State-Feedback Optimal Motion Planning in the Presence of Obstacles

In this letter, a solution to the kinematic optimal motion planning problem is presented, where a previous nearly globally optimal approach is extended to workspaces with internal obstacles. The method is inspired by fundamental properties of velocity fields in the presence of obstacles, where topological restrictions inhibit naive approaches. The topological perplexity problem presents itself as a challenging issue for optimal control, even for low-dimensional cases with simple dynamics. Our scheme is formulated such that a locally optimal workspace decomposition enables extracting a close-to-optimal solution. Several synthetic workspace examples are demonstrated, along with comparisons against existing optimal approaches, where our scheme is superior w.r.t. both cost value and execution time.