Towards a Unifying Framework for Pattern Transformation in Swarm Systems

Abstract

This paper identifies the major challenges in the area of pattern formation. The work is also motivated by the need for development of a single framework to surmount these challenges. A framework based on the control of macroscopic parameters is proposed. The issue of transformation of patterns is specifically considered. A definition for transformation and four special cases, namely elementary and geometrical transformations by repositioning all or some robots in the pattern are provided. Two feasible tools for pattern transformation namely, a macroscopic parameter method and a mathematical tool—Moebius transformation also known as the linear fractional transformation are introduced. The realization of the unifying framework considering planning and communication is reported.