Passivity-Based Attitude Synchronization in $SE(3)$

This paper addresses passivity-based motion coordination of rigid bodies in the special Euclidean group SE(3) under the assumption that the agents exchange information over strongly connected graphs. In this paper, we especially focus on one of the motion coordination problems on SE(3) called attitude synchronization. We first develop a passivity-based distributed velocity input law to achieve attitude synchronization. Using the notion of algebraic connectivity, we then establish a connection between the speed of convergence and the structure of the interconnection graph. We also prove attitude synchronization in the leader-follower case and in the cases of communication delay and temporary communication failures. Finally, the performance of our developed control laws is demonstrated through both numerical simulation and experiments on a planar (2D) test bed.