Modeling and Robust Control of Two Collaborative Robot Manipulators Handling a Flexibile Object

Robots are often used in industry to handle flexible objects, such as frames, beams, thin plates, rubber tubes, leather goods and composite materials. Moving long flexible objects in a desired path and also precise positioning and orienting the objects need a collaborative action between two robot arms. Most of the earlier studies have dealt with manipulation of rigid objects and only a few have focused on the collaborative manipulators handling flexible objects. Such studies on handling of flexible objects generally used finite element method or assumed mode method for deriving the dynamic model of the flexible objects. These approximation methods require more number of sensors to feedback the vibration measurements or require an observer. Unlike in the earlier studies, this thesis concerns with development of a dynamic model of the flexible object in partial differential equation (PDE) form and design of a robust control strategy for collaborative manipulation of the flexible objects by two rigid robot arms. Two planar rigid manipulators each with three links and revolute joints handling a flexible object is considered during the model development. Kinematic and dynamic equations of the flexible object are derived without using any approximation techniques. The resulting dynamic equation of the flexible object together with the manipulator dynamic equations form the combined dynamic model of the system. The developed complete system of dynamic equations is described by the PDE’s having rigid as well as flexible parameters coupled together. Such a coupled system must be controlled without using any form of approximation techniques and this is accomplished using the singular perturbation approach. By utilizing this technique, slow and fast subsystems are identified in two different time scales and controller is designed for each subsystem. The key issue in developing a control algorithm is that, it should be robust against uncertain parameters of the manipulators and the flexible object and it should also achieve the exponential convergence. Hence, for the slow subsystem, sliding mode control algorithm is developed and for the fast subsystem, a simple feedback control algorithm is designed. In general, usage of singular perturbation technique necessitates exponential stability of the slow and fast subsystems, which is evaluated by satisfying the Tikhnov’s theorem. Hence, the exponential stability analysis for both the subsystems is performed. Simulation results are presented to validate the composite control scheme. As a further consideration in the improvement of control law for the slow subsystem, two modified control algorithms are suggested. The first one focused on the avoidance of velocity signal measurement which is useful to eliminate the need of velocity sensors and the second controller aims at avoiding the complex regressor in the control law. The capability of those controllers is illustrated through simulation studies. The extension of earlier analysis has been carried out by developing the complete system of dynamic equations in joint space.