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 fortrajectory tracking of a 3-RPS (Revolute, Prismatic, Spherical) parallel manipulator. With ignoring smallinertial effects of all legs and joints compared with those of the end-effector of 3-RPS, the dynamical model ofthe manipulator is developed based on Lagrange method. By removing the unknown Lagrange multipliers, thedistribution matrix of control input vector disappears from the dynamical equations. Therefore, the calculationof the aforementioned matrix is not required for modeling the manipulator. It in trun results in decreasedmathematical manipulation and low computational burden. As a robust nonlinear control technique, a SMCsystem is designed for the tracking of the 3-RPS manipulator. According to Lyapunov’s direct method, theasymptotic stability and the convergence of 3-RPS manipulator to the desired reference trajectories areproved. Based on computer simulations, the robust performance of the proposed SMC system is evaluatedwith respect to FL (feedback linearization) method. The proposed model and control algorithms can beextended to different kinds of holonomic and non-holonomic constrained parallel manipulators.