Two-Time Scale Fuzzy Logic Controller and Observer Design for Trajectory Tracking of Two Cooperating Robot Manipulators Handling a Flexible Beam

Main purpose of the study presented in this papers is to demonstrate the fuzzy logic control design by singular perturbation approach for trajectory tracking of two cooperating planar rigid robots handling a flexible beam which does not require any vibration measurement of the beam. 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. In the proposed controller, fast (flexible) subsystem controller will damp out the vibration of the flexible beam by an optimal design and the other slow (rigid) subsystem fuzzy controller dominates the trajectory tracking. These two controllers constitute the composite control scheme. To avoid requiring any beam vibration measurement for the fast control law, a linear time-variant observer is also designed. A computer was utilized as a simulation tool; the simulation results show the control method is robust and quite effective in performance.