Sensitivity Analysis and Multi-objective Optimization Design of Parallel Manipulators

doi:10.3901/JME.2022.19.229

Abstract

Abstract: An efficient calculation method combining multivariate regression response surface model (RSM), variance based sensitivity analysis method, and intelligent optimization algorithm to solve the high computation-intensive of sensitivity analysis and multi-objective optimization design of parallel manipulators (PMs) caused by the high computational cost of global performance indices (GPIs). First, establish objective functions and design parameters of PMs, increase the node density to improve the calculation accuracy of GPIs, establish the analytical RSM between the GPI and the design parameters using the Latin hypercube sampling method and least squares multivariate fitting technique, and then combine with the RSM and variance based Sobol’s sensitivity analysis method to obtain the important design parameters to the objective influence. Second, simplify design parameters based on the sensitivity analysis results and establish the multi-objective optimization design mathematical model of PMs, including objective functions, design parameters and constraint functions. Combine with RSMs and intelligent optimization algorithm to carry out multi-objective optimization design of PMs. Finally, considering the regular workspace volume, global kinematic and dynamic performance indices as objective functions, the DELTA PM is taken as an example to implement the proposed method. The comparison of the results before and after optimization proves the effectiveness of the proposed method.

Key words: parallel manipulator, multi-objective optimization design, performance index, sensitivity analysis

CLC Number:

TH112

YANG Chao, YE Wei, CHEN Qiaohong. Sensitivity Analysis and Multi-objective Optimization Design of Parallel Manipulators[J]. Journal of Mechanical Engineering, 2022, 58(19): 229-241.

References

[1] ASADA H. A geometrical representation of manipulator dynamics and its application to arm design[J]. Transactions of ASME Journal of Dynamic systems，1983，105(3):131-142.
[2] D'EGIDIO M. Device for the movement and positioning of an element in space:US Patent 4976582[P]. 1990.
[3] HONG J H，YAMAMOTO M. A calculation method of the reaction force and moment for a Delta-type parallel link robot fixed with a frame[J]. Robotica，2009，27:579-587.
[4] YAN S J，ONG S K，NEE A Y C. Stiffness analysis of parallelogram-type parallel manipulators using a strain energy method[J]. Robotics and Computer-Integrated Manufacturing，2016，37:13-22.
[5] KUMAR V. Characterization of workspaces of parallel manipulators[J]. Journal of Mechanical Design，1992，114(3):368-375.
[6] 张伟中，李金平，叶敏，等. 2PUR-PSR并联机构尺度综合多目标优化[J]. 农业机械学报，2020，51(11): 403-410. ZHANG Weizhong，LI Jinping，YE Min，et al. Multi-objective optimization of dimensional synthesis for 2PUR-PSR parallel manipulator[J]. Transactions of the Chinese Society for Agricultural Machinery，2020，51(11):403-410.
[7] THANH V T，HUNG C X. Design optimization of Stewart platform for motion simulation systems using multi-objective genetic algorithm[C]// Proceedings of the 2019 IEEE/ASME International Conference on Advanced Intelligent Mechatronics，Hong Kong，China，July 8-12，2019:436-440.
[8] QUINTERO-RIAZA H F，MEJIA-CALDERON L A，DIAZ-RODRIGUEZ M. Synthesis of planar parallel manipulators including dexterity，force transmission and stiffness index[J]. Mechanics Based Design of Structures and Machines，2019，47(6):680-702.
[9] HUANG Guanyu，GUO Sheng，ZHANG Dan，et al. Kinematic analysis and multi-objective optimization of a new reconfigurable parallel mechanism with high stiffness[J]. Robotica，2018，36(2):187-203.
[10] STAN S-D，MATIES V，BALAN R，et al. Potentialities of optimal design methods for the development of mini parallel robots using genetic algorithms[C]// Proceedings of the IEEE，International Conference on Automation and Logistics，2007:1591-1596.
[11] BOUNAB B. Multi-objective optimal design based kineto-elastostatic performance for the delta parallel mechanism[J]. Robotica，2016，34(2):258-273.
[12] KELAIAIA R，ZAATRI A，COMPANY O，et al. Some investigations into the optimal dimensional synthesis of parallel robots[J]. International Journal of Advanced Manufacturing Technology，2016，83:1525-1538.
[13] SUN Tao，LIAN Binbin. Stiffness and mass optimization of parallel kinematic machine[J]. Mechanism and Machine Theory，2018，120:73-88.
[14] ZHANG Dan，WEI Bin. Interactions and optimizations analysis between stiffness and workspace of 3-upu robotic mechanism[J]. Measurement Science Review，2017，17(2):83-92.
[15] MIRSHEKARI E，GHANBARZADEH A，SHIRAZI K H. Structure comparison and optimal design of 6-rus parallel manipulator based on kinematic and dynamic performances[J]. Latin American Journal of Solids and Structures，2016，13(13):2414-2438.
[16] CHEN Qiaohong，YANG Chao. Hybrid algorithm for multi-objective optimization design of parallel manipulators[J]. Applied Mathematical Modelling，2021，98:245-265.
[17] LIAN Binbin，SUN Tao，SONG Yimin. Parameter sensitivity analysis of a 5-DoF parallel manipulator[J]. Robotics and Computer-Integrated Manufacturing，2017，46:1-14.
[18] SALTELLI A，ANNONI P，AZZINI I，et al. Variance based sensitivity analysis of model output. Design and estimator for the total sensitivity index[J]. Computer Physics Communications，2010，181(2):259-270.
[19] RABITZ H，ALI M F，SHORTER J，et al. Efficient input-output model representations[J]. Computer Physics Communications，1999，117:11-20.
[20] BABU S R，RAJU V R，RAMJI K. Design optimization of 3PRS parallel manipulator using global performance indices[J]. Journal of Mechanical Science and Technology，2016，30(9):4325-4335.
[21] YANG Chao，LI Qinchuan，CHEN Qiaohong. Multi-objective optimization of parallel manipulators using a game algorithm[J]. Applied Mathematical Modelling，2019，74:217-243.
[22] YANG Chao，LI Qinchuan，CHEN Qiaohong. Analytical elastostatic stiffness modeling of parallel manipulators considering the compliance of the link and joint[J]. Applied Mathematical Modelling，2020，78:322-349.
[23] 张伟中，徐灵敏，童俊华，等. 2-PUR-PSR并联机构的运动学分析及尺度综合[J]. 机械工程学报，2018，54(7):45-53. ZHANG Weizhong，XU Lingmin，TONG Junhua，et al. Kinematic analysis and dimensional synthesis of 2-pur-psr parallel manipulator[J]. Journal of Mechanical Engineering，2018，54(7):45-53.
[24] FATTAH A，GHASEMI A M H. Isotropic design of spatial parallel manipulators[J]. The International Journal of Robotics Research，2002，21:811-824.
[25] ANGELES J. Is there a characteristic length of a rigid-body displacement?[J]. Mechanism and Machine Theory，2006，41(8):884-896.
[26] 陈祥，谢福贵，刘辛军. 并联机构中运动/力传递功率最大值的评价[J]. 机械工程学报，2014，50(3): 1-9. CHEN Xiang，XIE Fugui，LIU Xinjun. Evaluation of the maximum value of motion/force transmission power in parallel manipulators[J]. Journal of Mechanical Engineering，2014，50(3):1-9.
[27] WANG Jinsong，WU Chao，LIU Xinjun. Performance evaluation of parallel manipulators: Motion/force transmissibility and its index[J]. Mechanism and Machine Theory，2010，45(10):1462-1476.
[28] 黄真，刘婧芳，李艳文. 论机构自由度[M]，北京: 科学出版社，2011. HUANG Zhen，LIU Jingfang，LI Yanwen. Degree of freedom of mechanism[M]. Beijing:Science Press，2011.
[29] WAN Xiaojin，YANG Junqiang，ZHANG Yan. Dynamic performance optimization of a novel 8-spu parallel walking mechanism[J]. Journal of Computing and Information Science in Engineering，2020，20(4):041004.
[30] YOSHIKAWA T. Dynamic manipulability of robot manipulators[C]// Proceedings of the IEEE International Conference on Robotics and Automation，St. Louis，MO，USA ，March 25-28，1985，1033-1038.
[31] ZHANG Jun，ZHAO Yanqin，CECCARELLI M. Elastodynamic model-based vibration characteristics prediction of a three prismatic-revolute-spherical parallel kinematic machine[J]. Journal of Dynamic Systems Measurement and Control-Transactions of the ASME，2016，138(4):041009.
[32] YANG Chao，LI Qinchuan，CHEN Qiaohong. Natural frequency analysis of parallel manipulators using global independent generalized displacement coordinates[J]. Mechanism and Machine Theory，2021，156:104145.
[33] FANG Jianguang，GAO Yunkai，SUN Guangyong，et al. Multiobjective reliability-based optimization for design of a vehicle door[J]. Finite elements in analysis and design，2013，67:13-21.