Relay-Based Coordination for Energy-Efficient Multi-Robot Pickup and Delivery

arXiv:2509.14127v2 Announce Type: replace Abstract: We consider the problem of delivering multiple packages from a single depot to distinct goal locations using a homogeneous fleet of robots with limited carrying capacity. We propose VCST-RCP, a Voronoi-Constrained Steiner Tree Relay Coordination Planning framework that explicitly treats inter-robot relays as a design primitive. The approach operates in two stages: (i) constructing a sparse relay backbone by combining Voronoi-derived exchange interfaces with Steiner tree optimization, and (ii) synthesizing robot-level pickup, relay, and delivery schedules under capacity and service-time constraints. Unlike traditional methods that rely on direct source-to-destination transport, our framework organizes package flow through a shared relay network, reducing redundant long-haul motion. Extensive experiments across multiple scales show that VCST-RCP reduces total fleet travel distance by an average of 31% (up to nearly 50%) compared to Hungarian assignment and significantly outperforms OR-Tools CVRP, with statistically significant improvements (p < 10^{-3}). These gains translate into over 50% higher delivery efficiency (packages per kilometer), directly improving energy utilization. An ablation study further reveals that optimizing relay placement yields substantially larger improvements than adapting spatial partitioning alone, establishing relay design as the dominant factor governing system performance. Overall, the results demonstrate that relay-based coordination provides a scalable and effective framework for energy-aware multi-robot delivery in real-world logistics settings.