Two-Time Scale Control and Observer Design for Trajectory Tracking of Two Cooperating Robot Manipulators Moving a Flexible Beam

In this paper, two-time scale control design for trajectory tracking of two cooperating planar rigid robots moving a flexible beam which does not require any vibration measurement of the beam is presented. First, kinematics and dynamics of the robots and the object are derived. Then, using the relations between different forces acting on the object by the manipulators´ end-effectors, the dynamic equations of the robots and the object are combined. Applying two-time scale control theory on the combined dynamics, a control scheme is elaborated which makes the position and orientation of the mass center of the beam track a desired trajectory while suppressing the beam vibration. For the controller algorithm, first a slow controller is applied for the slow (rigid) subsystem and then a fast stabilizing controller is considered for the fast (flexible) subsystem; these two controllers constitute the composite control scheme. To avoid requiring any beam vibration measurement for the fast control law, a linear observer is also designed. The simulation results show the efficiency of the proposed control scheme.