Self-Driving Car Engineer Nanodegree Program
In this project I present a variant of the PID controller model which I've termed "Stochastic-Temporal-Update-Proportional-Integral-Differential" controller - or STUPID for short. The STUPID model uses short term temporal differences which is optimised using stochastic gradient descent, to push the PID values to their optimum. Depending on the initialisation strategy the STUPID controller is gauranteed to converge, and in less epochs than a traditional PID controller.
To initialise the starting weights [Wp, Wi, Wd], a uniform distribution with partial ranges is utilised, where;
- Wp = 0.4 < x < 0.7
- Wi = 0.0 < x < 0.4
- Wd = 0.7 < x < 5.0
The above initialisation strategy ensures that the integral doesn't cause the gradients to explode or saturate the other gain values.
The update process is robust enough that symmetry breaking during initialisation is not required, however, it will cause delayed convergence. Tuning the convergence speed is done by modifying the learning rate (alpha).
Because the STUPID model doesn't require extensive parameter search for initialisation, it can be a used in an online learning setting. This is a big advantage over traditional PID controllers where proper tuning of parameters is paramount to their successes. It is also complete in that additional process noise induced during operation will not cause it to diverge in the case of other types of controllers.
Below are comparisons between the weight initialisation stategies for the STUPID controller in reference to traditional PID controllers.
Symmetric initialisation of 0.1
Non-symmetric initialisation using above strategy
Implementation of the PID controller for driving the vehicle within the @udacity simulator is done by using dual STUPID controllers.
The first controller computes the naive steering angle while the second combats the confirmation bias induced in the first. Its effects are most prominent during turns with noisy measurements, where the regulator prevents the first from steering towards the noisy error.
The outputs of both controllers are scaled and averaged with the angle at the previous timestep. This allows the model to drive quite stable at speeds of nearly 100km/h with very noisy waypoints.
During runtime, both controllers randomly initialise their gain weights as described by the above strategy. Optimisation is performed for the first 1200 epochs where both controllers remain static thereafter.
See Screenshot 1 and Screenshot 2 to see it in action.
- 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 == 0.13, but the master branch will probably work just fine
- Follow the instructions in the uWebSockets README to get setup for your platform. You can download the zip of the appropriate version from the releases page. Here's a link to the v0.13 zip.
- If you run OSX and have homebrew installed you can just run the ./install-mac.sh script to install this
- Simulator. You can download these from the project intro page in the classroom.
- Clone this repo.
- Make a build directory:
mkdir build && cd build - Compile:
cmake .. && make - Run it:
./pid.