An Intrinsic Approach to Formation Control of Regular Polyhedra for Reduced Attitudes

TL;DR

This paper introduces an intrinsic, parametrization-free control protocol for stabilizing regular polyhedral formations in reduced attitude systems, leveraging geometric properties and a novel coordinate transformation.

Contribution

It proposes a unified, intrinsic control framework for regular polyhedra formation in reduced attitudes, independent of specific parametrizations or desired formation details.

Findings

Proposed a control protocol using only relative attitude measurements.

Proved asymptotic stability of regular polyhedral formations.

Developed a new methodology for stability analysis of constrained nonlinear systems.

Abstract

This paper addresses formation control of reduced attitudes in which a continuous control protocol is proposed for achieving and stabilizing all regular polyhedra (also known as Platonic solids) under a unified framework. The protocol contains only relative reduced attitude measurements and does not depend on any particular parametrization as is usually used in the literature. A key feature of the control proposed is that it is intrinsic in the sense that it does not need to incorporate any information of the desired formation. Instead, the achieved formation pattern is totally attributed to the geometric properties of the space and the designed inter-agent connection topology. Using a novel coordinates transformation, asymptotic stability of the desired formations is proven by studying stability of a constrained nonlinear system. In addition, a methodology to investigate stability of such constrained systems is also presented.