Notes

Working notes on control and multi-agent systems. They are organised as an overview rather than a course: enough to place a problem, with pointers to what to read next.


Control theory

Describing a robotic system, and designing the law that drives it.

01
System modelling

What a model is made of and the handful of distinctions that decide which controllers are available to you: linear or nonlinear, continuous or discrete time, fully actuated or underactuated, nominal or uncertain.

state and input · continuous and discrete-time · linearization · control-affine form · disturbance models · observability
02
Common dynamic models

The small library of models that covers most of robotics, written in a common form with their dimensions and structure.

single and double integrator · unicycle · dubins · kinematic and dynamic bicycle · cart-pole · quadrotor on SO(3)
03
Control law design

Brief overview of the key techniques for designing control laws, through to designing under disturbance, unknown parameters, and hard safety constraints.

PID · pole placement · LQR and LQG · feedback linearization · CLF-QP · control barrier functions · MPC · robust and stochastic design
04
Personal notes on CBF-QP

Things about CBF-QP I keep getting confused on.

CBF definition · invaraince definitions · regularity conditions
05
Safety Definition

Defining safety in the context of control.

Safety definition · invaraince definitions · CBF definition
06
Gatekeeper

A safety filter that runs two controllers (performance and safety driven) and searches for the latest switching time the system can still be safe while remaining on the performance-driven controller.

backup policies · candidate and committed trajectories · validity · recursive feasibility · switching time as a decision variable · Backup CBF and MPS

Corrections and suggestions are welcome by email.