Abstract
In this paper we consider attitude coordination on balanced graphs, where kinematics of each rigid-body is modeled in SE (3). We show that the kinematics in SE (3) satisfies a passivity property with a positive definite storage function and propose an angular velocity, control law for each rigid-body that decreases the sum of the storage functions of the individual rigid-bodies. Attitude coordination results if all rigid-bodies rotation matrices are positive definite and the communication graph is connected. We show that the speed of convergence in the attitude coordination problem is determined by the second smallest eigenvalue of graph Laplacian. Our results are also extended to the case when there are delays in communication among rigid-bodies and communication failures. Using the concept of brief instability we show that attitude coordination is still achieved even if the graph is changed. Finally, the results are demonstrated through numerical simulations.
