Synchronization with partial state coupling on SO(n)

TL;DR

This paper investigates the problem of synchronizing agents on SO(n) with partial state information, proposing a gradient coupling law and analyzing convergence for fixed and time-varying references, with detailed focus on SO(3).

Contribution

It introduces a natural gradient coupling law for partial state synchronization on SO(n) and provides extensive convergence analysis, including fixed and time-varying reference vectors.

Findings

Proposed a gradient coupling law for partial state synchronization.

Proved convergence under fixed and time-varying reference vectors.

Analyzed special case of SO(3) with detailed insights.

Abstract

This paper studies autonomous synchronization of k agents whose states evolve on SO(n), but which are only coupled through the action of their states on one "reference vector" in Rn for each link. Thus each link conveys only partial state information at each time, and to reach synchronization agents must combine this information over time or throughout the network. A natural gradient coupling law for synchronization is proposed. Extensive convergence analysis of the coupled agents is provided, both for fixed and time-varying reference vectors. The case of SO(3) with fixed reference vectors is discussed in more detail. For comparison, we also treat the equivalent setting in Rn, i.e. with states in Rn and connected agents comparing scalar product of their states with a reference vector.