Risk-Aware and Scalable Hierarchical Motion Planning for Large-Scale Robotic Swarms via CVaR-Constrained MPC

Motion planning for large-scale robotic swarms presents significant challenges in terms of scalability and safety assurance in cluttered environments. To address these issues, this manuscript proposes a Closed-loop hierarchical Risk-aware swarm mOtion planner using Conditional ValuE at Risk (C-ROVER) that enables safe and efficient navigation for swarm robotic systems. The hierarchical structure of C-ROVER comprises a macroscopic planning stage that models the swarm state with Gaussian Mixture Models (GMMs) and generates trajectories for the swarm GMM, followed by a microscopic control stage that computes individual robot control using distributed model predictive control to track the GMM trajectories while achieving robot-level collision avoidance. Robot positions are periodically used to update the swarm GMM, closing the hierarchical planning and control loop. To achieve collision risk-awareness between the swarm and environmental obstacles at the macroscopic stage, C-ROVER leverages the stochastic Signed Distance Function to characterize the distance between the swarm GMM and obstacles, which is proven to follow a GMM. Then C-ROVER proposes an analytical expression of Conditional Value-at-Risk (CVaR) of a GMM to enable the swarm collision risk mitigation. Furthermore, C-ROVER designs a novel risk-aware space discretization approach to enhance the ability to navigate constrained spaces. To achieve efficient online motion planning, C-ROVER develops a convergent sequential convex programming approach for macroscopic planning, leveraging the concavity of CVaR constraints. C-ROVER has been evaluated through various simulations and real-world experiments, demonstrating its capability to ensure safe, scalable, and real-time swarm navigation in cluttered scenarios.