Controller Class for Rigid Body Tracking on $\\mathsf {SO}(3)$

Abstract

In this article, we propose a novel family of Lie algebra valued functions <inline-formula><tex-math notation= LaTeX >$\\mathcal {F}_R$</tex-math></inline-formula> on special orthogonal group <inline-formula><tex-math notation= LaTeX >$\\mathsf {SO}(3)$</tex-math></inline-formula>. Each function belonging to this family induces a novel controller that stabilizes a rigid body attitude. All controllers induced by the family <inline-formula><tex-math notation= LaTeX >$\\mathcal {F}_R$</tex-math></inline-formula> form a controller class <inline-formula><tex-math notation= LaTeX >$\\mathcal {C}_R$</tex-math></inline-formula>. This novel controller class <inline-formula><tex-math notation= LaTeX >$\\mathcal {C}_R$</tex-math></inline-formula> contains both local and almost-global asymptotically stable controllers, and this article presents geometric stability results of the whole controller class <inline-formula><tex-math notation= LaTeX >$\\mathcal {C}_R$</tex-math></inline-formula>.