Forward Kinematics of 6-UPS Parallel Manipulators with One Displacement Sensor

doi:10.3901/JME.2018.05.001

Abstract

Abstract: The closed-loop real-time feedback control requires the forward kinematics analysis, which has not been solved completely in the field of parallel robots. A system of high degree univariate polynomial equations of the analytical forward kinematics analysis of 6-UPS parallel manipulators (6-UPS) can be obtained by eliminating variables. Also they can be analyzed by adding at least 2 extra displacement sensors. Although with this progress, it is still not capable to be applied to the real-time closed-loop feedback control. In order to achieve the closed-loop feedback control with high performance, a new analytical algorithm is proposed. In the new algorithm, only one displacement sensor is installed in the center of 6-UPS to obtain the seventh rod length, the elements of rotation matrix based on quaternions are replaced by new symbols, and the 11 compatible equations can be solved by reducing the degree twice and then raising the degree of the equations' variables combining with algebraic elimination methods. The analytical forward kinematics solutions of 6-UPS, which is needed by the closed-loop real-time feedback control system, are obtained in the end. Taking advantages of the proposed method, the singularity problem is solved and the multi-solution problem is also solved because unique position and orientation can be obtained. Finally, one numerical example is presented and the result is verified. Results indicate that the proposed forward kinematics algorithm is both correct and effective.

Key words: analytical algorithm, displacement sensor, forward kinematics, parallel mechanisms

CLC Number:

TH112
TP242

LIU Yanli, CHENG Shili, JIANG Surong, YANG Xiaolong, LI Yao, WU Hongtao. Forward Kinematics of 6-UPS Parallel Manipulators with One Displacement Sensor[J]. Journal of Mechanical Engineering, 2018, 54(5): 1-7.

References

[1] MERLET J P. Parallel robots[M]. Dordrecht:Springer,2006.
[2] RAGHAVAN M. The Stewart platform of general geometry has 40 configurations[J]. ASME Journal of Mechanical Design,1993,115(2):277-282.
[3] WAMPLER C W. Forward displacement analysis of general six-in-parallel SPS platform manipulators using soma coordinates[J]. Mechanism and Machine Theory,1996,31(3):331-337.
[4] HUSTY M L. An algorithm for solving the direct kinematics of general Stewart-Gough platforms[J]. Mechanism and Machine Theory,1996,31(4):365-379.
[5] 黄昔光,廖启征,魏世民,等. 一般6-6型平台并联机构位置正解代数消元法[J]. 机械工程学报,2009,45(1):56-61. HUANG Xiguang,LIAO Qizheng,WEI Shimin,et al. Forward kinematics analysis of the general 6-6 platform parallel mechanism based on algebraic elimination[J]. Journal of Mechanical Engineering,2009,45(1):56-61.
[6] ZHANG C D,SONG S M. Forward position analysis of nearly general Stewart platforms[J]. ASME Journal of Mechanical Design,1994,116(1):54-60.
[7] 黄真,赵永生,赵铁石. 高等空间机构学[M]. 北京:高等教育出版社,2014. HUANG Zhen,ZHAO Yongsheng,ZHAO Tieshi. Advanced spatial mechanism[M]. Beijing:Higher Education Press,2014.
[8] 程世利,吴洪涛,王超群,等. 一般6-SPS并联机构运动学正解的解析化方法[J]. 中国机械工程,2010,21(11):1261-1264. CHENG Shili,WU Hongtao,WANG Chaoqun,et al. Analytical method for the forward kinematics analysis of the general 6-SPS parallel mechanisms[J]. China Mechanical Engineering,2010,21(11):1261-1264.
[9] WU W D,HUANG Y Z. The direct kinematic solution of the planar stewart platform with coplanar ground points[J]. MM Research Preprints,1996,14(3):263-272.
[10] 程世利,吴洪涛,姚裕,等. 6-SPS并联机构运动学正解的一种解析化方法[J]. 机械工程学报,2010,46(9):26-31. CHENG Shili,WU Hongtao,YAO Yu,et al. An analytical method for the forward kinematics analysis of 6-SPS parallel mechanisms[J]. Journal of Mechanical Engineering,2010,46(9):26-31.
[11] 程世利,吴洪涛,王超群,等. 基于正交补的6-3 Stewart并联机构运动学正解[J]. 中国机械工程,2011,22(5):505-509. CHENG Shili,WU Hongtao,WANG Chaoqun,et al. Forward kinematics analysis of 6-3 Stewart parallel mechanisms based on orthogonal complement method[J]. China Mechanical Engineering,2011,22(5):505-509.
[12] HUANG X G,LIAO Q Z,WEI S M. Closed-form forward kinematics for a symmetrical 6-6 Stewart platform using algebraic elimination[J]. Mechanism and Machine Theory,2010,45(2):327-334.
[13] JI P,WU H T. A closed form forward kinematicssolution for the 6-6P Stewart platform[J]. IEEE Transactions on Robotics and Automation,2001,17(4):522-526.
[14] YANG X Y,WU H T,CHEN B,et al. Fast numerical solution to forward kinematics of general Stewart mechanism using quaternion[J]. Transactions of Nanjing University of Aeronautics and Astronautics,2014,31(4):377-385.
[15] HE J,GU H,WANG Z,et al. Solving the forward kinematics problem of six-DOF Stewart platform using multi-task Gaussian process[J]. ARCHIVE Proceedings of the Institution of Mechanical Engineers Part C Journal of Mechanical Engineering Science 1989-1996(vols 203-210),2013,227(1):161-169.
[16] CARDONA M. A new approach for the forward kinematics of general Stewart-Gough platforms[C]//Proceedings of the 2015 IEEE Thirty Fifth Central American and Panama Convention (Concapan XXXV). Tegucigalpa City,Honduras:IEEE,2015,1-6.
[17] CHANDRA R,ROLLAND L. Global-local population memetic algorithm for solving the forward kinematics of parallel manipulators[J]. Connection Science,2015,27(1):22-39.
[18] MERLET J P. Closed-form resolution of the direct kinematics of parallel manipulators using extra sensors data[C]//Proceedings of IEEE International Conference on Robotics and Automation Robotics and Automation. Atlanta,U.S.A:IEEE,1993,200-204.
[19] BARON L,ANGELES J. The decoupling of the direct kinematics of parallel manipulators using redundant sensors[C]//Proceedings of IEEE International Conference on Robotics and Automation. San Diego,California:IEEE,1994:974-979.
[20] HAN K,CHUNG W,YOUM Y. Local structurization for the forward kinematics of parallel manipulators using extra sensor data[C]//Proceedings of IEEE International Conference on Robotics and Automation. Nagoya,Japan:IEEE,1995:514-520.
[21] ZUBIZARRETA A,MARCOS M,CABANES I,et al. Redundant sensor based control of the 3RRR parallel robot[J]. Mechanism and Machine Theory,2012,54:1-17.
[22] SAAFI H,LARIBI M A,ZEGHLOUL S. Forward kinematic model improvement of a spherical parallel manipulator using an extra sensor[J]. Mechanism and Machine Theory,2015,91:102-119.