Modeling and simulating a mathematical tool for multi-robot pattern transformation

The work reported in this paper is motivated by the need to investigate general methods for pattern transformation. A formal definition for pattern transformation is provided and four special cases namely, elementary and geometric transformation based on repositioning all and some agents in the pattern are introduced. The need for a mathematical tool and simulations for visualizing the behavior of a transformation method is highlighted. A mathematical method based on the Moebius transformation is proposed. The transformation method involves discretization of events for planning paths of individual robots in a pattern. Simulations on a particle physics simulator are used to validate the feasibility of the proposed method.