Solving Optimal Control Problems of Rigid-Body Dynamics with Collisions Using the Hybrid Minimum Principle

Understand

Collisions are common in many dynamical systems with real applications.

• They can be formulated as hybrid dynamical systems with discontinuities automatically triggered when states transverse certain manifolds.
• We present an algorithm for the optimal control problem of such hybrid dynamical systems based on solving the equations derived from the hybrid minimum principle (HMP).
• The algorithm is an iterative scheme following the spirit of the method of successive approximations (MSA), and it is robust to undesired collisions observed in the initial guesses.