Core Concepts: Linear Quadratic Regulators

We explore the concept of control in robotics, notably Linear Quadratic Regulators (LQR). We see that a powerful way to think about control is as a dynamic optimization, where the goal is to compute a mapping from states to action that minimize a user-specified cost, e.g. land a rocket without exploding. Moreover, you can do this efficiently thanks to Bellman’s insight that the optimal value of a state at your current time is simply the minimum one-step cost + the optimal value at the next time, suggesting an elegant iterative procedure. What makes LQR special is that you can do this analytically because the optimal value function is a quadratic! This property grants LQR a first-class status as theoretically fundamental and practically powerful.

Notebook for LQR applied to inverted pendulum: https://colab.research.google.com/dri...

References:
1. Bagnell, Boots: https://homes.cs.washington.edu/~bboo...
2. Russ Tedrake's lecture: https://underactuated.mit.edu/lqr.html

Check out the full series "Core Concept in Robotics":    • Core Concepts in Robotics