A PID controller is implemented in C++ to maneuver the self-driving car around the Udacity lake track. The simulator provides the cross track error (CTE) and the velocity (mph) in order to compute the appropriate steering angle.
The project's rubric can be found here.
The steering angle is calculated from the PID equation:
steering = -Kp * CTE - Kd * CTE' - Ki * Σ(CTE)
Where,
P = -Kp * CTE, is the Proportional term
D = - Kd * CTE', is the Differential term
I = - Ki * Σ(CTE), is the Integral term
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The Proportional term (P) is responsible for the angle that the car intercepts the reference trajectory. However, without the aid of the other two terms, P alone gets the vehicle into a marginally stable condition in which the car oscillates around the reference condition. Eventualy the car will never converge to the reference.
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The Differential term (D) is responsible for the interception of the reference condition. It takes into account both the CTE of the previous step as well as the current CTE. DIfferentiates them over time and adjust the interception angle in a way so that the car is able to eventually converge to the reference condition.
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The Integral term (I) is responsible for the elimination of possible bias due to missalignment of the wheels or any other implementation flaw in the car. If only the other two terms were to be implemented, the car would converge to the bias instead of the reference condition. The integral term, takes into account all previous CTEs, integrates them over time, eliminates the bias, and allows the car to converge to the reference condition.
Having in mind the above principles, the final hyperparameters (P, I, D coefficients) had been manually tuned in order to achieve normal vehicle behavior while it circles around the track.
To further investigate the contribution of each coefficient to the control of the car, the simulation was done three times with each of the coefficients set to zero:
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With Kp set to zero, the car cannot recover fast after having an offset from the reference condition as expected -youtube video (Kp = 0).
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With Kd set to zero, the car gets out of the road just after the starting point. This behavior showcases the significance of the differential coefficient in controlling the car - youtube video (Kd = 0).
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With Ki set to zero, does not cause significant issues in the behavior of the car mostly because the simulator is an optimal device and without biases - youtube video (Ki = 0).
This project involves the Term 2 Simulator which can be downloaded here
This repository includes two files that can be used to set up and intall uWebSocketIO for either Linux or Mac systems. For windows you can use either Docker, VMware, or even Windows 10 Bash on Ubuntu to install uWebSocketIO.
- cmake >= 3.5
- All OSes: click here for installation instructions
- make >= 4.1 (Linux, Mac), 3.81 (Windows)
- Linux: make is installed by default on most Linux distros
- 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
- Windows: recommend using MinGW
Once the install for uWebSocketIO is complete, the main program can be built and ran by doing the following from the project top directory.
- Clone this repo
- Make a build directory:
mkdir build && cd build - Compile:
cmake .. && make
- On windows, you may need to run:
cmake .. -G "Unix Makefiles" && make
- Run it:
./pid
$ mkdir build && cd build
$ cmake .. && make
$ ./pid
Tips for setting up your environment can be found here