Optimal torque and energy paths in the first four joints of a redundant robotic arm with a study on singularities

The purpose of this study consists of two main parts; First, to develop a simple mathematical procedure to find the workspace singularities of a revolute redundant robotic arm while considering the arm itself as a physical obstacle. The solution presented is a straight-forward application of the homogeneous transformation matrices between any two joints in the arm.The approach is completetly new and can be easily modified and applied to any revolute manipulator. In the past, most of the work done in this area has been based on experimental observation.

The second part of this study consists of applications of the pseudoinverse and the null-space methods to optimize the energy and the torque paths of the first four joints of the redundant Man-Equivalent-Tele-Operator (METR) arm which is the arm that has been suggested by NASA for some of its space application. These methods have been used by Hollerbach, [7], but he applied his methods to a two-dimensional space, while this study expands the application to a real three-dimensional space.

A straight line path for the end effector has been chosen, but this does not limit the results of this study.

The results of this study show that the weighted pseudoinverse method yields better results than the null-space method.