Distributed attitude synchronization for multiple rigid bodies with euler-lagrange equations of motion

In this paper, distributed attitude synchronization problems are considered for multiple rigid bodies with attitude dynamics represented by Euler-Lagrange equations of motion. Three distributed control laws for attitude synchronization are proposed and analyzed. The first control law introduces bounded functions to reduce the required control torque. The second control law applies a passivity approach to remove the requirement for relative angular velocity measurement between neighboring rigid bodies. The third control law incorporates a time-varying reference attitude, where the reference attitude is allowed to be available to only a subset of the group members. It is shown that the first two control laws guarantee distributed attitude synchronization under any undirected connected communication topology. The third control law guarantees that all rigid bodies track the time-varying reference attitude as long as a virtual node whose state is the time-varying reference attitude has a directed path to all of the rigid bodies in the group. Simulation results are presented to demonstrate the effectiveness of the three control laws.