Proposal of a Forward Kinematics Calculating Method, a Control Law of Parallel Link Manipulators, and Stability Analysis of the Control System Taking Advantage of Characteristic of the Jacobian

In this paper, we propose a design method of task coordinated feedback control law for parallel link manipulators (PLMs) . In general, since it is the last purpose to control the coordinates of an End-effector by a manipulator's control, a task coofdinated feedback control suits the purpose rather than a joint coordinated one. However, control with a parallel link manipulator's work coordinates has the following two problems which should be solved. First, it is difficult for PLMs to have the information of task coordinate from joint infomation, though it is easy for serial link manipulators to do this. Second, it is necessary to calculate the Inverse Matrix of Jacobian for calculating Driving force of a joint. In this paper, we propose a novel solving method of forward kinematics problem for PLMs and construct a task coordinated feedback control which used the character of Jacobian and made calculation easy. Then we prove the stability of this control system and verify the validity by the simulation and experiment.