Abstract：A kinematic-parameter calibration method for the reconfigurable modular robot system is studied based on the local product of exponential (local POE) formula, and a calibration method for modular robot based on sub-assemblies is presented. Firstly, the sub-assemblies are described in the twist exponential form, and their kinematic model is established. Then, an actual kinematic model for modular robot based on sub-assemblies is established by using the local POE formula, which includes the joint constraint conditions. By differentiating the kinematic model and employing the explicit expression of the differential of the exponential mapping, the explicit expression of the mapping relationship between the position errors at the end of the modular robot and the errors in the joint twists of the sub-assemblies and in the local position of the terminal sub-assembly is given. Finally, a modular reconfigurable robot system is taken as the experiment platform, and some tests are carried out with the help of a laser tracker. The test result shows that the calibration process can converge to a stable value. After the parameter calibration, the mean value of the modulus of the positioning errors of the 6-DOF (degree-of-freedom) modular manipulator in the tests, is reduced by about 95% and the maximum value is reduced by about 92%.
 Yang G L, Chen I M. A novel kinematic calibration algorithm for reconfigurable robotic systems[C]//IEEE International Conference on Robotics and Automation. Piscataway, USA:IEEE, 1997:3197-3202.  Wang H X, Shen S H, Lu X. A screw axis identification method for serial robot calibration based on the POE model[J]. Industrial Robot, 2012, 39(2):146-153.  Chen G, Li T, Chu M, et al. Review on kinematics calibration technology of serial robots[J]. International Journal of Precision Engineering and Manufacturing, 2014, 15(8):1759-1774.  Chen J, Chao L M. Positioning error analysis for robot manipulators with all rotary joints[J]. IEEE Journal of Robotics and Automation, 1987, 3(6):539-545.  Lin Y, Xi F F, Mohamed R P, et al. Calibration of modular reconfigurable robots based on a hybrid search method[J]. Journal of Manufacturing Science and Engineering, 2010, 132(6):0610021-0610028.  Hayati S, Mirmiranl M. Improving the absolute positioning accuracy of robot manipulators[J]. Journal of Robotic Systems, 1985, 2(4):397-413.  陈根良. 操作机构尺寸与变形误差传递的统一建模方法研究[D].上海:上海交通大学, 2014. Chen G L. A unified error transmission model of robot manipulators considering both kinematic and deformation errors[D]. Shanghai:Shanghai Jiao Tong University, 2014.  谷乐丰,杨桂林,方灶军,等. 一种新型机器人自标定装置及其算法[J].机器人, 2020, 42(1):100-109. Gu L F, Yang G L, Fang Z J, et al. The calibration algorithms for industrial robots based on a novel self-calibration device[J]. Robot, 2020, 42(1):100-109.  Park F C. Computational aspects of the product-of-exponentials formula for robot kinematics[J]. IEEE Transactions on Automatic Control, 1994, 39(3):643-647.  Chen I M, Yang G L, Tan C T, et al. Local POE model for robot kinematic calibration[J]. Mechanism and Machine Theory, 2001, 36(11):1215-1239.  He R B, Zhao Y J, Yang S N, et al. Kinematic-parameter identification for serial-robot calibration based on POE formula[J]. IEEE Transactions on Robotics, 2010, 26(3):411-423.  Lou Y J, Chen T N, Wu Y Q, et al. Improved and modified geometric formulation of POE based kinematic calibration of serial robots[C]//IEEE/RSJ International Conference on Intelligent Robots and Systems. Piscataway, USA:IEEE, 2009:52615266.  高文斌,王洪光,姜勇,等. 一种模块化机器人的标定方法研究[J].机械工程学报, 2014, 50(3):33-40. Gao W B, Wang H G, Jiang Y, et al. Research on the calibration for a modular robot[J]. Journal of Mechanical Engineering, 2014, 50(3):33-40.  Wang R C, Yang G L, Zhao Z H, et al. Robot kinematic calibration with plane constraints based on POE formula[C]//IEEE International Conference on Information and Automation. Piscataway, USA:IEEE, 2016:1887-1892.  Chen I M, Yang G L. Kinematic calibration of modular reconfigurable robots using product-of-exponentials formula[J]. Journal of Robotic Systems, 1997, 14(11):807-821.  高文斌,王洪光,姜勇,等. 模块化可重构机器人标定方法的研究[J].机械工程学报, 2013, 49(17):92-100. Gao W B, Wang H G, Jiang Y, et al. Research on the calibration of modular reconfigurable robot[J]. Journal of Mechanical Engineering, 2013, 49(17):92-100.  Lin Y, Xi F F, Mohamed R P, et al. Calibration of modular reconfigurable robots based on a hybrid search method[J]. Journal of Manufacturing Science and Engineering, 2010, 132(6):061002-061010.  Liu H, Zhu W D, Dong H Y, et al. An improved kinematic model for serial robot calibration based on local POE formula using position measurement[J]. Industrial Robot, 2018, 45(5):573584.  王殿君,王超星,陈亚,等. 模块化六自由度机器人运动学标定与实验研究[J].高技术通讯, 2016, 26(6):577584. Wang D J, Wang C X, Chen Y, et al. Kinematic calibration and experimental study of a modular six-DOF robot[J]. Chinese High Technology Letters, 2016, 26(6):577-584.  Lynch K M, Park F C. Modern robotics[M]. Cambridge, UK:Cambridge University Press, 2017.  Selig J M. Geometric fundamentals of robotics[M]. 2nd ed. New York, USA:Springer-Verlag, 2004.