A unified approach for robot motion planning with moving polyhedral obstacles

A unified approach suitable for path planning with moving polyhedral obstacles is presented. The planner views the space-time configuration of free space as disjoint polytopes that represent a time-dependent environment consisting of moving and stationary objects. Each point in the space-time domain is mapped into a unique polytope set. The planner then constructs a family of feasible collision-free trajectories by searching connected polytopes between the start polytope and the goal polytope that satisfy the speed and time constraints. Finally, a near-optimal trajectory is determined by constrained optimization. This approach does not require that obstacles be nonoverlapping or noncolliding. In addition, the obstacle is allowed to move faster than the planned robot. However, the speed of the obstacle must be piecewise-constant. The proposed approach can be easily extended to motion planning in higher dimensional spaces