Sampling-based motion planning methods, while effective in high-dimensional spaces, often suffer from inefficiencies due to irregular sampling distributions, leading to suboptimal exploration of the configuration space. In this paper, we propose an approach that enhances the efficiency of these methods by utilizing low-discrepancy distributions generated through Message-Passing Monte Carlo (MPMC). MPMC leverages Graph Neural Networks (GNNs) to generate point sets that uniformly cover the space, with uniformity assessed using the the $\cL_p$-discrepancy measure, which quantifies the irregularity of sample distributions. By improving the uniformity of the point sets, our approach significantly reduces computational overhead and the number of samples required for solving motion planning problems. Experimental results demonstrate that our method outperforms traditional sampling techniques in terms of planning efficiency.

翻译：基于采样的运动规划方法虽在高维空间中有效，但常因采样分布不规则导致构型空间探索不充分，从而存在效率低下的问题。本文提出一种利用消息传递蒙特卡洛（MPMC）生成低差异分布来提升此类方法效率的新途径。MPMC借助图神经网络（GNNs）生成均匀覆盖空间的点集，其均匀性通过$\cL_p$-差异度量进行评估——该指标可量化采样分布的不规则程度。通过提升点集的均匀性，本方法显著降低了运动规划问题的计算开销与所需样本数量。实验结果表明，该方法在规划效率方面优于传统采样技术。