Improvement of the Algorithm of the Inverse Kinematics Calculation for 6R Series Robots Based on One Novel Paden-Kahan Sub-problem

doi:10.3901/JME.2016.01.079

Abstract

Abstract: For an improved 6-DOR series robot of which the axes of the last three rotating joints intersect to one point and the axes of the first three rotating joints are non-intersect each other, its workspace is better than the workspaces of traditional industrial robots. But the inverse kinematics calculation for this improved 6-DOR series robot is complicate and cost large computing, which limit its application. In order to improve the performance of the algorithm for its inverse kinematics calculation, a novel Paden-Kahan sub-problem which can be described as letting a point rotate about two disjoint and non-parallel subsequent axes to the point appointed, and its extended problem which can be described as letting a point rotate about two disjoint and non-parallel subsequent axes to two points fixed with two distance appointed to each, are proposed and solved. By constructing a plane perpendicular to the motion trajectory of the rotating point, the forward and inverse kinematics problems of this novel Paden-Kahan sub-problem were solved. Combining with other known Paden-Kahan sub-problems, the inverse kinematics of the 6R series robots are simplified and solved. Then the constraint conditions and the situations of the number of its inverse kinematics solutions are discussed. With the method proposed, the geometrical significance signed for the inverse kinematics is clearer than that with traditional algebraic elimination method, and the operation efficiency of the inverse kinematics is improved. The effectiveness of the solving methods is verified through an instance with exact parameters.

Key words: inverse kinematics calculation, Paden-Kahan sub-problems, series robot, workspace

CLC Number:

TP241
TP242

SUN Henghui, ZHAO Aiwu, LI Da, ZHANG Maofeng. Improvement of the Algorithm of the Inverse Kinematics Calculation for 6R Series Robots Based on One Novel Paden-Kahan Sub-problem[J]. Journal of Mechanical Engineering, 2016, 52(1): 79-86.

References

[1] 理查德?摩雷，李泽湘，厦恩卡?萨思特里.机器人操作的数学导论[M]. 北京：机械工业出版社，1998.MURRAY R M，LI Zexiang，SASTRY S S. A mathematical introduction to robotic manipulation[M]. Beijing：China Machine Press，1998.
[2] HUNT K H. Kinematic geometry of mechanisms[M]. New York：Oxford University Press，1978.
[3] SARIYILDIZ E，TEMELTAS H. Solution of inverse kinematic problem for serial robot using quaterninons[C]// IEEE International Conference on Mechatronics and Automation，Aug. 9-12，2009，Changchun University，Changchun，China. New York：IEEE，2009：26-31.
[4] 赵杰，刘玉斌，蔡鹤皋. 一种运动旋量逆解子问题的求解及其应用[J]. 机器人，2005，27(2)：163-167.ZHAO Jie，LIU Yubin，CAI Hegao. Solution for one type of inverse kinematics sub-problem in screw theory and its application[J]. Robot，2005，27(2)：163-167.
[5] 孔民秀，孙立宁，杜志江，等. 一类运动支链逆解问题的旋量指数积求解方法[J]. 哈尔滨工业大学学报，2008，40(3)：372-375.KONG Minxiu，SUN Lining，DU Zhijiang，et al. Solution to inverse kinematics of a type of kinematic chain using screw theory and exponential product method[J]. Journal of Harbin Institute of Technology，2008，40(3)：372-375.
[6] 陈庆诚，朱世强，王宣银，等. 基于旋量理论的串联机器人逆解子问题求解算法[J]. 浙江大学学报，2014，48(1)：8-14，20. CHEN Qingcheng，ZHU Shiqiang，WANG Xuanyin，et al. Inverse kinematics sub-problem solution algorithm for serial robot based on screw theory[J]. Journal of Zhejiang University，2014，48(1)：8-14，20.
[7] 吕世增，张大卫，刘海年. 基于吴方法的 6R 机器人逆运动学旋量方程求解[J]. 机械工程学报，2010，46(17)：35-41.Lü Shizeng，ZHANG Dawei，LIU Hainian. Solution of screw equation for inverse kinematics of 6R robot based on Wu's method[J]. Journal of Mechanical Engineering，2010，46 (17)：35-41.
[8] 钱东海，王新峰，赵伟，等. 基于旋量理论和Paden-Kahan子问题的6自由度机器人逆解算法[J]. 机械工程学报，2009，45(9)：72-81. QIAN Donghai，WANG Xinfeng，ZHAO Wei，et al. Algorithm for the inverse kinematics calculation of 6-DOF robots based on screw theory and Paden-Kahan sub-problems[J]. Journal of Mechanical Engineering，2009，45(9)：72-81.
[9] 杨明明，陈伟海，于守谦，等. 基于Paden-Kahan子问题的冗余度机器人运动学求解[J]. 机器人，2004，26(3)：250-255.YANG Mingming，CHEN Weihai，YU Shouqian，et al. Kinematic solutions for redundant robot based on Paden-Kahan sub-problems[J]. Robot，2004，26(3)：250-255.
[10] 陈鹏，刘璐，余飞，等. 一种仿人机械臂的运动学逆解的几何求解方法[J]. 机器人，2012，34(2)：211-216. CHEN Peng，LIU Lu，YU Fei，et al. A geometrical method for inverse kinematics of a kind of humanoid manipulator[J]. Robot，2012，34(2)：211-216.
[11] 宫金良，黄风安，张彦斐. 基于指数积的Delta机器人运动学正解建模[J]. 北京理工大学学报，2013，33(6)：581-585.GONG Jinliang，HUANG Fengan，ZHANG Yanfei. Direct kinematics analysis of Delta robot based on exponential product[J]. Transactions of Beijing Institute of Technology，2013，33(6)：581-585.
[12] 覃刚. 复杂机械系统建模方法及在多轴底盘研发中的应用研究[D]. 武汉：华中科技大学，2011.QIN Gang. Research on complex mechanical system modeling and its application in multi-axis chassis development[D]. Wuhan：Huazhong University of Science & Technology，2011.
[13] 蔡自兴. 机器人学[M]. 北京：清华大学出版社，2000 . CAI Zixing. Robotics[M]. Beijing：Tsinghua University Press，2000.
[14] KWON S J，YOUM Y，CHUNG W K. General algorithm for automatic generation of the workspace for n-link planar redundant manipulators[J]. Journal of Mechanical Design，1994，116(3)：967-969.
[15] 田海波，马宏伟，魏娟. 串联机器人机械臂工作空间与结构参数研究[J]. 农业机械学报，2013，44(4)：196-201.TIAN Haibo，MA Hongwei，WEI Juan. Workspace and structural parameters analysis for manipulator of serial robot[J]. Transactions of the Chinese Society for Agricultural Machinery，2013，44(4)：196-201.