Taming Heterogeneity and Complexity of Embedded Control

Dead-locks and Break of Symmetry in Robot Coordination

Isaac Corro Ramos¹ — Benedetto Piccoli²

¹ Department of Mathematics and Computer Science, Eindhoven University of Technology, P.O. Box 513, 5600 MB Eindhoven, The Netherlands [e-mail]

² Istituto per le Applicazioni del Calcolo “Mauro Picone”, Consiglio Nazionale delle Ricerche, Viale del Policlinico 137, 00161 Roma, Italy [e-mail]

ABSTRACT. The aim of this paper is to study the dead-locks produced by locally coordinate motion of robots with simplified dynamics. We assume that each agent is a point in the plane with the possibility of moving in any direction with bound on the norm of the velocity. The algorithms designed using cooperative controls are quite simple, thus it is possible to understand in detail the dead-locks that may appear. Once the typical dead-locks are analyzed, a special break of symmetry procedure is designed to exit the dead-lock manifold. Agents activate such procedure when they detect to be in dead-lock position.

KEYWORDS: Robot coordination, dead-locks, cooperative controls

1. Introduction

There is an increasing interest in the control community for agent team’s coordination by control methods [COR 03], [FAX 04], [KUM 05] and [LEO 01]. Such interest is motivated by various applications, among which most models come from robotics, where the technological progresses indicate the possibility of using large robot groups in near future, and biology, for natural group coordination ...