control

A static execution schedule is an open-loop policy: it commits to a plan before seeing anything. This lesson formulates execution as an MDP so the plan can react, and computes the ceiling on what any adaptive policy could win, which turns out to collapse as market impact grows.

Where the pure feedforward story breaks: sensory entrainment, dynamic movement primitives for non-rhythmic motion, how CPGs combine with reinforcement learning in current legged robots, and the exoskeleton applications.

How a handful of phase oscillators produce coordinated gaits: limit cycles and why they resist disturbance, phase coupling that locks oscillators into fixed relationships, and the travelling waves that swim a robot.

Walking is rhythmic, fast, and must survive disturbances no planner anticipated. The biological answer is a spinal circuit that generates rhythm without the brain, and it suggests a fundamentally different control architecture.

How the Kalman filter fuses a motion model with noisy measurements by carrying a Gaussian belief, growing uncertainty on predict and shrinking it on update, weighting the two by the Kalman gain, plus the EKF and UKF for nonlinear systems.