Distributed Control of Rigid Body Reduced Attitude: Synchronization and Balancing

This paper proposes distributed control algorithms for asymptotically stable synchronization and balancing of a multi-agent rigid body reduced attitude system using Lyapunov analysis. In the synchronization of the reduced attitudes and velocities of the rigid bodies, the feedback control design is conducted on the dynamic level in which inertias are not negligible. However, in the balancing problem, the feedback control scheme is designed on the kinematic level while the control objective is the maximization of the minimum relative angular distance between each pair of rigid body reduced attitudes. In both cases, the rigid bodies share their states according to a static communication topology. Asymptotic stability to the desired formation in the nonlinear state space is demonstrated both analytically and through numerical simulations.