Consensus under Misaligned Orientations

TL;DR

This paper introduces a consensus algorithm designed to operate effectively despite various types of misalignments in coordinate frames, control, and sensing, providing stability conditions and analyzing convergence properties.

Contribution

It offers a novel mathematical framework and sufficient conditions for consensus under misaligned orientations, along with stability and convergence analysis.

Findings

Sufficient conditions for consensus or divergence are identified.

Eigenvalue analysis reveals convergence characteristics.

Numerical simulations demonstrate the algorithm's behavior under misalignments.

Abstract

This paper presents a consensus algorithm under misaligned orientations, which is defined as (i) misalignment to global coordinate frame of local coordinate frames, (ii) biases in control direction or sensing direction, or (iii) misaligned virtual global coordinate frames. After providing a mathematical formulation, we provide some sufficient conditions for consensus or for divergence. Besides the stability analysis, we also conduct some analysis for convergence characteristics in terms of locations of eigenvalues. Through a number of numerical simulations, we would attempt to understand the behaviors of misaligned consensus dynamics.