Nonlinear Model Predictive Control of a Stewart Platform Motion Stabilizer

Abstract In an operating room of a hospital ship, to remotely perform surgery on a patient laid on an operating table utilizing the surgical manipulators attached to the table, the rotation and translation of the operating table must be properly isolated from the wave-induced motion of the floor. Similarly, on a moving vehicle, when a sensitive equipment is transported or a manipulator is utilized to perform precise positioning tasks, it becomes necessary to isolate them from undesirable motion of the vehicle. In response to the need for a motion stabilizer, which isolates a manipulator from undesirable ship or vehicle motion, we present a nonlinear model predictive control (NMPC) of a six degrees-of-freedom, base-moving Stewart platform. Analytical nonlinear equations of motion are utilized for nonlinear model predictive control, wherein an optimization problem in a finite time horizon at each time step is solved adopting C/GMRES algorithm. To predict the future motion caused by a ship or a moving vehicle, we employ an auto regressive moving average model which forecasts future behavior based on past behavior. Furthermore, to incorporate prediction errors as disturbance at each time step, we endow NMPC with the robustness. As a result, even if prediction errors exist, the set of all possible output states are predicted using the equations of motion in a finite time, while the system kinematic constraints are precisely satisfied. In order to assess the performance of the proposed controller, numerical simulations are presented for a base-moving Stewart platform.