Output Regulation for Systems on Matrix Lie-group

TL;DR

This paper addresses output regulation for systems on matrix Lie-Groups, proposing a control approach that handles partial measurements and is applicable to various real-world fields like aerospace and robotics.

Contribution

It introduces a novel control structure embedding a copy of the exosystem kinematic for systems on matrix Lie-Groups with partial measurements.

Findings

Effective regulation achieved on matrix Lie-Groups.

Applicable to aerospace, robotics, and geometry systems.

Handles invariant partial measurements.

Abstract

This paper deals with the problem of output regulation for systems defined on matrix Lie-Groups. Reference trajectories to be tracked are supposed to be generated by an exosystem, defined on the same Lie-Group of the controlled system, and only partial relative error measurements are supposed to be available. These measurements are assumed to be invariant and associated to a group action on a homogeneous space of the state space. In the spirit of the internal model principle the proposed control structure embeds a copy of the exosystem kinematic. This control problem is motivated by many real applications fields in aerospace, robotics, projective geometry, to name a few, in which systems are defined on matrix Lie-groups and references in the associated homogenous spaces.