SwarmPRM: Probabilistic Roadmap Motion Planning for Swarm Robotic Systems

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.

ROVER: Risk-Aware Swarm Robotics MOtion Planner Using Conditional ValuE at Risk

The field of swarm robotics has attracted considerable interest for its capacity to complete intricate and synchronized tasks. Existing methodologies for motion planning within swarm robotic systems mainly encounter difficulties in scalability and safety guarantee. To address these two limitations, we propose a Risk-aware swarm mOtion planner using conditional ValuE at Risk (ROVER) that systematically modulates the safety and conservativeness and navigates the swarm to the target area through cluttered environments. Our approach formulates a finite-time model predictive control (FTMPC) problem predicated upon the macroscopic state of the robot swarm represented by Gaussian Mixture Model (GMM) and integrates conditional value-at-risk (CVaR) to avoid collision. We leverage the linearized Signed Distance Function for the efficient computation of CVaR concerning the proximity between the robot swarm to obstacles. The key component of this method is implementing CVaR constraint under GMM uncertainty in the FTMPC to measure the collision risk that a robot swarm faces. However, the non-convex constrained FTMPC is nontrival to solve. To navigate this complexity, we develop a computationally tractable strategy through 1) an explicit linear approximation of the CVaR constraint; and 2) a sequential quadratic programming formulation. Simulations and comparisons with other approaches demonstrate the effectiveness of the proposed method in flexibility, scalability, and risk mitigation.