen::Map<Eigen::VectorXd, Eigen::Unaligned>(ptsx.data(), ptsx.size());
Eigen::VectorXd eigenY = Eigen::Map<Eigen::VectorXd, Eigen::Unaligned>(ptsy.data(), ptsy.size());
Eigen::VectorXd coeffs = polyfit(eigenX, eigenY, 3);
This gives us a model for the vehicle's desired trajectory.
Velocity was in mph so we need to convert this to m/s. This tripped me up for awhile.
Adding latency of 100ms threw off the controller significantly. The project mimics latency with the following:
this_thread::sleep_for(chrono::milliseconds(100));
To cater for latency, I implemented as suggested in the course material: to project forward 100ms before passing the state into the MPC.
double x = 0;
double y = 0;
psi = 0; //psi will be 0 since 0 will always be front
//simulate latency of 100ms
double latency = 0.1;
x = x + v * cos(psi) * latency;
y = y + v * sin(psi) * latency;
psi = - (v / 2.67) * delta * latency;
double cte = polyeval(coeffs, x);
double epsi = psi - atan(polyeval(coeffs, x));
v = v + a * latency;
Cost function weights had to be tuned again as well as the time steps and delta t.
- 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.shorinstall-ubuntu.sh. - If you install from source, checkout to commit
e94b6e1, i.e.Some function signatures have changed in v0.14.x. See this PR for more details.git clone https://github.com/uWebSockets/uWebSockets cd uWebSockets git checkout e94b6e1
- Run either
- 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.
- Mac:
- Ipopt
- Mac:
brew install ipopt - Linux
- You will need a version of Ipopt 3.12.1 or higher. The version available through
apt-getis 3.11.x. If you can get that version to work great but if not there's a scriptinstall_ipopt.shthat will install Ipopt. You just need to download the source from the Ipopt releases page or the Github releases page. - Then call
install_ipopt.shwith the source directory as the first argument, ex:sudo bash install_ipopt.sh Ipopt-3.12.1.
- You will need a version of Ipopt 3.12.1 or higher. The version available through
- Windows: TODO. If you can use the Linux subsystem and follow the Linux instructions.
- Mac:
- CppAD
- Mac:
brew install cppad - Linux
sudo apt-get install cppador equivalent. - Windows: TODO. If you can use the Linux subsystem and follow the Linux instructions.
- Mac:
- 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.
- Clone this repo.
- Make a build directory:
mkdir build && cd build - Compile:
cmake .. && make - Run it:
./mpc.
- 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.csvfile 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.
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)
Please (do your best to) stick to Google's C++ style guide.
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.
- 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.
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./