Numerical Solution of Hybrid Optimal Control Problems with Applications in Robotics

Abstract: Numerical solution techniques for a class of hybrid (discrete event / continuous variable) optimal control problems (HOCP) are described, and their potential use in robotic applications is demonstrated. HOCPs are inherently combinatorial due to their discrete event aspect which is one of the main challenges when numerically solving for optimal hybrid trajectories. One may associate a continuous nonlinear multi-phase problem with each possible discrete state sequence. Two solution techniques for obtaining suboptimal solutions are presented (both based on numerical direct collocation): one fixes interior point constraints on a grid, another uses branch-and-bound. Numerical results of a robotic multi-arm transport task and an underactuated robot are presented.