Symmetry Invariance of Multiagent Formations in Self-Pursuit

Structure in the interconnection topology among individuals of a multiagent system plays a fundamental role in the system's steady-state and transient behaviors. This paper explores how certain interconnection topologies influence symmetry in a multiagent system's trajectories. It is shown how circulant connectivity preserves rotation, and in particular instances, dihedral group symmetries in a formation of locally interacting planar integrators. Moreover, it is revealed to what extent circulant connectivity is also necessary in order that symmetric formations remain symmetric under the multiagent system's dynamics.