Nonlinear Controllability Assessment of Aerial Manipulator Systems using Lagrangian Reduction

TL;DR

This paper assesses the nonlinear controllability of aerial manipulators using Lagrangian reduction, demonstrating they are small-time locally controllable near equilibrium with Lie brackets up to degree three.

Contribution

It introduces a Lagrangian reduction approach for analyzing nonlinear controllability of underactuated aerial manipulators, accounting for symmetry-breaking energy terms.

Findings

Aerial manipulators are STLC near equilibrium.

Lagrangian reduction simplifies controllability analysis.

Lie brackets up to degree three are needed for control.

Abstract

This paper analyzes the nonlinear Small-Time Local Controllability (STLC) of a class of underatuated aerial manipulator robots. We apply methods of Lagrangian reduction to obtain their lowest dimensional equations of motion (EOM). The symmetry-breaking potential energy terms are resolved using advected parameters, allowing full $SE(3)$ reduction at the cost of additional advection equations. The reduced EOM highlights the shifting center of gravity due to manipulation and is readily in control-affine form, simplifying the nonlinear controllability analysis. Using Sussmann's sufficient condition, we conclude that the aerial manipulator robots are STLC near equilibrium condition, requiring Lie bracket motions up to degree three.