A Techniques to Downgrade Objective Function in Parallel Robot Kinematics Problem

Abstract

Quadratic functions and quaternary functions are preferable forms solving parallel robot kinematics problems. In order to simplify and to use only one method to solve all forms of the objective functions, this article introduces prevalent techniques to downgrade mathematical model of the objective functions from quaternary function to quadratic function in parallel robot kinematics problem. By using equivalent alternative kinematic structure and additional mathematical constraints, we will change from the study of parallel robot kinematics problem with the form of quaternary objective function as the original configuration to equivalent alternative configuration in the form of quadratic objective function. The parallel robot kinematics problem based on alternative configuration with quadratic objective function is not only simpler but also helps to quickly identify the mathmatical relationships in the joint space and work space of parallel robot. Then, more accurate control solution of parallel robot kinematics problem can be identified. Moreover, by using techniques in this study, all forms of objective functions of parallel robot of any structure can be easily solved. The result from numerical simulation has been used to prove the presented approaches.