FORMICA: Decision-Focused Learning for Communication-Free Multi-Robot Task Allocation

This paper proposes a communication-free multi-robot task allocation framework based solely on local observations. In this study, tasks are defined as reaching target locations. Each robot estimates the positions of neighboring robots using a Labeled Multi-Bernoulli (LMB) filter and independently assigns tasks through a greedy auction-based strategy. By continuously updating state estimates and reallocating tasks during execution, the proposed method enables decentralized coordination without explicit communication. Monte Carlo simulations demonstrate that the proposed method enables effective cooperative task allocation without inter-robot communication while remaining robust to measurement clutter and observation uncertainty.

Multi-robot task allocation (MRTA) in dynamic environments faces a fundamental tension: effective coordination requires learned structure, but that structure must adapt when conditions change. Existing methods resolve this by assuming prior task knowledge, a utility function, a cost matrix, or a trained policy making them brittle when deployed without such knowledge or when task distributions shift. We present MORPH(Multi-agent Online Rewiring through Plasticity-guided Hierarchy), a training-free MRTA framework where global allocation quality emerges from 4 local plasticity rules (synaptic, homeostatic, structural, and metaplasticity) applied to a directed pairwise preference matrix updated from runtime co-occurrence and task-completion feedback. MORPH requires no task model, no bid computation, and no offline training; response decisions use learned AGV-to-Picker preferences rather than a fixed proximity rule. Within the Gerkey-Mataric MRTA taxonomy, MORPH is the first method in the single-task, single-robot, instantaneous-assignment class to learn directed pairwise allocation preferences online. Evaluated on the TA-RWARE warehouse benchmark (8-24 agents, 4 maps, 800 steps per episode, 5 seeds), MORPH achieves 110% of all-to-all throughput at N=24 while using only 21% of possible coordination links as an efficiency advantage that grows monotonically with fleet size. Under spatial task distribution shift, MORPH degrades 3x less than proximity-based methods while its learned preferences remain uncorrelated with Manhattan distance. Systematic ablation confirms all four plasticity rules contribute measurably. Two allocation properties emerge without programming: cross-type preference dominance and progressive preference sparsification, mirroring the developmental refinement of biological neural circuits. Learned preferences are driven by task co-occurrence history, not spatial proximity.

Multi-Robot Task Allocation (MRTA) is a central challenge in decentralized multi-agent systems, where teams of robots must cooperatively assign and execute tasks under limited communication while optimizing global performance objectives. Auction-consensus algorithms, such as the Consensus-Based Bundle Algorithm (CBBA), provide scalable decentralized coordination with provable convergence, but rely on hand-crafted greedy scoring functions that often lead to suboptimal task allocations. This paper proposes a learning-enhanced auction-consensus framework in which CBBA's deterministic bidding mechanism is replaced by a neural bidding policy trained using reinforcement learning. Under a centralized training and decentralized execution paradigm, agents learn to compute task bids from partial local observations while retaining the standard auction and consensus phases for decentralized coordination. The learned bidding policy is trained using Proximal Policy Optimization with rewards shaped by proximity to globally optimal solutions obtained via mixed-integer linear programming. Multiple neural architectures are evaluated, including a Neural Additive Model, the Long Short-Term Memory (LSTM) model, and the Set Transformer Model. Experimental results across varying swarm sizes demonstrate that learned bidding policies can improve solution quality over classical CBBA while preserving decentralized execution. The proposed approach highlights the effectiveness of integrating reinforcement learning with classical distributed coordination algorithms, offering a scalable pathway toward higher-quality decentralized multi-robot task allocation.