Beacon-referenced Mutual Pursuit in Three Dimensions
This work addresses formation control for unmanned systems, but it is incremental as it builds on existing constant bearing pursuit laws.
The paper tackles the problem of station-keeping for unmanned agents by introducing a modified steering control law that incorporates a beacon reference in three-dimensional mutual pursuit, demonstrating that it enables circling equilibria with agents moving on circular orbits of a common radius around a fixed beacon.
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.