In this paper, we investigate the Walk on Spheres algorithm (WoS) for motion planning in robotics. WoS is a Monte Carlo method to solve the Dirichlet problem developed in the 50s by Muller and has recently been repopularized by Sawhney and Crane, who showed its applicability for geometry processing in volumetric domains. This paper provides a first study into the applicability of WoS for robot motion planning in configuration spaces, with potential fields defined as the solution of screened Poisson equations. The experiments in this paper empirically indicate the method's trivial parallelization, its dimension-independent convergence characteristic of $O(1/N)$ in the number of walks, and a validation experiment on the RR platform.

翻译：本文研究了机器人运动规划中的球面行走算法。WoS是一种蒙特卡洛方法，最初由Muller于20世纪50年代提出用于解决狄利克雷问题，最近经Sawhney和Crane重新推广，展示了其在体积域几何处理中的适用性。本文首次研究了WoS在构型空间中机器人运动规划的适用性，其中势场定义为屏蔽泊松方程的解。实验结果表明该方法具有天然的并行性，其收敛特性与维度无关且满足$O(1/N)$的行走次数关系，并在RR平台上进行了验证实验。