Abstract：Traditional hand-eye calibration methods are practically inappropriate for RGB-D cameras, because that the RGB optical center and the depth optical center are not in the same location, and the depth-image is of poor measuring accuracy, low resolution, and no RGB or texture information. A hand-eye calibration method for robotic manipulator and RGB-D cameras using a simple low-cost 3D-printed ball as the calibration object is proposed. Only 3D position measurements of the calibration object are used, which avoids the inconvenience and inaccuracy of orientation measurements. A closed-form solution and an iterative optimal solution are formulated. Results of 100 simulations suggest that the calibration accuracy depends on the measuring accuracy of the RGB-D camera itself, the closed-form solution does not need time alignment between the manipulator and the RGB-D camera, and the calibration accuracy of the iterative optimal solution improves a little bit, while the maximum and variance errors are very stable. Finally, 7-DOF KUKA ⅡWA robot and the Kinect sensor are used to perform hand-eye calibration experiments, and the results are consistent with the simulations. In conclusion, the proposed method is simple and reliable, and can realize the quickly-deployable hand-eye calibration for robotic manipulator and RGB-D cameras.
 Zhang Z Y. Microsoft Kinect sensor and its effect[J]. IEEE MultiMedia, 2012, 19(2):4-10.
 Intel. Intel RealSense Technology[2018-04-05]. https://www.intel.com/content/www/us/en/architecture-and-technology/realsense-overview.html.
 Flacco F, Kroger T, de Luca A, et al. A depth space approach for evaluating distance to objects[J]. Journal of Intelligent and Robotic Systems, 2015, 80(1):7-22.
 Cherubini A, Passama R, Meline A, et al. Multimodal control for human-robot cooperation[C]//IEEE/RSJ International Conference on Intelligent Robots and Systems. Piscataway, USA:IEEE, 2013:2202-2207.
 Chen C, Stitt S, Zheng Y F. Robotic eye-in-hand calibration by calibrating optical axis and target pattern[J]. Journal of Intelligent and Robotic Systems, 1995, 12(2):155-173.
 Tsai R Y, Lenz R K. Real time versatile robotics hand/eye calibration using 3D machine vision[C]//IEEE International Conference on Robotics and Automation. Piscataway, USA:IEEE, 1988:554-561.
 Tsai R Y, Lenz R K. A new technique for fully autonomous and efficient 3D robotics hand/eye calibration[J]. IEEE Transactions on Robotics and Automation, 1989, 5(3):345-358.
 Miseikis J, Glette K, Elle O J, et al. Automatic calibration of a robot manipulator and multi 3D camera system[C]//IEEE/SICE International Symposium on System Integration. Piscataway, USA:IEEE, 2016:735-741.
 徐涛,贾松敏,张国梁.基于协同显著性的服务机器人空间物体快速定位方法[J].机器人,2017,39(3):307-315.Xu T, Jia S M, Zhang G L. Fast spatial object location method for service robot based on co-saliency[J]. Robot, 2017, 39(3):307-315.
 Andreff N, Espiau R. Robot hand-eye calibration using structure-from-motion[J]. International Journal of Robotics Research, 2001, 20(3):228-248.
 Heller J, Havlena M, Sugimoto A, et al. Structure-from-motion based hand-eye calibration using L∞ minimization[C]//IEEE Conference on Computer Vision and Pattern Recognition. Piscataway, USA:IEEE, 2011:3497-3503.
 Wu L, Ren H L. Finding the Kinematic base frame of a robot by hand-eye calibration using 3D position data[J]. IEEE Transactions on Automation Science and Engineering, 2017, 14(1):314-324.
 Wu L, Wang J, Qi L, et al. Simultaneous hand-eye, tool-flange, and robot-robot calibration for comanipulation by solving the AXB=YCZ problem[J]. IEEE Transactions on Robotics, 2016, 32(2):413-428.
 Christian F, Fetzner A, Frey C. Multi-sensor obstacle tracking for safe human-robot interaction[C]//International Symposium on Robotics. Berlin, Germany:VDE, 2014:784-791.
 Pachtrachai K, Allan M, Pawar V, et al. Hand-eye calibration for robotic assisted minimally invasive surgery without a calibration object[C]//IEEE/RSJ International Conference on Intelligent Robots and Systems. Piscataway, USA:IEEE, 2016:2485-2491.
 Daniilidis K. Hand-eye calibration using dual quaternions[J]. International Journal of Robotics Research, 1999, 18(3):286-298.
 Shiu Y C, Ahmad S. Calibration of wrist-mounted robotic sensors by solving homogeneous transform equations of the form AX=XB[J]. IEEE Transactions on Robotics and Automation, 1989, 5(1):16-29.
 Chou J C, Kamel M. Finding the position and orientation of a sensor on a robot manipulator using quaternions[J]. International Journal of Robotics Research, 1991, 10(3):240-254.
 Park F C, Martin B J. Robot sensor calibration:Solving AX=XB on the Euclidean group[J]. IEEE Transactions on Robotics and Automation, 1994, 10(5):717-721.
 Horaud R, Dornaika F. Hand-eye calibration[J]. International Journal of Robotics Research, 1995, 14(3):195-210.
 Zhuang H, Shiu Y C. A noise-tolerant algorithm for robotic hand-eye calibration with or without sensor orientation measurement[J]. IEEE Transactions on Systems, Man and Cybernetics, 1993, 23(4):1168-1175.
 Kukelova Z, Heller J, Pajdla T. Hand-eye calibration without hand orientation measurement using minimal solution[C]//Asian Conference on Computer Vision. Berlin, Germany:Springer-Verlag, 2013:576-589.
 Zhuang H, Roth Z S, Sudhakar R. Simultaneous robot/world and tool/flange calibration by solving homogeneous transformation equations of the form AX=YB[J]. IEEE Transactions on Robotics and Automation, 1994, 10(4):549-554.
 Dornaika F, Horaud R. Simultaneous robot-world and hand-eye calibration[J]. IEEE Transactions on Robotics and Automation, 1998, 14(4):617-622.
 Wang W, Liu F, Yun C. Calibration method of robot base frame using unit quaternion form[J]. Precision Engineering, 2015, 41(3):47-54.