Research Papers

Multi-Objective Optimization of Parallel Tracking Mechanism Considering Parameter Uncertainty

[+] Author and Article Information
Yang Qi

Key Laboratory of Mechanism,
Theory and Equipment Design of
Ministry of Education,
Tianjin University,
Tianjin 300350, China
e-mail: qiyang@tju.edu.cn

Tao Sun

Key Laboratory of Mechanism,
Theory and Equipment Design of
Ministry of Education,
Tianjin University,
Tianjin 300350, China
e-mail: stao@tju.edu.cn

Yimin Song

Key Laboratory of Mechanism,
Theory and Equipment Design of
Ministry of Education,
Tianjin University,
Tianjin 300350, China
e-mail: ymsong@tju.edu.cn

1Corresponding author.

Contributed by the Mechanisms and Robotics Committee of ASME for publication in the JOURNAL OF MECHANISMS AND ROBOTICS. Manuscript received June 23, 2017; final manuscript received March 9, 2018; published online April 18, 2018. Assoc. Editor: Clement Gosselin.

J. Mechanisms Robotics 10(4), 041006 (Apr 18, 2018) (12 pages) Paper No: JMR-17-1190; doi: 10.1115/1.4039771 History: Received June 23, 2017; Revised March 09, 2018

Multi-objective optimization of a typical parallel tracking mechanism considering parameter uncertainty is carried out in this paper. Both dimensional and sectional parameters are regarded as design variables. Workspace, kinematic, stiffness, and dynamic performances are simultaneously considered in formulating optimal objectives and constraint conditions. Considering manufacturing and assembling errors, parameter uncertainty is modeled and evaluated to minimize their effects on the optimized performances. Analytical models between objectives and design variables are established to improve the efficiency of optimization while its accuracy is assured. The study of parameter uncertainty and analytical mapping model is incorporated in the optimization of the parallel tracking mechanism. With the aid of particle swarm algorithm, a cluster of solutions, called Pareto frontier, are obtained. By proposing an index, a cooperative equilibrium point representing the balance among objectives is selected and the optimized parameters are determined. The present study is expected to help designers build optimized parallel tracking mechanism in an effective and efficient manner.

Copyright © 2018 by ASME
Your Session has timed out. Please sign back in to continue.


Mauro, S. , Battezzato, A. , Biondi, G. , and Scarzella, C. , 2015, “ Design and Test of a Parallel Kinematic Solar Tracker,” Mech. Eng., 7(12), pp. 1–16.
Li, J. J. , and Jia, Y. H. , 2014, “ Configuration Design of X-Y Style Antenna Pedestal,” Elec. Mech. Eng., 30(5), pp. 37–40.
Li, J. R. , 2010, “ Elementary Analysis on Vertex Tracking of X-Y Type Antenna Pedestal,” Mod. Elec. Tech., 11, pp. 21–23.
Wu, W. L. , and Shi, J. Z. , 2010, “ Research on Relation of Antenna Pedestal Type and High Elevation Tracking,” Comput. Networks, 7, pp. 48–51.
Wu, J. , Chen, X. L. , and Wang, L. P. , 2016, “ Design and Dynamics of a Novel Solar Tracker With Parallel Mechanism,” IEEE-ASME Trans. Mechatronics, 21(1), pp. 88–97.
Song, Y. M. , Qi, Y. , Dong, G. , and Sun, T. , 2016, “ Type Synthesis of 2-DoF Rotational Parallel Mechanism Actuating the Inter-Satellite Link Antenna,” Chin. J. Aeronaut., 29(6), pp. 1795–1805. [CrossRef]
Dunlop, G. R. , and Jones, T. P. , 1999, “ Position Analysis of a Two DOF Parallel Mechanism—The Canterbury Tracker,” Mech. Mach. Theory, 34(4), pp. 599–614. [CrossRef]
Gosselin, C. M. , and Caron, F. , 1999, “Two Degree-of-Freedom Spherical Orienting Device,” U. S. Patent No. 19995966991.
Lum, M. J. H. , Rosen, J. , Sinanan, M. N. , and Hannaford, B. , 2006, “ Optimization of a Spherical Mechanism for a Minimally Invasive Surgical Robot: Theoretical and Experimental Approaches,” IEEE Trans. Biomed. Eng., 53(7), pp. 1440–1445. [CrossRef] [PubMed]
Lum, M. J. H. , Rosen, J. , Sinanan, M. N. , and Hannaford, B. , 2004, “ Kinematic Optimization of a Spherical Mechanism for a Minimally Invasive Surgical Robot,” IEEE International Conference on Robotics and Automation (ICRA), New Orleans, LA, Apr. 26–May 1, pp. 829–834.
Cervantes-Sánchez, J. J. , Hernández-Rodríguez, J. C. , and González-Galván, E. J. , 2004, “ On the 5R Spherical, Symmetric Manipulator: Workspace and Singularity Characterization,” Mech. Mach. Theory, 39(4), pp. 409–429. [CrossRef]
Wu, C. , Liu, X. J. , Wang, L. P. , and Wang, J. S. , 2010, “ Optimal Design of Spherical 5R Parallel Manipulators Considering the Motion/Force Transmissibility,” ASME J. Mech. Des., 132(3), p. 031002. [CrossRef]
Wu, C. , Liu, X. J. , and Wang, J. S. , 2009, “ Transmission Analysis of Spherical 5R Parallel Manipulators,” ASME/IFToMM International Conference on Reconfigurable Mechanisms and Robots, London, June 22–24, pp. 331–336.
Nikulin, V. V. , Sofka, J. , and Skormin, V. A. , 2004, “ Decentralized Control of an OmniWrist Laser Beam Tracking System,” Proc. SPIE, 5338, pp. 194–203.
Sofka, J. , Nikulin, V. , Skormin, V. A. , and Hughes, D. H. , 2009, “ Laser Communication Between Mobile Platforms,” IEEE Trans. Aerosp. Electron. Syst., 45(1), pp. 336–346. [CrossRef]
Skormin, V. A. , Nikulin, V. , and Nicholson, D. J. , 2006, “ Omni-Wrist III—A New Generation of Pointing Devices—Part II: Gimbals Systems-Control,” IEEE Trans. Aerosp. Electron. Syst., 42(2), pp. 726–734. [CrossRef]
Dong, X. , Yu, J. J. , Chen, B. , and Zong, G. H. , 2012, “ Geometric Approach for Kinematic Analysis of a Class of 2-DOF Rotational Parallel Manipulators,” Chin. J. Mech. Eng., 25(2), pp. 24–247. [CrossRef]
Ding, H. F. , Huang, P. , Liu, J. F. , and Kecskeméthy, A. , 2013, “ Automatic Structural Synthesis of the Whole Family of Planar 3-Degrees of Freedom Closed Loop Mechanisms,” ASME J. Mech. Rob., 5(4), p. 041006. [CrossRef]
Jiang, Q. , and Gosselin, C. M. , 2008, “ The Maximal Singularity-Free Workspace of the Gough-Stewart Platform for a Given Orientation,” ASME J. Mech. Des., 130(11), pp. 1671–1676.
Vimal, K. , and Prince, S. , 2015, “ System Analysis for Optimizing Various Parameters to Mitigate the Effects of Satellite Vibration on Inter-Satellite Optical Wireless Communication,” IEEE International Conference on Signal Processing, Informatics, Communication and Energy Systems (SPICES), Kozhikode, India, Feb. 19–21, pp. 1–4.
Hu, Y. , and Rao, S. S. , 2009, “ Game Theory Approach for Multi-Objective Optimal Design of Stationary Flat-Plate Solar Collectors,” Eng. Optim., 41(11), pp. 1017–1035. [CrossRef]
Voglewede, P. A. , and Ebert-Uphoff, I. , 2005, “ Overarching Framework for Measuring Closeness to Singularities of Parallel Manipulators,” IEEE Trans. Rob., 21(6), pp. 1037–1045. [CrossRef]
Wu, J. , Wang, L. P. , and Guan, L. W. , 2013, “ A Study on the Effect of Structure Parameters on the Dynamic Characteristics of a PRRRP Parallel Manipulator,” Nonlinear Dyn., 74(1–2), pp. 227–235. [CrossRef]
Menon, C. , Vertechy, R. , Markot, M. C. , and Parenti-Castelli, V. , 2009, “ Geometrical Optimization of Parallel Mechanisms Based on Natural Frequency Evaluation: Application to a Spherical Mechanism for Future Space Applications,” IEEE Trans. Rob., 25(1), pp. 12–24. [CrossRef]
Alessandro, C. , and Rosario, S. , 2014, “ Elastodynamic Optimization of a 3T1R Parallel Manipulator,” Mech. Mach. Theory, 73, pp. 184–196. [CrossRef]
Wu, G. L. , Caro, S. , Bai, S. P. , and Kepler, J. , 2014, “ Dynamic Modeling and Design Optimization of a 3-DOF Spherical Parallel Manipulator,” Rob. Auton. Syst., 62(10), pp. 1377–1386. [CrossRef]
Bi, Z. M. , and Wang, L. H. , 2009, “ Optimal Design of Reconfigurable Parallel Machining Systems,” Rob. Comput. Integr. Manuf., 25(6), pp. 951–961. [CrossRef]
Shin, H. P. , Lee, S. C. , Jeong, J. I. , and Kim, J. W. , 2013, “ Antagonistic Stiffness Optimization of Redundantly Actuated Parallel Manipulators in a Predefined Workspace,” IEEE/ASME Trans. Mech., 18(3), pp. 1161–1169. [CrossRef]
Sun, T. , and Lian, B. B. , 2018, “ Stiffness and Mass Optimization of Parallel Kinematic Machine,” Mech. Mach. Theory, 120, pp. 73–88. [CrossRef]
Song, Y. M. , Gao, H. , Sun, T. , Dong, G. , Lian, B. B. , and Qi, Y. , 2014, “ Kinematic Analysis and Optimal Design of a Novel 1T3R Parallel Manipulator With an Articulated Travelling Plate,” Rob. Comput. Integr. Manuf., 30(5), pp. 508–516. [CrossRef]
Sun, T. , Wu, H. , Lian, B. B. , Qi, Y. , and Wang, P. F. , 2017, “ Stiffness Modeling, Analysis and Evaluation of a 5 Degree of Freedom Hybrid Manipulator for Friction Stir Welding,” Proc. Inst. Mech. Eng. Part C, 231(23), pp. 4441–4456. [CrossRef]
Klein, J. , Spencer, S. , Allington, J. , Bobrow, J. E. , and Reinkensmeyer, D. J. , 2010, “ Optimization of a Parallel Shoulder Mechanism to Achieve a High-Force, Low-Mass, Robotic-Arm Exoskeleton,” IEEE Trans. Rob., 26(4), pp. 710–715. [CrossRef]
Mukerjee, R. , and Ong, S. H. , 2015, “ Variance and Covariance Inequalities for Truncated Joint Normal Distribution Via Monotone Likelihood Ratio and Log-Concavity,” J. Multivar. Anal., 139, pp. 1–6. [CrossRef]
Wu, J. , Wang, J. S. , Wang, L. P. , and Li, T. M. , 2009, “ Dynamics and Control of a Planar 3-DOF Parallel Manipulator With Actuation Redundancy,” Mech. Mach. Theory, 44(4), pp. 835–849. [CrossRef]
Wang, G. G. , 2003, “ Adaptive Response Surface Method Using Inherited Latin Hypercube Design Points,” ASME J. Mech. Des., 125(2), pp. 210–220. [CrossRef]
Witek-Krowiak, A. , Chojnacka, K. , Podstawczyk, D. , Dawiec, A. , and Pokomeda, K. , 2014, “ Application of Response Surface Methodology and Artificial Neural Network Methods in Modelling and Optimization of Biosorption Process,” Bioresour. Technol., 160, pp. 150–160. [CrossRef] [PubMed]
Agarwal, H. , and Renaud, J. , 2004, “ Reliability Based Design Optimization Using Response Surfaces in Application to Multidisciplinary Systems,” Eng. Optim., 36(3), pp. 291–311. [CrossRef]
Ishaque, K. , and Salam, Z. , 2013, “ A Deterministic Particle Swarm Optimization Maximum Power Point Tracker for Photovoltaic System Under Partial Shading Condition,” IEEE Trans. Ind. Electron., 60(8), pp. 3195–3206.
Miranda, C. S. , and Zuben, F. J. V. , 2017, “ Necessary and Sufficient Conditions for Surrogate Functions of Pareto Frontiers and Their Synthesis Using Gaussian Processes,” IEEE Trans. Evol. Comput., 21(1), pp. 1–13. [CrossRef]


Grahic Jump Location
Fig. 1

Structure and parameters of 4-RSR&SS mechanism

Grahic Jump Location
Fig. 2

Schematic diagram of 4-RSR&SS mechanism

Grahic Jump Location
Fig. 3

Structure of RS part

Grahic Jump Location
Fig. 4

Performances toward one set of design variables with uncertainty

Grahic Jump Location
Fig. 5

Relative dispersion extents of performance indices

Grahic Jump Location
Fig. 6

Pareto frontier of multi-objective optimization of 4-RSR&SS mechanism

Grahic Jump Location
Fig. 7

Efficiency comparison between numerical and analytical models




Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In