Symmetries of Multiagent Systems and Formation Stability

This work is part of a larger research effort investigating the role of symmetries in control of large-scale cyberphysical-systems (CPS). Most prior efforts have considered discrete symmetries, and the work in this paper reflects our initial efforts directed toward investigating continuous symmetries. Specifically, we consider a formation control problem, limited for now to only two agents, and determine all the point transformation symmetries associated with that system. We also determine a reduced description of the dynamics of the system particularly important for formation control and show stability of the system in those coordinates.