Bearing-Based Formation Stabilization with Directed Interaction Topologies

TL;DR

This paper extends bearing-based formation stabilization to directed interaction topologies, introducing the concept of bearing persistence to ensure stability, and demonstrates that a known control law can be adapted to this more complex setting.

Contribution

It introduces the notion of bearing persistence for directed graphs and shows how to achieve formation stability under these conditions.

Findings

Linear control law applies to directed topologies with bearing persistence.

Formation stability depends on the bearing Laplacian and persistence.

Undesired equilibria occur if the formation is not bearing persistent.

Abstract

This paper studies the problem of stabilizing target formations specified by inter-neighbor bearings with relative position measurements. While the undirected case has been studied in the existing works, this paper focuses on the case where the interaction topology is directed. It is shown that a linear distributed control law, which was proposed previously for undirected cases, can still be applied to the directed case. The formation stability in the directed case, however, relies on a new notion termed bearing persistence, which describes whether or not the directed underlying graph is persistent with the bearing rigidity of a formation. If a target formation is not bearing persistent, undesired equilibriums will appear and global formation stability cannot be guaranteed. The notion of bearing persistence is defined by the bearing Laplacian matrix and illustrated by simulation examples.