A Method of Robot Base Frame Calibration by Using Dual Quaternion Algebra

When the robot is required to execute a certain task in the world coordinate system (WCS), it is necessary to find the coordinate transformation between the robot base coordinate system (RBCS) and WCS to enable the high precision motion planning. This paper presents a simple and accurate method that allows a simultaneous computation of the coordinate transformations (i.e., rotation and translation) from WCS to RBCS. Based on the dual quaternion, the robot kinematic model and formulas for calculating the transformation are derived, which allow calculating the rotation and translation simultaneously. Taking the unit dual quaternion as a constraint, the Lagrangian multiplier method is employed to obtain the optimum transformation. Both simulation and experiment results show that higher calibration precision is obtained. The proposed approach has certain reference value and guiding sense for other calibration problems.

[1]  Morris Driels,et al.  Vision-based automatic theodolite for robot calibration , 1991, IEEE Trans. Robotics Autom..

[2]  E. Study.  Von den Bewegungen und Umlegungen , 1891 .

[3]  Tao Sun,et al.  Kinematic calibration of a 3-DoF rotational parallel manipulator using laser tracker , 2016 .

[4]  Yahui Gan,et al.  Base frame calibration for coordinated industrial robots , 2011, Robotics Auton. Syst..

[5]  Weidong Zhu,et al.  Robot base frame calibration with a 2D vision system for mobile robotic drilling , 2015 .

[6]  Ilian A. Bonev,et al.  Absolute calibration of an ABB IRB 1600 robot using a laser tracker , 2013 .

[7]  Karl Henning Halse,et al.  Dual Quaternion Variational Integrator for Rigid Body Dynamic Simulation , 2016, ArXiv.

[8]  Clifford,et al.  Preliminary Sketch of Biquaternions , 1871 .

[9]  Hongliang Ren,et al.  Finding the Kinematic Base Frame of a Robot by Hand-Eye Calibration Using 3D Position Data , 2017, IEEE Transactions on Automation Science and Engineering.

[10]  Fei Liu,et al.  Calibration method of robot base frame using unit quaternion form , 2015 .

[11]  Ilian A. Bonev,et al.  A new method for measuring a large set of poses with a single telescoping ballbar , 2013 .

[12]  Sergey A. Kolyubin,et al.  Optimising Configurations of KUKA LWR4+ Manipulator for Calibration with Optical CMM , 2015 .

[13]  Chao Yun,et al.  Calibration method of robot base frame using procrustes analysis , 2016, 2016 Asia-Pacific Conference on Intelligent Robot Systems (ACIRS).

[14]  Yahui Gan,et al.  Robot Calibration for Cooperative Process under Typical Installation , 2014, J. Appl. Math..

[15]  J. Denavit,et al.  A kinematic notation for lower pair mechanisms based on matrices , 1955 .

[16]  John Norrish,et al.  Recent Progress on Programming Methods for Industrial Robots , 2010, ISR/ROBOTIK.

[17]  Jonghyuk Kim,et al.  Dual quaternion-based graphical SLAM , 2016, Robotics Auton. Syst..

[18]  Alfredo Valverde,et al.  Dynamic modeling and control of spacecraft robotic systems using dual quaternions , 2018 .

[19]  Nassir Navab,et al.  Camera Pose Filtering with Local Regression Geodesics on the Riemannian Manifold of Dual Quaternions , 2017, 2017 IEEE International Conference on Computer Vision Workshops (ICCVW).

[20]  Morris Driels,et al.  Full-pose calibration of a robot manipulator using a coordinate-measuring machine , 1993 .

[21]  Guillaume Leclercq,et al.  3D kinematics using dual quaternions: theory and applications in neuroscience , 2013, Front. Behav. Neurosci..

[22]  J. Michael McCarthy,et al.  Introduction to theoretical kinematics , 1990 .

[23]  Erol Ozgur,et al.  Kinematic modeling and control of a robot arm using unit dual quaternions , 2016, Robotics Auton. Syst..

[24]  William Rowan Hamilton,et al.  ON QUATERNIONS, OR ON A NEW SYSTEM OF IMAGINARIES IN ALGEBRA , 1847 .