Trajectory Optimization

Trajectory optimization finds motions or control inputs that achieve goals efficiently while respecting dynamics, obstacles, actuator limits, and sometimes uncertainty or contact. Common approaches include direct optimal-control methods such as sequential convex programming and differential dynamic programming, spline-based formulations, and sampling methods such as MPPI and cross-entropy search; recent work also uses diffusion models and learned warm starts. Applications range from robot manipulation and legged locomotion to autonomous driving, UAV planning, and spacecraft guidance, with evaluation spanning simulation benchmarks and real-robot or flight tests. A central challenge is balancing fast, reliable solutions with global exploration and strong feasibility or safety guarantees, especially for contact-rich, uncertain, and high-dimensional systems.