This article has been accepted for inclusion in a future issue of this journal. Content is final as presented, with the exception of pagination. IEEE TRANSACTIONS ON AUTOMATION SCIENCE AND ENGINEERING 1 Finding the Kinematic Base Frame of a Robot by Hand-Eye Calibration Using 3D Position Data Liao Wu and Hongliang Ren, Member, IEEE Abstract—When a robot is required to perform specific tasks de- fined in the world frame, there is a need for finding the coordinate transformation between the kinematic base frame of the robot and the world frame. The kinematic base frame used by the robot con- troller to define and evaluate the kinematics may deviate from the mechanical base frame constructed based on structural features. Besides, by using kinematic modeling rules such as the product of exponentials (POE) formula, the base frame can be arbitrarily lo- cated, and does not have to be related to any feature of the me- chanical structure. As a result, the kinematic base frame cannot be measured directly. This paper proposes to find the kinematic base frame by solving a hand-eye calibration problem using 3D position measurements only, which avoids the inconvenience and inaccuracy of measuring orientations and thus significantly facili- tates practical operations. A closed-form solution and an iterative solution are explicitly formulated and proved effective by simula- tions. Comprehensive analyses of the impact of key parameters to the accuracy of the solution are also carried out, providing four guidelines to better conduct practical operations. Finally, experi- ments on a 7-DOF industrial robot are performed with an optical tracking system to demonstrate the superiority of the proposed method using position data only over the method using full pose data. Note to Practitioners—Robot-world calibration plays an impor- tant role in practical robotic applications where offline program- ming is adopted. By finding the precise transformation between the base frame of the robot and the world frame, tasks that are usually defined in the world frame can be accurately transformed into the base frame of the robot, enabling successive motion plan- ning and programming. The base frame calibration is also useful in multirobot cooperation where coordination of the robot bases is essential for cooperative manipulations. This paper presents a two-stage method to find the base frame of a robot in the world frame. A closed-form method serves as an initial value finder, and Manuscript received March 17, 2015; revised September 27, 2015; accepted December 30, 2015. This paper was recommended for publication by Asso- ciate Editor P. Lutz and Editor J. Wen upon evaluation of the reviewers’ com- ments. This work was supported by the Singapore Academic Research Fund under Grant R397000227112 and Grant R397000166112. (Corresponding au- thor: Hongliang Ren.) L. Wu was with the Department of Biomedical Engineering, National Univer- sity of Singapore, Singapore 117575, Singapore. He is now with the School of Electrical Engineering and Computer Science, Queensland University of Tech- nology, Brisbane, QLD 4000, Australia (e-mail: wuliaothu@gmail.com; liao. wu@qut.edu.au). H. Ren is with the Department of Biomedical Engineering, National Univer- sity of Singapore, Singapore 117575, Singapore (e-mail: ren@nus.edu.sg). This paper has supplementary downloadable multimedia material available at http://ieeexplore.ieee.org provided by the authors. The Supplementary Ma- terial contains a video outlining the main content of the manuscript, including the “Background,” “Problem formulation,” “Method,” “Simulation results,” and “Experiment results.” In particular, it demonstrates how the experiments men- tioned in this paper were carried out. This material is 27.2 MB in size. Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/TASE.2016.2517674 an iterative method refines the calibration accuracy. Comprehen- sive simulations and experiments are conducted to validate the ef- fectiveness of the proposed method. Theoretical analyses show that the accuracy of the solution will improve when: 1) the movement range of the robot is enlarged; 2) the size of the robot is expanded; 3) the distance between the base frame of the robot and the mea- surement/world frame is reduced; and 4) the distance between the marker and the origin of the hand frame is decreased. These con- clusions provide useful guidance for the practical operations. Index Terms— , hand-eye calibration, kinematic base frame calibration, position measurement. I. INTRODUCTION B ASE frame is a coordinate frame attached to the base link of a robot. It is the reference where the kinematics of a robot is defined and evaluated [1]. Typically, a robot controller determines the orientation and position of the end-effector with respect to the base frame. Therefore, a need for finding the coor- dinate transformation between the base frame of the robot and the world frame arises when the robot is required to perform tasks defined in the world frame and offline programming is adopted, which is common in robotic applications [1]. It also provides an approach for coordinating the base frames of mul- tiple cooperative robots [2]–[4] by identifying them in the same measurement frame. Two base frames exist for a robot: the mechanical base frame that is defined by features such as planes and cylinder axes of the robot structure, and the kinematic base frame that is used by the robot controller. For most of the time, these two base frames are assumed to be identical, as is suggested by the Denavit-Harten- berg (D-H) model [5] and adopted by most robot producers. In practice, however, troubles may occur when we simply use the mechanical base frame as the kinematic base frame. One draw- back is that the mechanical base frame may be difficult or even impossible to measure, for instance, when the robot is mounted onto a platform where the features constructing the base frame are occluded from the measurement machine. Even though the mechanical base frame can be measured, there can be devia- tion between the mechanical base frame and the kinematic base frame, due to the inaccuracy of the structure. In addition, in the case of using the product of exponential (POE) formula to model the robot kinematics [6]–[8], which is increasingly popular in the robotics society, the base frame is allowed to be arbitrarily placed. Then, there can be no relationship at all between the kinematic base frame and the mechanical structural features. All these set a requirement for a specific method of finding the kine- matic base frame. 1545-5955 © 2016 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. See http://www.ieee.org/publications_standards/publications/rights/index.html for more information.