Control

Trajectory Optimization

Trajectory optimization is the computation of a robot motion by minimizing a cost functional, such as time, energy, or control effort, subject to the system's dynamics, actuation limits, and constraints like obstacle avoidance and contact. Methods divide into indirect approaches based on optimality conditions and direct methods, including direct collocation and shooting, that transcribe the problem for nonlinear programming solvers, with DDP and iLQR as prominent dynamic-programming variants. Contact-implicit formulations optimize through contact sequence changes.

Why it matters for physical AI

Optimized trajectories provide dynamically feasible, constraint-respecting motion for legged robots and manipulators, serving both as real-time controllers via MPC and as sources of expert supervision for training learned policies.