On the modeling and control of the Cartesian Parallel Manipulator

Abstract

The Cartesian Parallel Manipulator (CPM) which proposed by Han Sung Kim, and Lung-Wen Tsai [1] consists of a moving platform that is connected to a fixed base by three limbs. Each limb is made up of one prismatic and three revolute joints and all joint axes are parallel to one another. In this way, each limb provides two rotational constraints to the moving platform and the combined effects of the three limbs lead to an over-constrained mechanism with three translational degrees of freedom. The manipulator behaves like a conventional X-Y-Z Cartesian machine due to the orthogonal arrangement of the three limbs.

In this paper, the dynamics of the CPM has been presented using Lagrangian multiplier approach to give a more complete characterization of the model dynamics. The dynamic equation of the CPM has a form similar to that of a serial manipulator. So, the vast control literature developed for serial manipulators can be easily extended to this class of manipulators. Based on this approach, four control algorithms; simple PD control with reference position and velocity only, PD control with gravity compensation, PD control with full dynamic feedforward terms, and computed torque control, are formulated. Then, the simulations are performed using Matlab and Simulink to evaluate the performance of the four control algorithms.