A Game-theoretic Formulation of the Homogeneous Self-Reconfiguration Problem

In this paper we formulate the homogeneous two- and three-dimensional self-reconfiguration problem over discrete grids as a constrained potential game. We develop a game-theoretic learning algorithm based on the Metropolis-Hastings algorithm that solves the self-reconfiguration problem in a globally optimal fashion. Both a centralized and a fully distributed algorithm are presented and we show that the only stochastically stable state is the potential function maximizer, i.e. the desired target configuration. These algorithms compute transition probabilities in such a way that even though each agent acts in a self-interested way, the overall collective goal of self-reconfiguration is achieved. Simulation results confirm the feasibility of our approach and show convergence to desired target configurations.Comment: 8 pages, 5 figures, 2 algorithm

Self-Reconfiguration Using Graph Grammars for Modular Robotics

Presented at the 4th IFAC Conference on Analysis and Design of Hybrid Systems, June 6-8, 2012, Eindhoven, Netherlands.DOI: 10.3182/20120606-3-NL-3011.00050In this paper, we apply graph grammars to self-reconfigurable modular robots and present a method to reconfigure arbitrary initial configurations into pre specified target configurations thus connecting the motions of modules to formal assembly rules. We present an approach for centralized reconfiguration planning and decentralized, rule-based reconfiguration execution for three-dimensional modular structures. The reconfiguration is done in two stages. In the first stage, paths are planned for each module and then rewritten into production rules as defined for graph grammars. In stage two, these rules are applied in a decentralized fashion by each node individually. We show that our approach yields a unique reconfiguration sequence and a graph grammar that results in the target configuration being the only reachable stable configuratio