Dispersive Tree Agreements for Multi-Robot Coordination

Abstract

Multi-robot coordination of nonlinear systems is naturally formulated as joint-space optimal control subject to constraints over groups of robots. Existing methods that approach joint optimality remain largely centralized, offline, and confined to collision-free motion planning, while decentralized, real-time counterparts target safe navigation without pursuing the joint optimum. This paper develops a decentralized, real-time planner that approaches the joint optimum as an anytime process. We extend a recent single-robot framework that searches dispersive trees of forward-propagated commands for differentially flat systems to coordinate a multi-robot team near-optimally. We first show that the inter-robot coupling can be effectively replaced by some local constraints, under which locally grown dispersive trees contain a near-optimal agreement. It is this structure that the robots pursue by decentralized column generation, negotiating rents on the shared space that guide the search of each robot's tree. The negotiation settles on an agreement whose near-optimality is certified at quiescence. Our protocol, WarpWeaver, implements this negotiation as an asynchronous real-time loop over a receding horizon, and demonstrates effective closure to quiesced agreements even when real-time deadlines cut the negotiation short. In simulation, WarpWeaver reduces total travel time by up to 22% against centralized offline planners on the Dynobench suite and by up to 37% against a decentralized real-time baseline, and nearly doubles the success rate of a task-specific planner on graph connectivity. Hardware experiments on six robots planning onboard demonstrate real-world implementability.