Kinematic calibration of modular reconfigurable robots using product-of-exponentials formula

Abstract

A modular reconfigurable robot system is a collection of individual link and joint components that can be assembled into different robot geometries for specific task requirements. However, the machining tolerance and assembly errors at the module interconnections affect the positioning accuracy of the end-effector. This article describes a novel kinematic calibration algorithm for modular robots based on recursive forward dyad kinematics. The forward kinematic model derived from the Product-of-Exponentials formula is configuration independent. The error correction parameters are assumed to be in the relative initial positions of the dyads. Two calibration models, namely the six- and seven-parameter methods, are derived on the grounds of the linear superposition principle and differential transformation. An iterative least square algorithm is employed for the calibration solution. Two simulation examples of calibrating a three-module manipulator and a 4-DOF SCARA type manipulator are demonstrated. The result has shown that the average positioning accuracy of the end-effector increases two orders of magnitude after the calibration. © 1997 John Wiley & Sons, Inc.