Enhancing Self-similar Patterns by Asymmetric Artificial Potential Functions in Partially Connected Swarms

Extended Abstract The control of mobile robotic agents is required to be highly reliable. Artificial potential function (APF) methods have previously been assessed in the literature for providing stable and verifiable control, whilst maintaining a high degree of nonlinearity. Further, these methods can, in theory, be characterised by a full analytic treatment. Many examples are available in the literature of the employment of these methods for controlling large ensembles of agents that evolve into minimum energy configurations corresponding in many cases to regular lattices [1-2]. Although regular lattices can present naturally centric symmetry and self-similarity characteristics, more complex formations can also be achieved by several other means. In [3] the equilibrium configuration undergoes bifurcation by changing a parameter belonging to the part of artificial potential that couples the agents to the reference frame. In this work it is shown how the formation shape produced can be controlled in two further ways, resulting in more articulated patterns. Specifically the control applied is to alter the symmetry of interactions amongst agents, and/or by selectively rewiring interagent connections. In the first case, the network of connections remains the same, and may be fully connected. In the second some links are rewired with possible changes of APF parameters, this can be better understood considering a group of 5 mobile agents interacting through Morse-like potentials, which Ca, Cr, la, lr to defined the potential shaping parameters and ij x as the inter-agent distance is defined as;     exp / exp / ij a ij r ij U C x la C x lr      . When all the agents are subjected to the