Collision-Free Bearing-Driven Formation Tracking for Euler-Lagrange Systems

TL;DR

This paper presents a novel bearing-based formation control method for heterogeneous Euler-Lagrange systems that ensures collision avoidance and does not require prior system parameter knowledge.

Contribution

It introduces a distributed observer and control law that estimate leader states and guide formation tracking without prior parameter knowledge, ensuring collision avoidance.

Findings

Effective formation tracking demonstrated in simulations.

Collision avoidance condition depends on initial configuration.

Distributed observer successfully estimates leader velocities and accelerations.

Abstract

In this paper, we investigate the problem of tracking formations driven by bearings for heterogeneous Euler-Lagrange systems with parametric uncertainty in the presence of multiple moving leaders. To estimate the leaders' velocities and accelerations, we first design a distributed observer for the leader system, utilizing a bearing-based localization condition in place of the conventional connectivity assumption. This observer, coupled with an adaptive mechanism, enables the synthesis of a novel distributed control law that guides the formation towards the target formation, without requiring prior knowledge of the system parameters. Furthermore, we establish a sufficient condition, dependent on the initial formation configuration, that ensures collision avoidance throughout the formation evolution. The effectiveness of the proposed approach is demonstrated through a numerical example.