A decentralized design for group alignment and synchronous rotation without inertial frame information

We study a motion coordination problem where the objective is to achieve identical orientation and synchronous rotation for a group of rigid bodies. Unlike existing designs which assume that the the inertial frame is available to each agent, we develop a passivity-based design which relies only on relative attitude information with respect to neighboring agents. The desired equilibria, where all the rigid bodies possess the same attitude and rotate at a desired angular velocity, are shown to be locally asymptotically stable and a manifold of undesired equilibria may exist. We then consider the situation where the reference angular velocity is available only to the leader, and propose a distributed adaptive controller with which the other agents reconstruct this reference angular velocity.