  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.
