Direction-only Orientation Alignment of Leader-Follower Networks

TL;DR

This paper introduces a leader-following orientation alignment method for multi-agent systems in 3D space using only directional vectors, enabling agents to align orientations without a shared global frame.

Contribution

It presents a novel orientation alignment scheme that relies solely on inter-agent directional vectors and landmark directions, without requiring a global coordinate system.

Findings

Orientations converge almost globally and asymptotically to the leader's orientation.

The method works with directional vectors expressed in local frames.

Numerical simulations confirm the effectiveness of the proposed scheme.

Abstract

When a team of agents, such as unmanned aerial/underwater vehicles, are operating in $3$-dimensional space, their coordinated action in pursuit of a cooperative task generally requires all agents to either share a common coordinate system or know the orientations of their coordinate axes with regard to the global coordinate frame. Given the coordinate axes that are initially unaligned, this work proposes an orientation alignment scheme for multiple agents with a type of leader-following graph typologies using only inter-agent directional vectors, and the direction measurements to one or more landmarks of the first two agents. The directional vectors are expressed in the agents' body-fixed coordinate frames and the proposed alignment protocol works exclusively with the directional vectors without the need of a global coordinate frame common to all agents or the construction of the agents' orientation matrices. Under the proposed alignment scheme, the orientations of the agents converge almost globally and asymptotically to the orientation of the leader agent. Finally, numerical simulations are also given to illustrate the effectiveness of the proposed method.