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.
The following analysis is generated by AI and may contain errors. It is separate from the authors’ abstract and is not peer review.
Research summary
WarpWeaver introduces a decentralized, real-time multi-robot coordination protocol that achieves near-optimal joint control by extending dispersive forward tree search via decentralized column generation, providing certified near-optimality at quiescence and demonstrating significant improvements over centralized and decentralized baselines in both simulation and hardware.
Methodology
The paper proposes WarpWeaver, a decentralized, real-time multi-robot coordination protocol that leverages dispersive forward tree search (DFT) for differentially flat systems. The core innovation is the formulation of joint optimal control as a decentralized column generation problem. The authors prove that inter-robot coupling can be replaced by local constraints (corridors) such that locally grown trees contain a near-optimal agreement. They utilize the dual variables of a restricted master problem (an ILP relaxation) as "rents" on shared space, which guide the local tree search of each robot. This creates a negotiation loop where robots propose columns (trajectories) based on current prices, and the pool of columns is updated until quiescence or a real-time deadline. The theoretical contribution is significant, providing a certificate of near-optimality at quiescence relative to the joint optimum, which is a strong guarantee for decentralized methods that often lack such bounds. The extension from single-robot DFT to multi-robot coordination via column generation is a clever and rigorous application of operations research techniques to robotics.
Results & evaluation
The evaluation is comprehensive, covering simulation benchmarks (Dynobench) and hardware experiments. In simulation, WarpWeaver outperforms centralized offline planners in travel time (up to 22% reduction) and decentralized real-time baselines (up to 37% reduction). It also demonstrates superior success rates on connectivity maintenance tasks compared to task-specific planners. The hardware experiments on six robots planning onboard validate the real-time feasibility and robustness of the approach. The use of high-fidelity nonlinear quadrotor models and differentially flat systems (unicycles, integrators) shows the method's generality. The comparison against both centralized (offline) and decentralized (real-time) baselines is appropriate and highlights the trade-off between optimality and real-time performance.
Reproducibility
The paper provides detailed algorithmic descriptions (Algorithm 1) and specifies search parameters, command sets, and dynamics for various platforms in Table 1. The use of standard benchmarks like Dynobench aids reproducibility. However, specific implementation details of the "dispersive tree" generation and the exact solver for the dual problem are not fully detailed in the provided text, though references to prior single-robot work are made. The code availability is not explicitly stated in the abstract or intro, but the level of detail suggests it is reproducible by experts in the field.
Limitations
The method assumes differentially flat dynamics, which limits its applicability to systems that are not flat or where flatness is difficult to establish. The computational cost of growing dispersive trees, while polynomial, can still be high for large teams or long horizons, though the decentralized nature mitigates this. The "rents" mechanism relies on the structure of the ILP, which may not generalize easily to non-convex or highly complex joint constraints beyond the Lipschitz predicates assumed. The real-time performance depends on communication delays and computational resources, which may vary in real-world deployments.
Broader impact
This work bridges the gap between rigorous optimal control theory and practical real-time multi-robot coordination. It provides a framework for decentralized planning with optimality guarantees, which is valuable for applications requiring high precision and safety, such as drone swarms, autonomous vehicle fleets, and industrial automation. The use of column generation for coordination is a novel paradigm that could inspire further research in distributed optimization for robotics. WarpWeaver introduces a decentralized, real-time multi-robot coordination protocol that achieves near-optimal joint control by extending dispersive forward tree search via decentralized column generation, providing certified near-optimality at quiescence and demonstrating significant improvements over centralized and decentralized baselines in both simulation and hardware.
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