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Necessary Background

This page will have the necessary resources for you to understand the basic intuition behind how we model the dynamics of the car. We won't have to go into too much detail on system modeling since we will not have to predict the state (position, velocity, steering angle etc.) of the car, we will just believe what the state estimation team tells us and decide based on that. The point of this document is simply to ensure the controls team understands what it is they are doing by forming an input based on the current state, the target state and a control law.

Optional

If you have experience with/feel comfortable with the idea of state spaces, basic non-linear matrix differential equations and control laws, feel free to skip this section.

What Even is Control Theory?​

MATLAB generously provides an excellent overview of what control even is here. This can also serve as a good refresher.

State Space Modeling​

  • This video by MATLAB explains the basics behind state space and what makes it so powerful. You can skip the last bit about "modal forms", they will not be relevant.

  • This video is entirely mathematical and has no other purpose. Try to follow along until ~8:11, where he talks about linearization.

  • This video defines the process of linearization. Watch to about 2 minutes, then skip to about 4:20 and watch to the end.