Distributed Passivity-Based Control for Multiple Space Manipulators Holding Flexible Beams

This paper proposes a distributed passivity-based control scheme for the consensus and vibration suppression of multiple space manipulators holding flexible beams. A space manipulator holding a flexible beam is essentially a rigid–flexible underactuated system. The bending deformation of the flexible beam is discretized by employing the assumed modes method. Based on Lagrange’s equations of the second kind, the dynamics model of each manipulator holding a flexible beam is established. By connecting such underactuated systems with the auxiliary Euler–Lagrange systems, a distributed passivity-based controller is designed under undirected communication graphs. To suppress flexible vibration effectively, a distributed controller with the feedback of the velocity of deflection at the free end of the flexible beam is proposed to achieve the manipulator synchronization and vibration suppression simultaneously. The stability of the proposed controller is analyzed with LaSalle’s invariance principle. Numerical simulations and experiments are conducted to show the effectiveness of the designed controllers.