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

This work introduces a generalization of the leader-first follower (LFF) graph structure for solving the bearing-only formation control problem on 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, termedorderedLFF 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.