Large-scale swarm robotic systems consisting of numerous cooperative agents show considerable promise for performing autonomous tasks across various sectors. Nonetheless, traditional motion planning approaches often face a trade-off between scalability and solution quality due to the exponential growth of the joint state space of robots. In response, this work proposes SwarmPRM, a hierarchical, scalable, computationally efficient, and risk-aware sampling-based motion planning approach for large-scale swarm robots. SwarmPRM utilizes a Gaussian Mixture Model (GMM) to represent the swarm's macroscopic state and constructs a Probabilistic Roadmap in Gaussian space, referred to as the Gaussian roadmap, to generate a transport trajectory of GMM. This trajectory is then followed by each robot at the microscopic stage. To enhance trajectory safety, SwarmPRM incorporates the conditional value-at-risk (CVaR) in the collision checking process to impart the property of risk awareness to the constructed Gaussian roadmap. SwarmPRM then crafts a linear programming formulation to compute the optimal GMM transport trajectory within this roadmap. Extensive simulations demonstrate that SwarmPRM outperforms state-of-the-art methods in computational efficiency, scalability, and trajectory quality while offering the capability to adjust the risk tolerance of generated trajectories.

翻译：由大量协同智能体构成的大规模群体机器人系统在跨领域自主任务执行中展现出显著潜力。然而，传统运动规划方法由于机器人联合状态空间的指数级增长，往往在可扩展性和求解质量之间存在权衡。针对此问题，本文提出SwarmPRM——一种面向大规模群体机器人、具有分层可扩展、计算高效且风险感知特性的基于采样的运动规划方法。SwarmPRM采用高斯混合模型（GMM）表征群体宏观状态，并在高斯空间中构建概率路线图（称为高斯路线图）以生成GMM的传输轨迹，随后每个机器人在微观阶段跟踪该轨迹。为增强轨迹安全性，SwarmPRM在碰撞检测过程中引入条件风险价值（CVaR），赋予所构建高斯路线图风险感知特性。进而，SwarmPRM设计线性规划公式计算该路线图内的最优GMM传输轨迹。大量仿真结果表明，SwarmPRM在计算效率、可扩展性和轨迹质量方面优于现有最优方法，同时具备调节生成轨迹风险容忍度的能力。