Trajectory optimization describes a broad set of numerical techniques for computing open-loop solutions to optimal control problems. These techniques are particularly useful for high-dimensional dynamical systems, and are widely used in the aerospace industry. I use trajectory optimization in my research to compute optimal gaits for walking robots.

Here I will provide an introduction to trajectory optimization and show an in-depth example, using direct collocation to compute an optimal swing-up trajectory for a cart-pole system.

The focus of this talk is on practical implementation details and understanding the concepts behind trajectory optimization, rather then careful mathematical proofs.