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

Resilient network theory

What the communication graph has to look like when some agents cannot be trusted.

01
r-robustness

Why W-MSR consensus needs a (2F+1)-robust graph rather than a well-connected one, why computing the exact value is coNP-complete, and what minimum degree and connectivity can and cannot tell you instead.

r-reachable sets · r-robustness · W-MSR consensus · per-node deletion budget · (r,s)-robustness · coNP-completeness · degree and connectivity bounds

Optimization and Learning

Understanding the theories of optimization and machine learning tools.

01
GATv2

Studying the structure of GATv2

Message Passing · Attention
02
Conformal Prediction

Studying the theory and intuition of conformal prediction.

Exchangeability · calibration dataset · score

Corrections and suggestions are welcome by email.