Formation control of a leader-follower structure in three dimensional space using bearing measurements

TL;DR

This paper develops a bearing-based formation control method for 3D leader-follower structures, guaranteeing exponential stabilization of shape and scale using only bearing and velocity measurements under PE conditions.

Contribution

It introduces a novel control approach that ensures exponential convergence to desired formations in 3D space using only bearing and relative velocity data, extending previous bearing rigidity results.

Findings

Exponential stabilization achieved under PE conditions.

Control law based on bearing and velocity measurements.

Validated through simulation results.

Abstract

This paper addresses the problem of bearing leader-follower formation control in three-dimensional space by exploring the persistence of excitation (PE) of the desired formation. Using only bearing and relative velocity measurements, distributed control laws are derived for a group of agents with double-integrator dynamics. The key contribution is that the exponential stabilization of the actual formation to the desired one in terms of both shape and scale is guaranteed as long as the PE conditions on the desired formation are satisfied. The approach generalizes stability results provided in prior work for leader-first follower (LFF) structures which are based on bearing rigidity and constraint consistency to ensure the exponential stabilization of the actual formation to a desired static geometric pattern up to a scale factor. Simulations results are provided to illustrate the performance of the proposed control method.