Attitude synchronization of multiple rigid bodies in space while preserving connectivity

This paper investigates the attitude synchronization problem of the dynamical model of a group of moving rigid bodies in SE(3). Two rigid bodies are said to be neighbors if their distance is less than a pre-defined interaction radius. We design the control laws for the torque and the force of the rigid bodies using the potential function method, and prove that under some conditions on the initial states of the rigid bodies, the neighbor graphs keep connected, and thus the rigid body system reaches the attitude synchronization and no collision occurs. The numerical simulations demonstrate the feasibility of the proposal control schemes.