Forward Kinematics and Workspace Analysis of Screw Theory of Seven-DOF Dual-arm Robot
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摘要: 机器人关节空间与工作空间的关系是通过正向运动学方程建立的，正向运动学分析是实现轨迹规划和控制的关键。介绍了比D-H参数法计算简单、描述全面的旋量理论法，应用指数积公式分别对七自由度和六自由度双臂机器人的单臂进行运动学分析并建立正向运动学方程。利用ADAMS进行运动仿真，对比发现：仿真结果与通过正向运动学方程求解的数据接近，误差不超过3 mm，验证了结合旋量理论建立的正向运动学方程的正确性；利用MATLAB软件进行工作空间分析，通过工作空间云图对比，得出七自由度双臂机器人有着更大的工作空间，表明拥有肩部关节的七自由度双臂机器人具有更好的运动学性能。Abstract: The relationship between robot joint space and working space is established by the forward kinematics equations. The forward kinematics analysis plays a key role in realizing the trajectory planning and control. The screw theory, which is simpler and more comprehensive than the D-H parameter method, is introduced. The kinematic analysis of the seven-DOF single-arm robot and the six-DOF dual-arm robot is carried out with the Product of Exponentials. The forward kinematics equation is established. The ADAMS software is applied for motion simulation. It is found that the simulation results are close to those obtained with the forward kinematics equation and that the error is less than 3 mm. The correctness of the forward kinematics equation established by combining the screw theory is verified. The MATLAB software is used to analyze the workspace. The comparison of the working space cloud map shows that the seven-DOF dual-arm robot has a larger workspace and that the seven-DOF double-arm robot with shoulder joints has a better kinematics performance.
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Key words:
- dual-arm robot /
- screw theory /
- product of exponentials /
- forward kinematics /
- software simulation /
- errors /
- workspace
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表 1 六自由度双臂机器人右臂各关节角取值及末端位移理论值与实际值
时间/s 1 2 3 θ1/(°) -30 -60 -60 θ2/(°) -30 -60 -60 θ3/(°) 30 45 45 θ4/(°) 30 75 75 θ5/(°) 30 60 60 θ6/(°) 45 0 0 px/mm 72.5 98.9 98.9 py/mm 220.4 88.1 88.1 pz/mm -40.2 -23.1 -23.1 px1/mm 70.2 101.9 101.9 py1/mm 218.4 89.8 89.8 pz1/mm -39.5 -22.1 -22.1 注:px, py, pz为理论值; px1, py1, pz1为实际值。 
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表 2 七自由度双臂机器人右臂各关节角取值及末端位移理论值与实际值
时间/s 1 2 3 θ1/(°) 30 -15 -15 θ2/(°) -30 -60 -60 θ3/(°) -30 0 0 θ4/(°) 30 45 45 θ5/(°) 30 -15 -15 θ6/(°) 30 60 60 θ7/(°) 45 0 0 px/mm 46.4 18.5 18.5 py/mm 226.3 243.6 243.6 pz/mm -84.6 122.2 122.2 px2/mm 44.5 20.5 20.5 py2/mm 224.3 245.2 245.2 pz2/mm -84.5 122.1 122.1 注:px, py, pz为理论值; px2, py2, pz2为实际值。
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[1] Denavit J, Hartenberg R S. A kinematic notation for lower-pair mechanisms based on matrices[J]. Journal of Applied Mechanics, 1995, 22:215-221 http://cn.bing.com/academic/profile?id=f3bd69d79310356292d19ebba2268879&encoded=0&v=paper_preview&mkt=zh-cn [2] Whitney D E. Mechanical assemblies:their design, manufacture, and role in product development[M]. New York:Oxford University Press, 2004:35-51 [3] Santolaria J, Aguilar J J, Yagüe J A, et al. Kinematic parameter estimation technique for calibration and repeatability improvement of articulated arm coordinate measuring machines[J]. Precision Engineering, 2008, 32(4):251-268 doi: 10.1016/j.precisioneng.2007.09.002 [4] 冯崇.工业机器人运动分析及控制研究[D].河南洛阳: 河南科技大学, 2015 http://cdmd.cnki.com.cn/Article/CDMD-10464-1015902303.htmFeng C. Study on industrial robot of kinematic analysis and control[D]. Henan Luoyang: Henan University of Science and Technology, 2015(in Chinese) http://cdmd.cnki.com.cn/Article/CDMD-10464-1015902303.htm [5] Rader S, Kaul L, Fischbach H, et al. Design of a high-performance humanoid dual arm system with inner shoulder joints[C]//2016 IEEE-RAS 16th International Conference on Humanoid Robots. Cancun, Mexico: IEEE, 2016: 523-529 [6] Krüger J, Schreck G, Surdilovic D. Dual arm robot for flexible and cooperative assembly[J]. CIRP Annals, 2011, 60(1):5-8 http://www.wanfangdata.com.cn/details/detail.do?_type=perio&id=379ba7cc80b5d63a0c0ad32419f022f0 [7] 吴长征, 刘殿富, 岳义, 等.空间双臂机器人运动学及动力学分析与建模研究[J].上海航天, 2017, 34(3):80-87 http://d.old.wanfangdata.com.cn/Periodical/shht201703011Wu C Z, Liu D F, Yue Y, et al. Kinematics and dynamics modeling for dual-arm space robot[J]. Aerospace Shanghai, 2017, 34(3):80-87(in Chinese) http://d.old.wanfangdata.com.cn/Periodical/shht201703011 [8] 白克强.双臂机器人拟人化动作实现与协调控制方法研究[D].合肥: 中国科学技术大学, 2017Bai K Q. Research on human-like arm motion generation and cooperation control method for humanoid dual-arm robots[D]. Hefei: University of Science and Technology of China, 2017(in Chinese) [9] 曹彩霞, 赵明扬, 朱思俊, 等.双臂机器人协调搬运运动的运动学分析[J].组合机床与自动化加工技术, 2017, (8):44-47 http://d.old.wanfangdata.com.cn/Periodical/zhjc201708011Cao C X, Zhao M Y, Zhu S J, et al. Kinematics analysis of dual arm robot coordinated motion[J]. Modular Machine Tool & Automatic Manufacturing Technique, 2017, (8):44-47(in Chinese) http://d.old.wanfangdata.com.cn/Periodical/zhjc201708011 [10] 敖天翔, 刘满禄, 张华, 等.结合旋量和代数方法的工业机械臂逆运动学解法[J].机械科学与技术, 2017, 36(8):1224-1229 http://journals.nwpu.edu.cn/jxkxyjs/CN/abstract/abstract6762.shtmlAo T X, Liu M L, Zhang H, et al. Inverse kinematic solution of industrial robot arm with combination of screw theory and algebraic methods[J]. Mechanical Science and Technology for Aerospace Engineering, 2017, 36(8):1224-1229(in Chinese) http://journals.nwpu.edu.cn/jxkxyjs/CN/abstract/abstract6762.shtml [11] 李君.基于旋量理论的Stanford臂的运动学分析[J].天津科技大学学报, 2010, 25(4):72-75 doi: 10.3969/j.issn.1672-6510.2010.04.018Li J. Kinematics analysis on Stanford arm based on screw theory[J]. Journal of Tianjin University of Science & Technology, 2010, 25(4):72-75(in Chinese) doi: 10.3969/j.issn.1672-6510.2010.04.018 [12] 方琛玮.基于ADAMS的机器人动力学仿真研究[D].北京: 北京邮电大学, 2009 http://www.wanfangdata.com.cn/details/detail.do?_type=degree&id=Y1568086Fang C W. The dynamic analysis of the robot based on ADAMS virtual console[D]. Beijing: Beijing University of Posts and Telecommunications, 2009(in Chinese) http://www.wanfangdata.com.cn/details/detail.do?_type=degree&id=Y1568086 [13] 李悦, 周利坤.基于旋量理论的RRRP机器人逆运动学分析研究[J].机械科学与技术, 2014, 33(6):820-824 http://journals.nwpu.edu.cn/jxkxyjs/CN/abstract/abstract4911.shtmlLi Y, Zhou L K. The research of RRRP robot inverse kinematics based on screw theory[J]. Mechanical Science and Technology for Aerospace Engineering, 2014, 33(6):820-824(in Chinese) http://journals.nwpu.edu.cn/jxkxyjs/CN/abstract/abstract4911.shtml [14] 陈庆诚.结合旋量理论的串联机器人运动特性分析及运动控制研究[D].杭州: 浙江大学, 2015: 19-21 http://cdmd.cnki.com.cn/Article/CDMD-10335-1015630225.htmChen Q C. Research on analysis of motion characteristics and motion control of serial robot combining screw theory[D]. Hangzhou: Zhejiang University, 2015: 19-21(in Chinese) http://cdmd.cnki.com.cn/Article/CDMD-10335-1015630225.htm [15] 李悦, 周利坤.基于旋量理论的RRRP机器人正运动学分析研究[J].机械科学与技术, 2014, 33(2):194-198 http://journals.nwpu.edu.cn/jxkxyjs/CN/abstract/abstract5038.shtmlLi Y, Zhou L K. The kinematics analysis of a RRRP robot based on the screw theory[J]. Mechanical Science and Technology for Aerospace Engineering, 2014, 33(2):194-198(in Chinese) http://journals.nwpu.edu.cn/jxkxyjs/CN/abstract/abstract5038.shtml [16] 何价来, 罗金良, 宦朋松, 等.基于蒙特卡洛法的七自由度拟人机械臂工作空间分析[J].组合机床与自动化加工技术, 2015, (3):48-51 http://d.old.wanfangdata.com.cn/Periodical/zhjc201503013He J L, Luo J L, Huan P S, et al. Workspace analysis of 7-DOF humanoid robotic arm based on monte carlo method[J]. Modular Machine Tool & Automatic Manufacturing Technique, 2015, (3):48-51(in Chinese) http://d.old.wanfangdata.com.cn/Periodical/zhjc201503013 [17] 周律, 周昱明, 汪亮, 等.基于蒙特卡罗方法的双臂机器人工作空间分析[J].机械传动, 2014, 38(6):85-87, 118 http://www.wanfangdata.com.cn/details/detail.do?_type=perio&id=jxcd201406023Zhou L, Zhou Y M Wang L, et al. Dual-arm robot workspace analysis based on the monte carlo method[J]. Journal of Mechanical Transmission, 2014, 38(6):85-87, 118(in Chinese) http://www.wanfangdata.com.cn/details/detail.do?_type=perio&id=jxcd201406023 -
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