Dispersion-Minimizing Motion Primitives for Search-Based Motion Planning

Search-based planning with motion primitives is a powerful motion planning technique that can provide dynamic feasibility, optimality, and real-time computation times on size, weight, and power-constrained platforms in unstructured environments. However, optimal design of the motion planning graph, while crucial to the performance of the planner, has not been a main focus of prior work. This paper proposes to address this by introducing a method of choosing vertices and edges in a motion primitive graph that is grounded in sampling theory and leads to theoretical guarantees on planner completeness. By minimizing dispersion of the graph vertices in the metric space induced by trajectory cost, we optimally cover the space of feasible trajectories with our motion primitive graph. In comparison with baseline motion primitives defined by uniform input space sampling, our motion primitive graphs have lower dispersion, find a plan with fewer iterations of the graph search, and have only one parameter to tune.