Title: Beacon-referenced Mutual Pursuit in Three Dimensions,
Abstract: Motivated by station-keeping applications in various unmanned settings, this
paper introduces a steering control law for a pair of agents operating in the
vicinity of a fixed beacon in a three-dimensional environment. This feedback
law is a modification of the previously studied three-dimensional constant
bearing (CB) pursuit law, in the sense that it incorporates an additional term
to allocate attention to the beacon. We investigate the behavior of the
closed-loop dynamics for a two agent mutual pursuit system in which each agent
employs the beacon-referenced CB pursuit law with regards to the other agent
and a stationary beacon. Under certain assumptions on the associated control
parameters, we demonstrate that this problem admits circling equilibria wherein
the agents move on circular orbits with a common radius, in planes
perpendicular to a common axis passing through the beacon. As the common radius
and distances from the beacon are determined by choice of parameters in the
feedback law, this approach provides a means to engineer desired formations in
a three-dimensional setting.