Self-Driving Car Engineer Nanodegree Program
This projects aims to implement a Model Predictive Control to drive a car around a track. An MPC is an advance method of process control, which allows the current timeslot to be optimized, while keeping future timeslots in account.
The car runs along a track in a simulator, which provides a stream of values containing the position, speed and heading direction. The model must predict the control and adjust it to the expected trajectory.
The implementation relies on a simplified model of the real world, the bycicle kinematic model. This model abstracts the kinematic model of a real car as if it was a two wheels system, which the front wheel being the steering one. It also neglects dynamical effects such as inertia, troque or friction. In the image below can be seen the main variables involved in the model:
The model involves the following variables:
- State: position (x, y), orientation angle (psi), velocity (v), cross-track error (cte) and psi error (epsi).
- output: acceleration (a) and delta (steer).
Which are combined with the following equations to predict the state from previous input:
The prediction horizon is the duration over which future predictions are made. The product of N and dt is the prediction horizon, T.
N is the number of timesteps in the horizon and dt is how much time elapses between actuations. For example, if N were 20 and dt were 0.5, then T would be 10 seconds. Short prediction horizons lead to more responsive controlers, but are less accurate and can suffer from instabilities when chosen too short. Long prediction horizons generally lead to smoother controls. Also, for a given T, shorter timesteps give as a result a more accurate control, but it increases the latency.
I chose the values doing try an error, and I chose a time horizon of 1 second with 0.1 timesteps, so N=10 and dt=0.1
The waypoints are processed to convert them to the vehicle coordinate system. Shifting and rotation is done to align the x-axis with the heading direction. The code can be found in main.cpp:
for (int i = 0; i < ptsx.size(); i++) {
double dx = ptsx[i] - px;
double dy = ptsy[i] - py;
waypoints_x.push_back(dx * cos(-psi) - dy * sin(-psi));
waypoints_y.push_back(dx * sin(-psi) + dy * cos(-psi));
}
The model must handle a 100 millisecond latency, which in our case is also the timestamp interval (dt=100). In MPC, the actuation is done a timestamp later, so we need to modify the equation to take into account t-2 timesteps for the actuator variables:
if (t > 1) { // use previous actuations (to account for latency)
a = vars[a_start + t - 2];
delta = vars[delta_start + t - 2];
}
In the lessons a penalization in the cost function is suggested. However, to provide a better control in steering, an additional cost penalizing has been added combining velocity and delta:
for (int i = 0; i < N - 1; i++) {
fg[0] += 1000*CppAD::pow(vars[delta_start + i] * vars[v_start+i], 2);
fg[0] += 3*CppAD::pow(vars[a_start + i], 2);
}
- 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
orinstall-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
- 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:
This error has been resolved by updrading ipopt withListening 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
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 scriptinstall_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
.
- 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.
- 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.
- 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.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.
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./
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