The dynamics of Mutual Motion Camouflage

In this paper we show that a biologically-plausible pursuit law, designed to implement the motion camouflage strategy, can be used as a building-block for generating collective motion. We introduce the fundamental case of two individuals in mutual pursuit, which we refer to as Mutual Motion Camouflage, and completely characterize its dynamics. The resulting system is of theoretical interest, because of its rich symmetry and a certain similarity with the Kepler problem of celestial mechanics, concerning the dynamics of two point particles under mutual gravitational attraction. It is also of practical interest, because the individual trajectories have useful spatial coverage properties.