This book is about building robots that move with speed, efficiency, and grace. I believe that this can only be achieve through a tight coupling between mechanical design, passive dynamics, and nonlinear control synthesis. Therefore, these notes contain selected material from dynamical systems theory, as well as linear and nonlinear control.
These notes also reflect a deep belief in computational algorithms playing an essential role in finding and optimizing solutions to complex dynamics and control problems. Algorithms play an increasingly central role in modern control theory; these days even rigorous mathematicians consider finding convexity in a problem (therefore making it amenable to an efficient computational solution) almost tantamount to an analytical result. Therefore, the notes necessarily also cover selected material from optimization theory, motion planning, and machine learning.
Although the material in the book comes from many sources, the presentation is targeted very specifically at a handful of robotics problems. Concepts are introduced only when and if they can help progress the capabilities we are trying to develop. Many of the disciplines that I am drawing from are traditionally very rigorous, to the point where the basic ideas can be hard to penetrate for someone that is new to the field. I've made a conscious effort in these notes to keep a very informal, conversational tone even when introducing these rigorous topics, and to reference the most powerful theorems but only to prove them when that proof would add particular insights without distracting from the mainstream presentation. I hope that the result is a broad but reasonably self-contained and readable manuscript that will be of use to any enthusiastic roboticist.