SwarmPRM: Probabilistic Roadmap Motion Planning for Large-Scale Swarm Robotic Systems

TL;DR

SwarmPRM is proposed, a hierarchical, scalable, computationally efficient, and risk-aware sampling-based motion planning approach for large-scale swarm robots that 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.

Abstract

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.

Figures (3)

• Figure 1: Illustration of the hierarchical motion planning for a large-scale robot swarm. (a) The macroscopic planning of the swarm robots. In the two-dimensional cluttered environment $\mathcal{W}$ with four obstacles $\mathcal{O}_1,\mathcal{O}_2,\mathcal{O}_3,\mathcal{O}_4$, the swarm's macroscopic state, represented as a PDF, is depicted as a blue cloud, and individual robots at time $T_0$ are represented by black dots. The macroscopic trajectory, as represented by the black dotted lines and colored arrows, guides the swarm from initial area at time $T_0$ to the target area at time $T_f$, passing through two intermediate macroscopic states at time $T_1$ and $T_2$, respectively. The trajectory may involve "splitting" or "merging" maneuvers, depicted by the orange and red dotted lines and arrows, respectively. (b) The microscopic state of robots in the swarm. The robots track the macroscopic state while avoiding collision with obstacles.
• Figure 2: SwarmPRM motion planning process at the macroscopic stage. (a) Projection of the risk-aware Gaussian roadmap onto the workspace $\mathcal{W}$, with obstacles $\mathcal{O}_1, \mathcal{O}_2, \mathcal{O}_3, \mathcal{O}_4$ colored in light orange. Each black dot represents a node in the Gaussian roadmap, corresponding to a two-dimensional Gaussian distribution. The black polyline depicts the shortest path between Gaussian distributions $g_{T_0}^i$ and $g_{T_f}^j$ on the roadmap. (b) Each polyline segment represents an edge in the Gaussian roadmap, illustrating the shortest geodesic path between two nodes based on the Wasserstein metric. The CVaR associated with each Gaussian node is required to be below the safe region threshold $\delta$. (c) Through graph search, the lowest transport cost $\mathcal{L}(g_{T_0}^i,g_{T_f}^j)$ between each pair of Gaussian distributions $(g_{T_0}^i,g_{T_f}^j)$ can be computed. The optimal GMM trajectory on the Gaussian roadmap is then calculated by solving a linear programming problem.
• Figure 3: Qualitative simulation results. The trajectories of the swarm robotic system comprised of $N=500$ robots obtained by (a) SwarmPRM, (b) Formation control, and (c) ADOC. The initial and final positions are represented by colored circles on the left and right sides of each subfigure, respectively, while the obstacles are depicted in black color.