State-Feedback Optimal Motion Planning in the Presence of Obstacles

In this work, a solution to the kinematic optimal motion planning problem is presented, where a previous nearly globally optimal approach is extended to workspaces with inter- nal 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.