A class of attractions/repulsion functions for stable swarm aggregations

Abstract

Abstract In this brief article, we consider an M-member `individual-based' continuous time swarm model in an n-dimensional space and extend the results in Gazi and Passino (Citation2003) by specifying a general class of attraction/repulsion functions that can be used to achieve swarm aggregation. These functions are odd functions that have terms for attraction and repulsion acting in opposite directions in compliance with real biological swarms. We present stability analysis for several cases of the functions considered to characterize swarm cohesiveness, size and ultimate motions while in a cohesive group. Moreover, we show how the model can be extended for achieving formation control. Furthermore, we discuss how the attraction repulsion functions can be modified to incorporate the finite body size of the swarm members. Numerical simulations are also presented for illustration purposes. Acknowledgements This work was supported by the DARPA MICA program via the AFRL under contract F33615-01-C-3151. Veysel Gazi was also partially supported by TÜBİTAK (the Scientific and Technical Research Council of Turkey). Veysel Gazi was originally with The Ohio State University, Department of Electrical Engineering, 2015 Neil Ave., Columbus, OH 43210, USA. Currently, he is with TOBB University of Economics and Technology (ETU), Department of Electrical and Electronics Engineering, Söğütözü Cad., No: 43, Söğütözü, 06530 Ankara, Turkey. Before joining TOBB ETU he spent two years at ATILIM University, Department of Electrical and Electronics Engineering, Kizilcaşar köyü, İncek, Gölbaşi, 06836 Ankara, Turkey.