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

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.