An Exact Optimal Kinodynamic Planner Based on Homotopy Class Constraints

This paper proposes a kinodynamic planning algorithm for vehicles with bounds on actuation. The proposed approach is based on identification of homotopy classes to decompose the global obstacle avoidance problem into several simpler subproblems. We formulate the homotopic trajectory planning problem in a multiple phase trajectory optimization scheme, such that at each phase different kinematic constraints are active. This novel formulation satisfies the collision-free constraints and homotopy constraints at the same time.