Decentralized consensus control of rigid bodies using exponential coordinates^⋆

In this paper, we propose algorithms for a multi-agent rigid body system for four cases of kinematic and dynamic consensus control of configurations and velocities based on the Laplacian matrix of the communication graph. The configurations of the rigid bodies are described in terms of the exponential coordinates associated with the Lie groups SO(3) and SE(3). The control objective is to stabilize the relative configurations (for kinematic consensus control) or the relative configurations and velocities (for dynamic consensus con-trol). For the control of rigid body pose (attitude and translational dynamics) it is desired for the bodies to obtain a desired formation with attitude synchronization. The design is first conducted on the kinematic level, where the velocities implement the steering control and then the controller is designed on the dynamic level, where the torques and the forces implement the feedback control of pose and velocities. Finally, a decentralized collision avoidance scheme is developed for one of the cases under study. Numerical examples are also provided to demonstrate the efficiency of the studied control laws.