Global Attitude Synchronization for Networked Rigid Bodies under Directed Topologies

This article is devoted to dealing with global attitude synchronization problems for networked rigid bodies subjected to directed topologies and arbitrary initial orientations. To avoid the asynchronous pitfall where only vector parts of rigid bodies reach agreement on some identical value but scalar parts do not, multiplicative quaternion errors are incorporated to develop attitude synchronization protocols for rigid bodies with absolute attitude measurements. In this work, it is shown that global synchronization of networked rigid bodies is achieved if and only if the directed topology is quasistrongly connected. Simultaneously, a novel double-energy-function analysis method, equipped with an ordering permutation technique for the scalar parts and a coordinate transformation mechanism, is constructed for the quaternion behavior analysis of networked rigid bodies. In particular, global synchronization works well 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 validate global synchronization performances under different directed topologies.