This repository contains my solution to the Udacity SDCND MPC Project. The goal of this project is to navigate a track in a Udacity-provided simulator, which communicates telemetry and track waypoint data via websocket, by sending steering and acceleration commands back to the simulator. The solution must be robust to 100ms latency, as one may encounter in real-world application.
This solution, as the Nanodegree lessons suggest, makes use of the IPOPT and CPPAD libraries to calculate an optimal trajectory and its associated actuation commands in order to minimize error with a third-degree polynomial fit to the given waypoints. The optimization considers only a short duration's worth of waypoints, and produces a trajectory for that duration based upon a model of the vehicle's kinematics and a cost function based mostly on the vehicle's cross-track error (roughly the distance from the track waypoints) and orientation angle error, with other cost factors included to improve performance.
The kinematic model includes the vehicle's x and y coordinates, orientation angle (psi), and velocity, as well as the cross-track error and psi error (epsi). Actuator outputs are acceleration and delta (steering angle). The model combines the state and actuations from the previous timestep to calculate the state for the current timestep based on the equations below:
The values chosen for N and dt are 10 and 0.1, respectively. Admittedly, this was at the suggestion of Udacity's provided office hours for the project. These values mean that the optimizer is considering a one-second duration in which to determine a corrective trajectory. Adjusting either N or dt (even by small amounts) often produced erratic behavior. Other values tried include 20 / 0.05, 8 / 0.125, 6 / 0.15, and many others.
The waypoints are preprocessed by transforming them to the vehicle's perspective (see main.cpp lines 108-113). This simplifies the process to fit a polynomial to the waypoints because the vehicle's x and y coordinates are now at the origin (0, 0) and the orientation angle is also zero.
The approach to dealing with latency was twofold (not counting simply limiting the speed): the original kinematic equations depend upon the actuations from the previous timestep, but with a delay of 100ms (which happens to be the timestep interval) the actuations are applied another timestep later, so the equations have been altered to account for this (MPC.cpp lines 104-107). Also, in addition to the cost functions suggested in the lessons (punishing CTE, epsi, difference between velocity and a reference velocity, delta, acceleration, change in delta, and change in acceleration) an additional cost penalizing the combination of velocity and delta (MPC.cpp line 63) was included and results in much more controlled cornering.
Self-Driving Car Engineer Nanodegree Program
install-mac.sh
or install-ubuntu.sh
.e94b6e1
, i.e.
git clone https://github.com/uWebSockets/uWebSockets
cd uWebSockets
git checkout e94b6e1
brew install gcc
(might not be required)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.brew install ipopt
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 or the Github releases page.install_ipopt.sh
with the source directory as the first argument, ex: bash install_ipopt.sh Ipopt-3.12.1
.brew install cppad
sudo apt-get install cppad
or equivalent.mkdir build && cd build
cmake .. && make
./mpc
.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.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:
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.
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:
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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