Dynamic Multi-Robot Task Allocation under Uncertainty and Communication Constraints: A Game-Theoretic Approach

Most multi-robot task allocation methods rely on communication to resolve conflicts and reach consistent assignments. In environments with limited bandwidth, degraded infrastructure, or adversarial interference, existing approaches degrade sharply. We introduce a learning-based framework that achieves high-quality task allocation without any robot-to-robot communication. The key idea is that robots coordinate implicitly by predicting teammates' bids: if each robot can anticipate competition for a task, it can adjust its choices accordingly. Our method predicts bid distributions to correct systematic errors in analytical mean-field approximations. While analytical predictions assume idealized conditions (uniform distributions, known bid functions), our learned approach adapts to task clustering and spatial heterogeneity. Inspired by Smart Predict-then-Optimize (SPO), we train predictors end-to-end to minimize Task Allocation Regret rather than prediction error. To scale to large swarms, we develop a mean-field approximation where each robot predicts the distribution of competing bids rather than individual bids, reducing complexity from $O(NT)$ to $O(T)$. We call our approach FORMICA: Field-Oriented Regret-Minimizing Implicit Coordination Algorithm. Experiments show FORMICA substantially outperforms a natural analytical baseline. In scenarios with 16 robots and 64 tasks, our approach improves system reward by 17% and approaches the optimal MILP solution. When deployed on larger scenarios (256 robots, 4096 tasks), the same model improves performance by 7%, demonstrating strong generalization. Training requires only 21 seconds on a laptop, enabling rapid adaptation to new environments.

Selecting a decentralized Multi-Robot Task Allocation (MRTA) method for embedded deployment on autonomous platforms requires considering more than route performance alone. We benchmark six decentralized MRTA allocators (CBAA, ACBBA, PI, HIPC, DMCHBA, and DGA) in the Collaborative Visit (CV) scenario to characterize tradeoffs among MinMax and MinSum travel, communication robustness and demand, allocation reliability, computational burden, and scale sensitivity. The core study uses 500 paired ten-target instances across 25 ideal and degraded communication conditions spanning Bernoulli loss, Gilbert--Elliott loss, and Rayleigh fading, with additional campaigns examining pre-allocation, execution-integrated computation, and sensitivity to grid size, robot density, and target load. Across the 24 impaired core conditions, DGA and DMCHBA achieved the lowest mean MinMax travel at 24.49 and 24.78 steps, respectively. HIPC narrowly led mean MinSum travel at 66.95 steps, followed by DGA at 67.22, with both methods occupying the top two in every impaired condition. DMCHBA had the lowest publication intensity at 2.08 publications per team step. In ten-target pre-allocation, HIPC and DMCHBA remained viable and stable in every tested condition, while ACBBA, PI, and DGA lost stability or viability as communication degraded. Under ideal delivery, median full-protocol computation $\Cterm$ in the primary ten-target comparison ranged from 4.88 ms for DMCHBA to 1.346 s for DGA. Static route quality preserved DGA and DMCHBA as the leading MinMax methods, while DGA led MinSum at three of four target loads and HIPC led at 50 targets. Static and execution-integrated computation rankings diverged as task load increased. The results identify distinct allocator operating regions across route objective, communication behavior, reliability, and computational constraints.

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.