About this book:

*Control Theory for Modern Robotics* provides a comprehensive technical guide to the evolution of robotic control, bridging the gap between traditional mathematical foundations and contemporary learning-based paradigms. The book begins by establishing essential mathematical tools—linear algebra, multivariate calculus, and Lagrangian dynamics—before moving into classical feedback mechanisms like PID control and frequency-domain analysis. It transitions into state-space representation, offering rigorous frameworks for analyzing controllability, observability, and Lyapunov stability, which form the bedrock for advanced regulation and state estimation techniques like the Kalman filter.

The text then delves into the realm of optimization, detailing the principles of Optimal Control through Pontryagin’s Minimum Principle, LQR, and LQG. A significant portion of the book is dedicated to constraint-aware strategies, specifically Model Predictive Control (MPC) and robust methods like H∞ and μ-synthesis, which address the inherent uncertainties and physical limits of real-world hardware. Specialized chapters explore the complexities of contact-rich dynamics, including impedance control for manipulation and whole-body control for legged locomotion, highlighting the challenges of hybrid systems where continuous motion meets discrete impact events.

In its later sections, the book integrates machine learning into the control loop. It covers supervised, imitation, and reinforcement learning, presenting them not as replacements for classical models but as "residual" or hybrid components that adapt to unmodeled dynamics. Throughout this integration, the author foregrounds safety through Control Barrier Functions and risk-aware optimization. Practical engineering concerns such as system identification, Gaussian Processes, and Bayesian Optimization are discussed as essential tools for data-efficient tuning and model refinement.

The final chapters address the pragmatic hurdles of deployment, focusing on the "sim-to-real" gap, domain randomization, and real-time implementation using middleware like ROS 2 and RTOS scheduling. The book concludes with a rigorous overview of verification, validation, and benchmarking, emphasizing the importance of safety standards and objective performance metrics. By synthesizing elegant mathematics with data-driven adaptability, the text serves as a roadmap for developing precise, safe, and autonomous robotic systems capable of performing in unpredictable environments.