Chapter 11 - Geometric calibration of robots

Abstract

This chapter presents various approaches for the geometric calibration of serial robots. The geometric parameters of the robot, the base frame parameters, and the end-effector frame parameters are defined using the Hayati modification of Khalil-Kleinfmger notations. All of the calibration methods are described by a unified nonlinear equation and a general linear equation. The Jacobian matrix of each calibration method is obtained as a function of the generalized Jacobian matrix relating the variation of the end-effector location with the geometric parameter variation. The generalized Jacobian matrix is computed using an efficient method making use of the elements of the transformation matrices of the link frames. The identifiable parameters are determined numerically by studying the QR decomposition of the observation matrix using random configurations satisfying the constraints of the calibration method. The nonlinear estimation problem is resolved using the Levenberg-Marquardt method or using an iterative pseudoinverse method. The optimum selection of the calibration configurations is treated by minimizing the condition number of the observation matrix. These methods can be extended to include the calibration of joint elasticity and link flexibility. Further, this chapter presents the geometric calibration of parallel robots when the measurement of the end-effector location is available. The problem can be formulated either with inverse or with direct geometric models.