Risk-Aware and Scalable Hierarchical Motion Planning for Large-Scale Robotic Swarms Via CVaR-Constrained MPC (I)

Abstract

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 riskawareness 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 Valueat-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.