Abstract

Abstract—This paper computes all the continuous point-transformation symmetries for a planar multi-agent dynamical control system. The relative configuration among the agents is often the most important aspect of this problem, and this paper presents a method to “factor out ” the location and orientation on the plane of a multi-agent formation problem. This is useful in the case where only the relative positioning of the agents is of concern. Furthermore, in the case where the location of the formation is still important, it provides a basis for splitting the problem into the “formation ” part and the “location of the formation ” part. The method to compute the symmetries and determine the reduced coordinates is well-established. The contributions of this paper are 1) computing the symmetries for a multi-agent system, 2) highlighting the utility of the reduction for the formation control application such as formation stability