An Algorithm for Trajectory Generation in Redundant Manipulators with Joint Transmission Accommodation

Abstract

Trajectory generation for manipulators involves generating incremental updates of joint variables to achieve a desired end–effector motion. The Jacobian matrix maps incremental joint motion to incremental end–effector motion in a linear fashion and is typically used in manipulator trajectory generation algorithms. In the case of a redundant manipulator, the Jacobian matrix is not square or invertible and therefore algorithms based on pseudoinverses and their variations are commonly used for trajectory generation. These methods either are computationally not efficient or do not utilize all the joints in motion generation and therefore do not completely exploit the redundancy of the manipulator. The method presented in this paper is a simple method that maximizes transmission of all joint variables onto a desired end–effector motion trajectory. The method is based on aligning the null–space of an augmented Jacobian matrix with the path of the desired end–effector motion, from which a linear combination of joints that projects fully onto the desired end–effector trajectory is obtained. In this manner, all joints of the redundant manipulator are used to generate the end–effector trajectory accommodating the ability of each joint in terms of its motion transmission.