Passivity-based Output Synchronization and Flocking Algorithm in SE(3)

This paper addresses passivity-based output synchronization and a collision avoidance problem of rigid bodies in the Special Euclidean group SE(3) under the assumption that the rigid bodies exchange information over weighted digraphs. We first develop a passivity-based distributed velocity input law to achieve output synchronization. Using the notion of algebraic connectivity, we then establish a connection between the speed of convergence and the structure of the interconnection graph in SE(3). We also prove output synchronization in the presence of temporary communication failures. We next develop a flocking algorithm by modifying the present velocity input so that it embodies cohesion, separation and alignment rules introduced by Reynolds. Finally, we demonstrate the effectiveness of the present input through numerical simulations.