Implementation of the velocities of the end-effector with the distributed arithmetic architecture

Abstract

The fast implementation of the linear and of the angular velocities of the end-effector of robotic manipulators, using the distributed arithmetic technique is described. The linear and angular velocities of the end-effector as well as the positional and the orientational jacobian matrices is calculated by a cascade configuration of two pipelined arrays. The building blocks of the arrays are the distributed arithmetic-based circuits that implement the matrix-vector multiplications involved in the calculations. The digit-serial configuration of the proposed implementation of the linear and angular velocities of the end-effector is described, while the serial and the parallel configurations may result as special cases of the digit-serial configuration. The proposed distributed arithmetic computer architecture may be used in the real-time operation of the robot control system that requires the on-line computation of the position, of the linear and angular velocities of the end-effector and of the Jacobian matrix.