Global Controllability of Multidimensional Rigid Body by Few Torques

TL;DR

This paper investigates the global controllability of multidimensional rigid bodies using few torques, employing geometric control methods to analyze algebraic structures and establish controllability criteria for different damping scenarios.

Contribution

It introduces new controllability criteria for multidimensional rigid bodies controlled by few torques, addressing algebraic challenges in geometric control analysis.

Findings

Established controllability criteria for damped MRBs

Analyzed algebraic structures from quadratic Euler-Frahm equations

Identified problems in geometric control analysis

Abstract

We study global controllability of 'rotating' multidimensional rigid body (MRB) controlled by application of few torques. Study by methods of geometric control requires analysis of algebraic structure introduced by the quadratic term of Euler-Frahm equation. We discuss problems, which arise in the course of this analysis, and establish several global controllability criteria for damped and non damped cases.