A Self-Learning Approach to Heterogeneous Multi-Robot Coalition Formation Under Uncertainty

Coalition structure is an effective cooperation architecture for task implementation in the field of multi-robot systems. Nevertheless, the presence of uncertainty inherently complicates the decision-making process for robots and may potentially result in suboptimal coordination. To tackle this challenge, this paper considers an uncertain multi-robot coalition formation scenario in which task information (the types of all tasks) is incompletely known to robots. Given the local beliefs of robots, the problem of multi-robot coalition formation under uncertainty is formulated as a coalition formation game. In this game, each robot is a rational and self-interested player and tends to join a coalition according to its preference. A polynomial-time coalition formation algorithm is proposed to identify the social agreement, i.e., Nash stable partition, among the robots. The convergence of the proposed algorithm is strictly guaranteed as long as the communication topology of the considered system is strongly connected. The coalition formation game is then extended to a dynamic game, and we propose a belief updating algorithm that enables robots to update their beliefs as the game is played repeatedly. Simulation results demonstrate the effectiveness of our proposed algorithms, and the robots will eventually learn the true type of each task. Note to Practitioners-The work reported in this article will be beneficial for deploying multi-robot systems to support cooperative surveillance applications. In these scenarios, robots can form stable coalitions to perform surveillance tasks, even when the task information is incompletely known due to sensor noise or limited sensor range. The problem of multi-robot coalition formation is known to be NP-hard, which becomes even more challenging when uncertainty is taken into account. This paper proposes game-based algorithms to solve the problem of multi-robot coalition formation under uncertainty. Some practical schemes are introduced as benchmarks to further illustrate the performance improvement brought by our proposed algorithms. The proposed algorithms are further evaluated through a real-world experiment, demonstrating their effectiveness for practical application.