3-RPS Parallel Manipulator Dynamical Modelling and Control Based on SMC and FL Methods

In this paper, a dynamical model-based SMC (Sliding Mode Control) is proposed for trajectory tracking of a 3-RPS (Revolute, Prismatic, Spherical) parallel manipulator. With ignoring small inertial effects of all legs and joints compared with those of the end-effector of 3-RPS, the dynamical model of the manipulator is developed based on Lagrange method. By removing the unknown Lagrange multipliers, the distribution matrix of control input vector disappears from the dynamical equations. Therefore, the calculation of the aforementioned matrix is not required for modeling the manipulator. It in trun results in decreased mathematical manipulation and low computational burden. As a robust nonlinear control technique, a SMC system is designed for the tracking of the 3-RPS manipulator. According to Lyapunov’s direct method, the asymptotic stability and the convergence of 3-RPS manipulator to the desired reference trajectories are proved. Based on computer simulations, the robust performance of the proposed SMC system is evaluated with respect to FL (feedback linearization) method. The proposed model and control algorithms can be extended to different kinds of holonomic and non-holonomic constrained parallel manipulators.