Global Attitude Synchronization of Networked Rigid Bodies Under Directed Topologies

TL;DR

This paper develops a novel approach for achieving global attitude synchronization of networked rigid bodies under directed topologies using quaternion errors, with a new analysis method that handles nonlinearities and coupling.

Contribution

It introduces a double-energy-function analysis and a quaternion-based protocol ensuring global synchronization under quasi-strongly connected directed graphs.

Findings

Global synchronization achieved under quasi-strongly connected topologies

New analysis method handles nonlinear quaternion dynamics

Simulations demonstrate effectiveness for spacecraft networks

Abstract

The global attitude synchronization problem is studied for networked rigid bodies under directed topologies. To avoid the asynchronous pitfall where only vector parts converge to some identical value but scalar parts do not, multiplicative quaternion errors are leveraged to develop attitude synchronization protocols for rigid bodies with the absolute measurements. It is shown that global synchronization of networked rigid bodies can be achieved if and only if the directed topology is quasi-strongly connected. Simultaneously, a novel double-energy-function analysis method, equipped with an ordering permutation technique about scalar parts and a coordinate transformation mechanism, is constructed for the quaternion behavior analysis of networked rigid bodies. In particular, global synchronization is achieved with our analysis method regardless of the highly nonlinear and strongly coupling problems resulting from multiplicative quaternion errors, which seriously hinder the traditional analysis of global synchronization for networked rigid bodies. Simulations for networked spacecraft are presented to show the global synchronization performances under different directed topologies.