Balanced deployment of multiple robots using a modified kuramoto model

In this paper, we study the problem of making multiple agents spread out equidistantly on a circle. The proposed solution is a new Kuramoto-like model for multi-robot coordination, in which the standard sine-terms have been replaced by cosines. This new interaction model enables the balanced deployment of agents on a circle, while only taking into account the local information of each agent´s two neighbors on a cycle graph. This means that individual agents do not need to know the (relative) states of all agents nor how many other agents are indeed present in the network. We illustrate the operation of the proposed protocol in simulation as well as extend it to a nonlinear scenario by optimizing over the coupling weights.