Beacon-referenced Mutual Pursuit in Three Dimensions

TL;DR

This paper develops a control law for two agents to maintain formations around a fixed beacon in 3D space, enabling engineered circular orbits for station-keeping in unmanned systems.

Contribution

It introduces a beacon-referenced modification to the 3D pursuit law, allowing formation control around a stationary beacon with predictable circular orbits.

Findings

Agents achieve stable circular orbits around the beacon.

Formation parameters can be tuned via control law parameters.

The approach enables precise formation engineering in 3D environments.

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.