Dispertio: Optimal Sampling for Safe Deterministic Sampling-Based Motion Planning

A key challenge in robotics is the efficient generation of optimal robot motion with safety guarantees in cluttered environments. Recently, deterministic optimal sampling-based motion planners have been shown to achieve good performance towards this end, in particular in terms of planning efficiency, final solution cost, quality guarantees as well as non-probabilistic completeness. Yet their application is still limited to relatively simple systems (i.e., linear, holonomic, Euclidean state spaces). In this work, we extend this technique to the class of symmetric and optimal driftless systems by presenting Dispertio, an offline dispersion optimization technique for computing sampling sets, aware of differential constraints, for sampling-based robot motion planning. We prove that the approach, when combined with PRM*, is deterministically complete and retains asymptotic optimality. Furthermore, in our experiments we show that the proposed deterministic sampling technique outperforms several baselines and alternative methods in terms of planning efficiency and solution cost.