This paper presents a generic error model, which is based on the product of exponentials (POEs) formula, for serial-robot calibration. The identifiability of parameters in this error model was analyzed. The analysis shows the following: 1) Errors in all joint twists are identifiable. 2) The joint zero-position errors and the initial transformation errors cannot be identified when they are involved in the same error model. With either or neither of them, three practicable error models were obtained. The joint zero-position errors are identifiable when the following condition is satisfied: Coordinates of joint twists are linearly independent. 3) The maximum number of identifiable parameters is 6n + 6 for an n-degree-of-freedom (DOF) generic serial robot. Simulation results show the following: 1) The maximum number of identifiable parameters is 6r + 3t + 6, where r is the number of revolute joints, and t is the number of prismatic joints. 2) All the kinematic parameters of the selective compliant assembly robot arm (SCARA) robot and programmable universal machine for assembly (PUMA) 560 robots were identified by using the three error models, respectively. The error model based on the POE formula can be a complete, minimal, and continuous kinematic model for serial-robot calibration.

Kinematic-Parameter Identification for Serial-Robot Calibration Based on POE Formula

Local POE model for robot kinematic calibration

The paper deals with geometric calibration of industrial robots and focuses on reduction of the measurement noise impact by means of proper selection of the manipulator configurations in calibration experiments. Particular attention is paid to the enhancement of measurement and optimization techniques employed in geometric parameter identification. The developed method implements a complete and irreducible geometric model for serial manipulator, which takes into account different sources of errors (link lengths, joint offsets, etc). In contrast to other works, a new industry-oriented performance measure is proposed for optimal measurement configuration selection that improves the existing techniques via using the direct measurement data only. This new approach is aimed at finding the calibration configurations that ensure the best robot positioning accuracy after geometric error compensation. Experimental study of heavy industrial robot KUKA KR-270 illustrates the benefits of the developed pose strategy technique and the corresponding accuracy improvement. Geometric calibration of industrial robotsReduction of the measurement noise impact by means of proper selection of the manipulator configurations in calibration experimentsA new industry-oriented performance measure for optimal measurement configuration selectionExperimental study of heavy industrial robot KUKA KR-270

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Geometric calibration of industrial robots using enhanced partial pose measurements and design of experiments

We present a method for kinematic calibration of open chain mechanisms based on the product of exponentials (POE) formula. The POE formula represents the forward kinematics of an open chain as a product of matrix exponentials, and is based on a modern geometric interpretation of classical screw theory. Unlike the kinematic representations based on the Denavit-Hartenberg (D-H) parameters, the kinematic parameters in the POE formula vary smoothly with changes in the joint axes; ad hoc methods designed to address the inherent singularities in the D-H parameters are therefore unnecessary. After introducing the POE formula, we derive a least-squares kinematic calibration algorithm for general open chain mechanisms.

https://www.cambridge.org/core/services/aop-cambridge-core/content/view/S0263574700019810

Kinematic calibration using the product of exponentials formula

Robot kinematics calibration is of great significance for improving robot absolute pose accuracy, which can be divided into modelbased and non-parametric kinematics calibration. For model-based kinematics calibration, kinematics calibration modeling, pose measurement of end-effector, kinematics parameters calibration and error compensation are systematically analyzed. And with the increasing demand for autonomy, the autonomous kinematics calibration is introduced. On the other hand, research status of nonparametric kinematics calibration is elaborated, the advantages and disadvantage of which are discussed respectively. On the basis, comprehensive and organized description and summarization of the three kinds of calibrations are given. Overall, aiming at robot kinematics calibration, existing achievements are summarized, a typical calibration process is carried out and calibration precautions are detailed, then calibration results of various methods are compared and analyzed. Finally, existing problems in kinematics calibration are analyzed and development prospects are presented.

Review on Kinematics Calibration Technology of Serial Robots

A kinematic modeling convention for robot manipulators is proposed. The kinematic model is named for its completeness and parametric continuity (CPC) properties. Parametric continuity of the CPC model is achieved by adopting a singularity-free line representation consisting of four line parameters. Completeness is achieved through adding two link parameters to allow arbitrary placement of link coordinate frames. The transformations from the world frame to the base frame and from the last link frame to the tool frame can be modeled with the same modeling convention used for internal link transformations. Since all the redundant parameters in the CPC model can be systematically eliminated, a linearized robot error model can be constructed in which all error parameters are independent and span the entire geometric error space. The focus is on model construction, mappings between the CPC model and the Denavit-Hartenberg model, the study of the model properties, and its application to robot kinematic calibration. >

F. Hamano

Papers

A complete and parametrically continuous kinematic model for robot manipulators