Overview

Turn the mathematics of living systems into engineering models that actually run on robots. This book connects biological principles like homeostasis, rhythmic coordination, sensory fusion, adaptation, and collective behavior to the core mathematical tools used in modern robotics, including nonlinear dynamics, stability theory, stochastic modeling, optimal feedback control, and distributed systems. You will move from state-space modeling and contact rich locomotion to limit cycles, phase reduction, and coupled oscillator networks that generate stable gaits. Build bio-inspired actuation and compliance models using muscle and tendon style dynamics, then quantify performance using energetics and cost metrics. Extend from deterministic control to uncertainty aware robotics with Bayesian inference, Kalman style filtering, and stochastic differential equations that capture signal-dependent motor noise. Explore learning and adaptation through plasticity rules, internal models, predictive control viewpoints, and evolutionary style optimization. Scale up to multi-agent systems with mean-field models, flocking dynamics, task allocation, and game theoretic stability. Finish with mathematically grounded modeling for soft bodies and fluid-structure interaction in swimming and flying. Every chapter includes multiple choice questions plus practice problems, all with fully explained answers, so concepts are not only presented but verified through active problem solving. The result is a rigorous, implementation minded reference for bio-inspired modeling, analysis, and control.

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