Extending the Leader-First Follower Structure for Bearing-only Formation Control on Directed Graphs

TL;DR

This paper extends the leader-first follower graph structure for bearing-only formation control on directed graphs, introducing ordered LFF graphs that improve convergence speed and are validated through simulations.

Contribution

It introduces ordered LFF graphs, extending the classic LFF structure, and provides stability analysis for multi-leader systems not originally in the LFF class.

Findings

Ordered LFF graphs enable bearing-only formation control on directed graphs.

The proposed structure improves convergence speed over traditional LFF graphs.

Numerical simulations validate the theoretical results.

Abstract

This work proposes an extension to the leader-first follower (LFF) class of graphs used to solve the bearing-only formation control problem over directed graphs. The first contribution provides an equilibrium, stability, and convergence analysis for a one-follower, multi-leader system (which is not an LFF graph). We then propose an extension to the LFF structure, termed \emph{ordered} LFF graphs, that allows for additional forward directed edges to be included. Using the results of the one-follower multi-leader system we show that the ordered LFF graphs can be used to solve the directed bearing-only formation control problem. We also show that these structures offer improved convergence speed as compared to the LFF graphs. Numerical simulations are provided to validate the results.