Swarm Patterns: Trends and Transformation Tools

The domain of multi-robot systems incorporates research which is inspired by nature. The aim of this research is to design man-made systems which incorporate principles observed in multi-agent natural systems. The mapping of these principles to man-made systems is referred to as biomimetics (Habib et al., 2007) and the area within multi-robot systems that explores this mapping is generally referred to as swarm robotic systems (Sahin & Spears, 2005). Research within swarm robotics includes self-organisation and an interesting aspect of self organisation is pattern formation (Camazine et al., 2003). The term pattern formation in literature is used in at least two different ways. Firstly, to define an area of study within multi robot systems that covers distinct aspects of patterns such as the establishment, maintenance and reconfiguration of patterns. Secondly, to report the natural phenomenon of flocking whereby loose or deformed geometric patterns emerge, and not necessarily strict geometric patterns (Arkin, 1998). In this chapter, the first usage of the term is adopted. The research in this chapter is motivated by two observations based on an extensive review of literature based on pattern formation and swarm robotics. Firstly, it was noted that there are no mathematical models that exist for pattern formation in swarm robotic systems. Secondly, it was also noted that though pattern formation was a classic area of research, yet the challenges that have emerged in due course have not been addressed through a unifying model. Hence, it was necessary to address the need for a unifying mathematical model that can surmount the identified challenges in pattern formation. The remainder of this chapter is organised as follows. The next section presents eight challenges identified in pattern formation. The second section sets the basic framework for mathematical modelling required to address the challenges. The fourth section presents a definition for transformation, four cases of transformation and tools for transformation. Simulation studies and a discussion are presented in the penultimate section. The last section concludes this chapter.