Title: Towards a unifying mathematical framework for pattern transformation in swarm systems

Authors: Blesson Varghese, Gerard McKee

Addresses: School of Systems Engineering, University of Reading, Whiteknights Campus, Reading, Berkshire RG6 6AY, UK. ' School of Systems Engineering, University of Reading, Whiteknights Campus, Reading, Berkshire RG6 6AY, UK

Abstract: This paper identifies major challenges in the area of pattern formation and motivates the need for developing a single framework to surmount these challenges. A framework based on macroscopic parameters for transforming patterns is proposed. A definition for transformation and four special cases, namely elementary and geometrical transformations by repositioning all or a few robots in a pattern are provided. Two feasible tools for transforming patterns namely, a macroscopic parameter method and a mathematical tool based on Moebius transformation are introduced. Simulation of the latter method and real-time issues in realising the tools are also reported in this paper.

Keywords: unifying framework; swarm systems; pattern formation; pattern transformation; simulation; robot formations; robot cooperation; multiple robots; multi-robot systems; Moebius transformation.

DOI: 10.1504/IJVAS.2011.038180

International Journal of Vehicle Autonomous Systems, 2011 Vol.9 No.1/2, pp.63 - 77

Received: 16 Aug 2009
Accepted: 30 Mar 2010
Published online: 10 Apr 2015 *

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