Integration of Robotic Tracking/Measuring-machining Applying the Closed and Smooth Properties of Lie Groups: I System Calibration and Path Generation

doi:10.3901/JME.2025.20.001

Abstract

Abstract: The aircraft skin is the primary component forming the aerodynamic shape of an aircraft, characterized by large size, thin wall (thickness 2～6 mm) and complex structure. Currently, manufacturers generally adopt a manual comparison-marking-trimming method to remove the edge allowance of the skin parts, leading to large cumulative human errors and difficulties in controlling assembly quality. Vision/force-guided industrial robot milling with high-flexibility and large operation range provides a novel approach to solving these problems. However, difficulties in simultaneous calibration of dual-robot systems, smooth path generation for machining and accurate control of the robot’s trajectory have become the bottlenecks restricting the application of robot milling for the aircraft skin. The above challenges can be summarized as the simultaneous decoupling of spatial transformation and the quantitative control of pose errors. To address these issues, this paper conducts in-depth research on dual-robot system calibration, smoothing machining path generation and closed-loop feedback control of the robot’s end-effector. The Part I proposes simultaneous calibration method of dual-robot system for robotic tracking/measuring-machining, establishes kinematics model of robot-tracking system and studies method to generate a smooth machining path for aircraft skin. The Part II studies closed-loop feedback control model for robot’s end-effector under external tracking system, develops closed-loop feedback control system for robot. The simultaneous calibration accuracy test of dual-robot, the trajectory accuracy test of end pose with closed-loop control, and the robotics milling accuracy test of typical skin samples are carried out to validate the effectiveness of the proposed methods.

Key words: integration of tracking/measuring and machining, lie group and lie algebra, closed and smooth property, pose simultaneous calibration, milling path generation

CLC Number:

TH161

LI Wenlong, JIANG Cheng, XU Wei, DING Han. Integration of Robotic Tracking/Measuring-machining Applying the Closed and Smooth Properties of Lie Groups: I System Calibration and Path Generation[J]. Journal of Mechanical Engineering, 2025, 61(20): 1-15.

References

[1] DENAVIT J，HARTENBERG R S. A kinematic notation for lower-pair mechanisms based on matrices[J]. Journal of Applied Mechanics，1955，22(2)：215-221.
[2] HE R，ZHAO Y，YANG S，et al. Kinematic-parameter identification for serial-robot calibration based on POE formula[J]. IEEE Transactions on Robotics，2010，26(3)：411-423.
[3] NUBIOLA A，BONEV I A. Absolute calibration of an ABB IRB 1600 robot using a laser tracker[J]. Robotics and Computer-Integrated Manufacturing，2013，29(1)：236-245.
[4] LI C，WU Y，LOWE H，et al. POE-based robot kinematic calibration using axis configuration space and the adjoint error model[J]. IEEE Transactions on Robotics，2016，32(5)：1264-1279.
[5] 高文斌，罗瑞卿，江自真. 基于局部指数积的模块化机器人运动学参数标定[J]. 机器人，2021，43(1)：66-73. GAO Wenbin，LUO Ruiqing，JIANG Zizhen. Kinematic- parameter calibration for modular robots based on the local POE[J]. Robot，2021，43(1)：66-73.
[6] ANDREFF N，HORAUD R，ESPIAU B. Robot hand-eye calibration using structure-from-motion[J]. The International Journal of Robotics Research，2001，20(3)：228-248.
[7] HELLER J，HAVLENA M，PAJDLA T. Globally optimal hand-eye calibration using branch-and-bound[J]. IEEE Transactions on Pattern Analysis and Machine Intelligence，2016，38(5)：1027-1033.
[8] 李巍，吕乃光，董明利，等. 基于对偶四元数的机器人方位与手眼关系同时标定方法[J]. 机器人，2018，40(3)：301-308. LI Wei，LÜ Naiguang，DONG Mingli，et al. Simultaneous robot-world/hand-eye calibration using dual quaternion[J]. Robot，2018，40(3)：301-308.
[9] LI A G，WANG L，WU D. Simultaneous robot-world and hand-eye calibration using dual-quaternions and Kronecker product[J]. International Journal of Physical Sciences，2010，5(10)：1530-1536.
[10] 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.
[11] WANG G，LI W L，JIANG C，ZHU D H，et al. Simultaneous calibration of multicoordinates for a dual-robot system by solving the AXB = YCZ problem[J]. IEEE Transactions on Robotics，2021，37(4)：1172-1185.
[12] 樊晶晶，马骊群，孙安斌，等. 模式向量法提取点云数据线轮廓点[J]. 光学精密工程，2019，27(7)：1640-1648. FAN Jingjing，MA Liqun，SUN Anbin，et al. Extraction of line contour points from point cloud data using pattern vector method[J]. Optics and Precision Engineering，2019，27(7)：1640-1648.
[13] 陈浩，丁其川，潘磊. 基于梯度聚类的有序点云边缘优化提取方法[J]. 仪器仪表学报，2022，43(5)：165-174. CHEN Hao，DING Qichuan，PAN Lei. Edge optimized extraction from the organized point-cloud data base on the gradient clustering[J]. Chinese Journal of Scientific Instrument，2022，43(5)：165-174.
[14] HE X Z，WANG R Q，FENG C，et al. A novel type of boundary extraction method and its statistical improvement for unorganized point clouds based on concurrent delaunay triangular meshes[J]. Sensors，2023，23(4)：1915.
[15] MATVEEV A，RAKHIMOV R，ARTEMOV A，et al. DEF：Deep estimation of sharp geometric features in 3D shapes[J]. ACM Transactions on Graphics，2022，41(4)：108(22 pp).
[16] WANG G，LI W L，JIANG C，et al. Trajectory planning and optimization for robotic machining based on measured point cloud[J]. IEEE Transactions on Robotics，2022，38(3)：1621-1637
[17] XIONG G，DING Y，ZHU L M. Stiffness-based pose optimization of an industrial robot for five-axis milling[J]. Robotics and Computer-Integrated Manufacturing，2019，55：19-28.
[18] LU L，HAN J，DONG F，et al. Joint-smooth toolpath planning by optimized differential vector for robot surface machining considering the tool orientation constraints[J]. IEEE/ASME Transactions on Mechatronics，2022，27(4)：2301-2311.
[19] SHOEMAKE K. Animating rotation with quaternion curves[C]// 12th Annual Conference on Computer Graphics and Interactive Techniques，1985，San Francisco，California. New York：ACM，1985：245-254.
[20] SHOEMAKE K. Quaternion calculus and fast animation[C]// 14th Annual Conference on Computer Grphics and Interactive Techniques，1987，Anaheim，California. New York：ACM，1987：101-122.
[21] XIE H，WANG Q，ONG S K，et al. Automatic generation of interference-free and posture-smooth toolpath for robotic belt grinding of complex workpieces[J]. IEEE/ASME Transactions on Mechatronics，2023，28(1)：518-530.
[22] 庞智慧，王桂荣，陈晓. 基于NURBS和SLERP插补机器人S型速度规划[J]. 计算机仿真，2023，40(8)：451-457. PANG Zhihui，WANG Guirong，CHEN Xiao. Research on S-velocity profile of industrial robot based on NURBS curve and slerp interpolation[J]. Computer Simulation，2023，40(8)：451-457.
[23] HU Q Y，YANG B，XIE L H，et al. RandLA-Net：Efficient semantic segmentation of large-scale point clouds[C]// 2020 IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR)，June 13-19，2020，Seattle，Washington. New York：IEEE，2020：11105-11114.
[24] 李文龙，谢核，尹周平，等. 基于方差最小化原理的三维匹配数学建模与误差分析[J]. 机械工程学报，2017，53(16)：190-198. LI Wenlong，XIE He，YIN Zhouping，et al. Mathematical modeling and error analysis of 3D matching based on variance minimization principle[J]. Journal of Mechanical Engineering，2017，53(16)：190-198.
[25] XIE H，LI W L，YIN Z P，et al. Variance-minimization iterative matching method for free-form surface[J]. IEEE Transactions on Automation Science and Engineering，2019，16(3)：1181-1204.