Lie Group Robotics

Lie Group Robotics offers a comprehensive computational approach to robot kinematics, dynamics, and control, leveraging the geometry of R³, SO(3), and SE(3). Unlike traditional texts that treat Lie theory as abstract mathematics, this book transforms it into a practical tool, pairing geometric concepts with explicit, implementable formulas. Readers are guided seamlessly from theoretical insights to executable code, making it an essential resource for modern robotics. Key topics include exponential maps, trajectory interpolation, recursive dynamics, and control strategies tailored for industrial arms, drones, humanoids, and space robots. The book spans the entire modeling-to-control pipeline, addressing floating-, jointed-, and fixed-base systems within a unified framework. It introduces innovative results, such as closed-form expressions for the differential of the exponential map and its derivative, and the Principle of Dynamical Balance, which enables efficient recursive algorithms for articulated systems. The unified control theory progresses from Lyapunov stability to advanced methods like nonlinear H8 and impedance control directly on SE(3). Extensive worked examples, MATLAB libraries, and online appendices ensure practical application and mastery of the material. Targeting graduate students, researchers, and engineers, Lie Group Robotics bridges rigorous theory with field-tested solutions. Its computational methods underpin control software in commercial collaborative robots, offering a robust foundation for advancing robotics in industrial, aerospace, and autonomous systems markets.