Adaptive back–stepping robust control of a 3–[P2(US)] parallel robot on optimal trajectory

Abstract

This paper presents a robust control technique combining adaptive sliding mode control and back-stepping methods to control a 3-DOF translational parallel robot. Dynamic modeling of the robot is accomplished using the Lagrange method. Since the derived dynamic model suffers from uncertainties and disturbances, a combination of robust techniques namely back-stepping and sliding mode controllers are applied together with adaptive control. Determination of uncertainty bounds is intransitive in the design of the proposed controller. To prove the system stability, the system model is divided into several subsystems and stability is illustrated step by step using Lyapunov criteria, then an adaptive law is obtained to estimate the uncertainties. This controller is also robust in presence of time-varying disturbances. Performance of the controller is evaluated by simulations on optimal trajectories. Trajectory planning is performed by optimization of some accuracy points using Harmony Search Algorithm (HSA) and cubic spline interpolation. Simulation results show improved performance of the proposed control technique compared to conventional feedback linearization and sliding mode techniques.