Rotation-matrix-based attitude synchronization of multiple spacecraft without velocity measurements

Abstract

This paper proposes a distributed protocol for multiple spacecraft such that attitude synchronization is achieved in the absence of angular velocity measurements. The attitude of each spacecraft is represented by the rotation matrix. We first introduce two auxiliary systems for each spacecraft in the form of rotation matrix dynamics to deal with the issue caused by unavailability of angular velocities. Here, neither the absolute angular velocity nor the relative angular velocities with respect to the neighboring spacecraft are available. By implementing appropriate inputs into the auxiliary systems, a synchronization protocol is synthesized in terms of local information interaction, where only the information from the neighbors is exchanged for each spacecraft. It is shown that the proposed distributed protocol guarantees velocity-free attitude synchronization of multiple spacecraft given that the communication graph is a tree. Simulations verify the theoretical results.