Swarm robotic systems consisting of large-scale cooperative agents hold promise for performing autonomous tasks in diverse fields. However, existing planning strategies for swarm robotic systems often encounter a trade-off between scalability and solution quality. We introduce here SwarmPRM, a hierarchical, highly scalable, computationally efficient, and risk-aware sampling-based motion planning approach for swarm robotic systems, which is asymptotically optimal under mild assumptions. We employ probability density functions (PDFs) to represent the swarm's macroscopic state and utilize optimal mass transport (OMT) theory to measure the swarm's cost to go. A risk-aware Gaussian roadmap is constructed wherein each node encapsulates a distinct PDF and conditional-value-at-risk (CVaR) is employed to assess the collision risk, facilitating the generation of macroscopic PDFs in Wasserstein-GMM space. Extensive simulations demonstrate that the proposed approach outperforms state-of-the-art methods in terms of computational efficiency and the average travelling distance.

翻译：由大规模协同智能体组成的集群机器人系统有望在多个领域自主执行任务。然而，现有集群机器人系统规划策略常在可扩展性与解质量之间面临权衡。本文提出SwarmPRM——一种层次化、高度可扩展、计算高效且具有风险意识的基于采样的运动规划方法，该方法在温和假设下具有渐近最优性。我们采用概率密度函数表征集群的宏观状态，并利用最优质量传输理论衡量集群的移动代价。通过构建风险感知高斯路线图，其中每个节点封装不同的概率密度函数，并采用条件风险值评估碰撞风险，从而在Wasserstein-GMM空间中生成宏观概率密度函数。大量仿真结果表明，所提方法在计算效率与平均移动距离方面均优于现有先进方法。