随着产品柔性化、定制化的生产模式快速发展，作为制造业智能装备的工业机器人，其单台独立运行的工作模式难以满足复杂零部件的焊接加工，因此，本文研究建立由工业机器人与变位机组成的协作焊接工作站。

首先，在分析工业机器人与变位机之间的运动形式及其轨迹约束的基础上，建立了基于主从运动链的机器人协作焊接工作站耦合运动学模型，分别对工业机器人和变位机的运动学方程进行求解；基于最佳焊接效果的位姿要求，阐述了耦合运动学的求解流程；为获取实际焊接工作站的布局，采用适用于变位机基坐标系标定的关节轴线法；针对机器人与变位机的运动轨迹要求，分别设计了协作运动和同步运动的插补算法，并研究了基于圆弧的焊接轨迹平滑过渡方法；为实现工业机器人与变位机运行速度同步，采用了基于扩展联动轴的同步速度规划方法，并在梯形速度规划的基础上，分别研究了基于最短时间和基于给定时间的同步速度规划。

最后，以离线仿真软件Robotstudio6.08作为协作仿真平台，分别建立了采煤机电气控制箱和T型管道的离线焊接工作站，通过仿真实验证明了协作插补算法和同步速度规划的可行性；基于ADAMS分析了进行位姿过渡后的各个关节的动力学曲线图，证明了本文提出的圆弧位置过渡的有效性；通过实际焊接加工验证了离线焊接控制程序的正确性。

With the rapid development of production mode that product is flexible and the customized, as an equipment for intelligent manufacturing, industrial robot’s single independent operation mode is difficult to meet the welding processing of complex parts. Therefore, this paper studied the establishment of a collaborative welding workstation which composed of industrial robot and displacement machines.

Firstly, on the basis of analyzing the motion form and its positioning constraints between the industrial robot and the displacement machine, the coupling kinematics model based on the master-slave motion chains are established, additionally, the kinematics equations of the industrial robot and the displacement machine are solved respectively. The solving process of collaborative kinematics is elaborated based on the positional request of the best welding effect. In order to obtain the layout of the actual welding station, the joint axis method suitable for the calibration of the displacement machine base coordinate system is proposed. In response to the movement trajectory of the robot and the displacement machine, the interpolation algorithm for collaborative movement and synchronous motion are designed, and the smooth transition method based on circular welding track is proposed. In order to realize the running speed synchronous between industrial robot and the displacement machine, the synchronous speed planning method based on the extended linkage axis is proposed, and on the basis of trapezoidal speed planning, synchronous speed planning based on the shortest time and a given time has been studied.

Eventually, used offline simulation software Robotstudio6.08 as a collaborative simulation platform, the off-line welding workstation of the electrical control box of coal winning machine and T-type pipe is established. The feasibility of collaborative interpolation algorithm and synchronous speed planning is proved by simulation experiment. Based on ADAMS, the dynamic curves of each joint after postural transition were analyzed, which proves the effectiveness of the arc position transition proposed in this paper, the correctness of the off-line welding control procedure is verified by actual welding processing.

[1] 国家制造强国建设战略咨询委员会. 中国制造2025蓝皮书(2018)[M]. 北京: 电子工业出版社, 2018.

[2] 侯仰强, 王天琪, 李亮玉, 等. 基于双机器人协调焊接标定算法[J]. 焊接学报, 2017, 38(2):92-96+5.

[3] Wang H, Wang H, Huang JH, et al. Smooth point-to-point trajectory planning for industrial robots with kinematical constraints based on high-order polynomial curve[J]. Mechanism and Machine Theory, 2019, 139:284-293.

[4] 包翔宇, 张弓, 曹学鹏, 等. 双机器人协同旋转过程中的四元数插补路径规划[J]. 机械科学与技术, 2020, 39(10):1547-1554.

[5] 曹学鹏, 包翔宇, 张弓, 等. 基于模糊自适应和优化阻抗的双机器人力/位主从协作控制方法[J/OL].工程科学与技术:1-9[2020-08-23].https://doi.org/10.15961/j.jsuese. 201900729.

[6] 张涛, 刘天威, 李富章, 等. 基于改进烟花算法的多目标多机器人任务分配[J]. 信号处理, 2020, 36(8):1243-1252.

[7] 翟敬梅, 应灿, 张铁, 等. 双机器人协作焊接的轨迹优化[J]. 焊接学报, 2015, 36(1):91-95.

[8] 曾氢菲, 刘雪梅, 邱呈溶. 多臂协作焊接机器人运动学逆解及误差分析[J]. 焊接学报, 2019, 40(11):21-27.

[9] 何广中. 基于焊接位置数学模型的变位机逆运动学算法[J]. 机械工程学报, 2006, 42(6):86-91.

[10]万鸾飞, 戴先中, 甘亚辉. 双机器人协作弧焊过程的轨迹规划研究[J]. 控制工程, 2017, 24(7):1303-1309.

[11]侯仰强, 王天琪, 岳建锋, 等. 基于多目标遗传算法的双机器人协调焊接路径规划[J]. 中国机械工程, 2018, 29(16):1984-1989.

[12]许勇, 程浩, 王鑫. 阀体密封面变位焊接机器人系统运动学建模[J]. 计算机集成制造系统, 2016, 22(11):2580-2587.

[13]王美玲, 骆敏舟. 一种冗余自由度双臂机器人协调控制器设计[J]. 系统仿真学报, 2016, 28(8):1783-1789.

[14]赵文政, 刘银华, 金隼. 面向多机器人协调运动规划的层级化任务分配方法[J/OL]. 计算机集成制造系统:1-13[2021-01-09].http://kns.cnki.net/kcms/detail/11.5946.tp. 20201203.1132.006.html.

[15]王乐乐, 眭泽智, 蒲志强, 等. 一种改进RRT的多机器人编队路径规划算法[J]. 电子学报, 2020, 48(11):2138-2145.

[16]王琛,茅健.基于时间窗模型的双向机器人路径规划方法[J/OL].计算机工程与应用:1-11[2021-01-09].http://kns.cnki.net/kcms/detail/11.2127.TP.20201023.1737.011. html.

[17]李洋, 徐达, 周诚. 基于自适应步长RRT的双机器人协同路径规划[J]. 农业机械学报, 2019, 50(3):358-367.

[18]关英姿, 刘文旭, 焉宁, 等. 空间多机器人协同运动规划研究[J]. 机械工程学报, 2019, 55(12):37-43.

[19]潘建龙. 多机器人协作系统运动规划及位置力协调控制研究[D]. 东南大学, 2018.

[20]段晋军. 多机器人协作焊接中的轨迹规划和位置力协调控制研究[D]. 东南大学, 2019.

[21]徐意. 工业机器人协同运动控制技术的研究与实现[D]. 华中科技大学, 2019.

[22]韦瑞新. 工业机器人双机协作柔顺路径规划[D]. 华中科技大学, 2019.

[23]盛蕊. 机器人模块化双臂运动学与协作空间研究[D]. 安徽理工大学, 2019.

[24] Wu Q, Li M, Qi X. Coordinated control of a dual-arm robot for surgical instrument sorting tasks [J]. Robotics & Autonomous Systems, 2019, 2(112):1-12.

[25] Salehian SSM, Figueroa N, Billard A. A Unified Framework for Coordinated Multi-Arm Motion Planning[J]. International Journal of Robotics Research, 2018, 37(10):1-28.

[26] Kurosu J, Yorozu A, Takahashi M. Simultaneous dual-arm motion planning for minimizing operation time[J]. Applied Sciences, 2017, 7(12):1210.

[27] Erhart S, Hirche S. Internal Force Analysis and Load Distribution for Cooperative Multi-Robot Manipulation[J]. IEEE Transactions on Robotics, 2017, 31(5):1238-1243.

[28] Hernansanz A, Casals A, Amat J. A multi-robot cooperation strategy for dexterous task-oriented teleoperation[J]. Robotics and Autonomous Systems, 2015, 68(7):156-172.

[29] Tomi M, Chevallereau C, Jovanovi K, et al. Human to humanoid motion conversion for dual-arm manipulation tasks[J]. Robotica, 2018:1-21.

[30] Okamura K, Park FC. Kinematic calibration using the product of exponentials formula[J]. Robotica, 1996, 14(4):415-421.

[31] Craig J. 机器人学导论[M]. 第4版. 北京: 机械工业出版社, 2018.

[32] Jiang G, Luo M, Bai K, et al. A precise positioning method for a puncture robot based on a PSO-optimized BP neural network algorithm[J]. Applied Sciences, 2017, 7(10):969-982.

[33] Collinsm TJ, Shen WM. Particle swarm optimization for high DOF inverse kinematics[C]//IEEE International Conference on Control, Automation and Robotics. Piscataway, USA: IEEE, 2017: 6pp.

[34] Tabandeh S, Melek WW, Clark CM. An adaptive niching genetic algorithm approach for generating multiple solutions of serial manipulator inverse kinematics with applications to modular robots[J]. Robotica, 2010, 28(4):493-507.

[35]林阳, 赵欢, 丁汉．基于多种群遗传算法的一般机器人逆运动学求解[J]. 机械工程学报, 2017, 53(3):1-8.

[36] Wang Y, Li HX, Huang T, et al. Differential evolution based on covariance matrix learning and bimodal distribution parameter setting[J]. Applied Soft Computing Journal, 2014, 18(1):232- 247.

[37]谢习华, 范诗萌, 周烜亦, 等. 基于改进差分进化算法的机械臂运动学逆解[J]. 机器人, 2019, 41(1):50-57.

[38] Gonzalez C, Blanco D, Moreno L. A memetic approach to the inverse kinematics problem[C]//IEEE International Conference on Mechatronics and Automation. Piscataway, USA: IEEE, 2012:180-185.

[39] Uzcategui CG, Rojas DB. A memetic differential evolution algorithm for the inverse kinematics problem of robot manipulators[J]. International Journal of Mechatronics and Automation, 2013, 3(2):118-131.

[40] Starke S, Hendrich N, Magg S, et al. An efficient hybridization of genetic algorithms and particle swarm optimization for inverse kinematics[C]//IEEE International Conference on Robotics and Biomimetics. Piscataway, USA: IEEE, 2016:1782-1789.

[41] Paul RP, Stevenson CN. Kinematics of robot wrists[J]. International Journal of Robotics Research, 1983, 2(2):31-38.

[42] Yang DCH, Lai ZC. On the dexterity of robotic manipulators-service angle[J]. Journal of Mechanical Design, 1985, 107(2):262-270.

[43] Angeles J, Rojas A. Manipulator inverse kinematics via condition number minimization and continuation[J]. International Journal of Robotics & Automation, 1987, 2(2):61-69.

[44] Yoshikawa T. Dynamic manipulability of robot manipulators[C]//IEEE International Conference on Robotics and Automation. Piscataway, USA: IEEE, 1985:1033-1038.

[45] Lee S. Dual redundant arm configuration optimization with task-oriented dual rrm manipulability[J]. IEEE Transactions on Robotics & Automation, 1989, 5(1):78-97.

[46] Andrea C, Paolo R. Online planning of optimal trajectories on assigned paths with dynamic constraints for robot manipulators[C]//IEEE International Conference on Intelligent Robots and Systems. Piscataway, USA: IEEE, 2016:979-985.

[47]岳晴晴, 林明. 基于多项式加减速控制的轨迹规划的研究[J]. 计算机工程与科学, 2019, 41(12):2255-2260.

[48]韩江, 谷涛涛, 夏链, 等. 基于混合插值的工业机器人关节轨迹规划算法[J]. 中国机械工程, 2018, 29(12):1460-1466.

[49]谢文雅. 基于四元数的工业机器人姿态规划与插补算法的研究[D]. 华中科技大学, 2017.

[50] Chen YD, Li L. Collision-free trajectory planning for dual-robot systems using B-splines[J]. International Journal of Advanced Robotic systems, 2017, 14(4):122-141.

[51] Sencer B, Ishizaki K, Shamoto E. A curvature optimal sharp corner smoothing algorithm for high-speed feed motion generation of NC systems along linear tool paths[J]. The International Journal of Advanced Manufacturing Technology, 2015, 76(9-12):1977-1992.

[52] Pateloup V, Duc E, Ray P. B spline approximation of circle arc and straight line for pocket machining[J]. Computer-Aided Design, 2010, 42(9):817-827.

[53] Yang K, Moon S, Yoo S, et al. Spline-Based RRT Path Planner for Non-Holonomic Robots[J]. Journal of Intelligent & Robotic Systems, 2014, 73(1):763-782.

[54]陆政, 韩昊一, 纪良, 等. 基于ROS的UR机器人离线编程系统设计与开发[J]. 计算机仿真, 2017, 34(9):309-313+318.

[55]刘欢庆, 苏宇锋, 高建设, 等. 基于SolidWorks的涂胶机器人离线编程系统[J]. 组合机床与自动化加工技术, 2020(8):88-91.

[56] Rodrigues M, Kormann M, Schuhler C, et al. Robot Trajectory Planning Using OLP and Structured Light 3D Machine Vision[C]//International Symposium on Visual Computing. Berlin, Heidelberg, Germany: Springer, 2013:244-253.

[57] Perla M, Richard W, David B, et al. Flexible robot sealant dispensing cell using RGB-D sensor and off-line programming[J]. Robotics and Computer-Integrated Manufacturing, 2017, 48:188-195.

[58] Denavit J, Hartenberg.RS. A kinematic notation for lower-pair mechanisms based on matrices[J]. Journal of Applied Mechanics, 1955, 22:215-221.

[59]葛小川, 郑飂默, 吴纯赟, 等. 倍四元数在6R串联机器人逆解中的应用[J]. 组合机床与自动化加工技术, 2016(12):16-19.

[60]葛为民, 宇旭东, 王肖锋, 等. 基于对偶四元数的机械臂运动学建模及分析[J]. 机械传动, 2018, 42(7):112-117.

[61] E Sariyildiz，E Cakiray, H Temeltas．A comparative study of three inverse kinematic methods of serial industrial robot manipulators in the screw theory framework[J]. International Journal of Advanced Robotic Systems, 2011, 8(5):9-24.

[62]陈志翔, 卢振洋, 殷树言, 等. 焊缝位姿及焊枪位姿的模型[J]. 机械工程学报, 2003(7):59-62.

[63]田勇, 王洪光, 潘新安, 等. 一种协作机器人工作空间灵活度的求解方法[J]. 机器人, 2019, 41(3):298-306.

[64]杨凯, 黄晋英. 一种8自由度空间机械臂运动学及工作空间分析[J]. 机械传动, 2021, 45(3):147-152.

[65]李宪华, 石雪松, 吕磊, 等. 基于全局可操作度的6R机械臂尺寸优化方法[J]. 系统仿真学报, 2019, 31(12):2569-2574.

[66]张永贵, 刘文洲, 高金刚, 等. 任务空间上的机器人灵活性评价方法[J]. 兰州理工大学学报, 2015, 41(1):37-41.

[67] Lee H, Sohn J, Lee J. Optimization of dual-arm configurations for multiple object handling[J]. Industrial Electronics IEEE International Symposium on, 2012:1291-1296.