Towards a unifying mathematical framework for pattern transformation in swarm systems
by Blesson Varghese, Gerard McKee
International Journal of Vehicle Autonomous Systems (IJVAS), Vol. 9, No. 1/2, 2011

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.

Online publication date: Fri, 10-Apr-2015

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