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

TL;DR

This paper models the homogeneous self-reconfiguration problem as a constrained potential game and introduces a game-theoretic learning algorithm that guarantees convergence to the desired configuration in both centralized and distributed settings.

Contribution

It formulates the self-reconfiguration problem as a potential game and develops a novel Metropolis-Hastings based algorithm ensuring global optimality and convergence.

Findings

Algorithm converges to the target configuration

Both centralized and distributed algorithms are effective

Simulation confirms feasibility and convergence

Abstract

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.