Decentralized Task Allocation in Multi-Robot Systems via Bipartite Graph Matching Augmented with Fuzzy Clustering

TL;DR

This paper introduces a decentralized multi-robot task allocation algorithm that uses bipartite graph matching and fuzzy clustering, achieving near-optimal solutions with significantly improved scalability and robustness over centralized methods.

Contribution

The paper presents a novel Dec-MATA algorithm combining bipartite graph matching with fuzzy clustering for decentralized multi-robot task allocation, enhancing scalability and robustness.

Findings

Dec-MATA achieves 7-28% near-optimal cost compared to centralized MILP solutions.

Dec-MATA is 1-3 orders of magnitude faster than centralized algorithms.

Dec-MATA is minimally affected by task-to-robot ratios.

Abstract

Robotic systems, working together as a team, are becoming valuable players in different real-world applications, from disaster response to warehouse fulfillment services. Centralized solutions for coordinating multi-robot teams often suffer from poor scalability and vulnerability to communication disruptions. This paper develops a decentralized multi-agent task allocation (Dec-MATA) algorithm for multi-robot applications. The task planning problem is posed as a maximum-weighted matching of a bipartite graph, the solution of which using the blossom algorithm allows each robot to autonomously identify the optimal sequence of tasks it should undertake. The graph weights are determined based on a soft clustering process, which also plays a problem decomposition role seeking to reduce the complexity of the individual-agents' task assignment problems. To evaluate the new Dec-MATA algorithm, a series of case studies (of varying complexity) are performed, with tasks being distributed randomly over an observable 2D environment. A centralized approach, based on a state-of-the-art MILP formulation of the multi-Traveling Salesman problem is used for comparative analysis. While getting within 7-28% of the optimal cost obtained by the centralized algorithm, the Dec-MATA algorithm is found to be 1-3 orders of magnitude faster and minimally sensitive to task-to-robot ratios, unlike the centralized algorithm.