Fat-based adaptive control (fatac) of cooperative manipulators for handling a deformable object

Abstract

Handling a flexible object by cooperative manipulators is more complicated than handling the rigid one as it involves the vibration of the object. Since the vibration has been known as the capacity for disturbance, discomfort, damage, and destruction, it needs to be suppressed. The system consists of two cooperative manipulators handling a flexible beam that is modelled in Partial Differential Equation (PDE) form and employed the singular perturbation method to produce slow and fast subsystems. Despite the advantages offered by the PDE-based system, less work has been conducted in designing a controller for handling deformable objects by cooperative manipulators based on the PDE-based model and considering the model uncertainties. This study proposes a composite controller that comprises Function Approximation Technique (FAT)-based Adaptive Controller (FATAC) for the slow subsystem to control two cooperative manipulators in handling the deformable object under uncertain model parameters and Velocity Feedback Controller (VFC) for the fast subsystem to suppress the vibration of the deformable object. Stability analysis has been carried out for each subsystem to satisfy Tikhonov’s Theorem. Simulation tests have been carried out to measure the performance of designed controllers. For the slow subsystem, the simulation results showed that the root-mean-square (RMS) tracking error of the beam’s midpoint are 0.004599 m for X-position, 0.001697 m for Y-position, and 0.005186 rad. for the orientation under the proposed FATAC. For the fast subsystem, the simulation results proved that the proposed VFC has successfully worked well as the transverse vibration of the beam is completely suppressed within 0.8 s. Hardware experimental tests have also been carried out to validate the proposed controller. For slow subsystem, the coding of proposed FATAC is developed to control two cooperative manipulators so that the positions of the beam’s midpoint track the circular desired trajectory. The experimental results showed that the position tracking of the beam’s midpoint which is controlled by two cooperative manipulators under the proposed FATAC has been successfully achieved with the RMS tracking error of 0.914 cm and 1.126 cm for X and Y-directions, respectively. For the fast subsystem, the calibration of the strain gauge sensor has been made for the preparation to design VFC. The ultimate stage in the fast subsystem is validating the VFC by experimental hardware test to suppress the vibration of the flexible beam. The experimental results proved that the proposed VFC for the fast subsystem has successfully suppressed the beam vibration while moving the flexible beam according to the desired trajectory. The simulation and hardware experiment results verified that the proposed composite controller comprises FATAC for the slow subsystem that has successfully driven cooperative manipulators to handle the deformable object to follow the desired trajectories and VFC for the fast subsystem that has successfully suppressed the transverse vibration of the deformable object.