Attitude Synchronization of a Group of Rigid Bodies Using Exponential Coordinates

Currently, managing a group of satellites or robot manipulators requires coordinating their motion and work in a cooperative way to complete complex tasks. The attitude motion coordination and synchronization problems are challenging since attitude motion evolves in non-Euclidean spaces. Moreover, the equation of motions of the rigid body are highly nonlinear. This paper studies the attitude synchronization problem of a group of fully actuated rigid bodies over a directed communication topology. To design the synchronization control law, we exploit the cascade structure of the rigid body’s kinematic and dynamic models. First, we propose a kinematic control law that induces attitude synchronization. As a second step, an angular velocity-tracking control law is designed for the dynamic subsystem. We use the exponential coordinates of rotation to describe the body’s attitude. Such coordinates are a natural and minimal parametrization of rotation matrices which almost describe every rotation on the Special Orthogonal group [Formula: see text]. We provide simulation results to show the performance of the proposed synchronization controller.