Intrinsic Tetrahedron Formation of Reduced Attitude

TL;DR

This paper presents an intrinsic control method for reduced attitude formation, enabling stable tetrahedron configurations using only relative information and geometric properties, with proven stability and a novel coordinate transformation.

Contribution

It introduces a new intrinsic control protocol for reduced attitude formation that relies solely on relative information and geometric properties, with stability analysis and a novel coordinate transformation.

Findings

Achieves stationary and rotating tetrahedron formations with asymptotic stability.

Provides almost global stability for stationary formation under certain gain restrictions.

Proposes an efficient coordinate transformation for reduced attitude representation.

Abstract

In this paper, formation control for reduced attitude is studied, in which both stationary and rotating regular tetrahedron formation can be achieved and are asymptotically stable under a large family of gain functions in the control. Moreover, by further restriction on the control gain, almost global stability of the stationary formation is obtained. In addition, the control proposed is an intrinsic protocol that only uses relative information and does not need to contain any information of the desired formation beforehand. The constructed formation pattern is totally attributed to the geometric properties of the space and the designed inter-agent connection topology. Besides, a novel coordinates transformation is proposed to represent the relative reduced attitudes in S^2, which is shown to be an efficient approach to reduced attitude formation problems.