Motion planning with time-varying polyhedral obstacles based on graph search and mathematical programming

A method is presented for path planning of a point robot moving among polyhedral obstacles with piecewise constant translating velocity. Representing the obstacles as polyhedra in the space-time domain allows a collision-free, minimum-time path to be obtained using graph search and linear programming. The planner views the space-time configuration of free space as disjoint polytopes where each point in the space-time domain is mapped into a unique polytope. The planner searches connected polytopes between the start and goal polytopes that satisfy the speed and time constraints. A near-optimal trajectory is determined by constrained optimization. In the proposed approach, the obstacle is allowed to move faster than the point robot, and the methodology can be easily extended to motion planning in higher-dimensional spaces