Inverse kinematics and optimal design of planar three degrees of freedom redundant lobot

Abstract

In this study, the moving acceleration radius (MAR) is proposed as a local performance index quantifying the dynamic uniformity of a redundant robot, which has no assumption of zero angular velocity such as in Yoshikawa``s dynamic manipulability. MAR can be calculated by a simple sequential algorithm and the resolution of the redundant joint angles are obtained by maximizing MAR locally. In addition, the reduction of the joint torques are achieved by maximizing the acceleration bound in the direction of work path for short motion. Also a new differentiation algorithm for angular acceleration is suggested for numerical efficiency as well as accuracy using a null space operator. For the real time calculation of the joint angles maximizing Yoshikawa``s manipulability and moving acceleration radius, a neural network approach is employed to find the joint angles corresponding to redundancy and then the remaining joint angles are found exactly by using the analytic inverse kinematic equations. A three degrees of freedom planar robot with one degree of redundancy is simulated using these algorithms for various situations and showed a marked improvement in dynamic characteristics. And the results from the modified neural network approach were favorable compared with those from conventional inverse kinematic method, neural network approach, and resolved motion rate control. For a planar three degrees of freedom redundant manipulator, an optimal design of the determination of manipulator parameters is carried out. Here IOABO, which can treat discrete continuous and discrete variable easily, is newly proposed and used for improvement of four performance indices: manipulability index, condition number of Jacobian matrix, moving acceleration radius, and isotropy index of moving acceleration polygon. From the results, it is found that the larger distal link case is more profitable for velocity and acceleration capability, and the smaller distal link case is more profitable f...