Passivity-based output synchronization in SE(3)

In this paper, we address an output synchronization problem in the Special Euclidean group of dimension three (SE(3)) under the situation that rigid-bodies modeled in SE(3) exchange information along strongly connected graphs. We develop a velocity control law, which is defined only by local information i.e. information of neighbors on position errors and relative orientations. The achievement of the output synchronization and hence the convergence of all the rigid- bodies to any prescribed trajectory is proven by using a property called passivity. Our results are also extended to the case with delays in communication among rigid-bodies. Finally, we demonstrate the effectiveness of the present input through numerical simulations and experiments.