Symmetry Analysis Applied to Multi-Agent Systems

The multi-agent system of interest is a planar formation control problem, where each agent references a pre-specified number of agents. Since the formation control law does not specify the location and orientation of the formation in planar space, continuous symmetries arise. Through a previously established methodology, it is possible to calculate the continuous symmetries for a system of second order differential equations. The symmetries were found for a specific neighbor graph and were extended to the general case. The symmetries associated with planar motion were used to define coordinate transformations that reduced the system of interest to one in which the origin is the set of all possible formations. It is now possible to perform stability analysis of the formation by studying the stability properties of the origin of the reduced system. This will be beneficial for showing extended stability properties, like boundedness.