Research Papers

Density-Convex Model Based Robust Optimization to Key Components of Surgical Robot

[+] Author and Article Information
Shan Jiang

Centre for Advanced Mechanisms and Robotics,
School of Mechanical Engineering,
Tianjin University,
Tianjin 300072, China
e-mail: shanjmri@tju.edu.cn

Xuesheng Gao

School of Mechanical Engineering,
Tianjin University,
Tianjin 300072, China
e-mail: gaoxues@tju.edu.cn

Jun Liu

e-mail: cjr.liujun@vip.163.com

Jun Yang

e-mail: yeyang_918@sina.com
Department of Imaging,
Tianjin Union Medicine Center,
Tianjin 300121, China

Yan Yu

Division of Medical Physics,
Department of Radiation Oncology,
Thomas Jefferson University,
Kimmel Cancer Center,
111 South 11th Street,
Philadelphia, PA 19107
e-mail: yan.yu@jefferson.edu

1Corresponding author.

Contributed by the Mechanisms and Robotics Committee of ASME for publication in the JOURNAL OF MECHANISMS AND ROBOTICS. Manuscript received November 18, 2012; final manuscript received July 7, 2013; published online October 1, 2013. Assoc. Editor: Philippe Wenger.

J. Mechanisms Robotics 5(4), 041012 (Oct 01, 2013) (11 pages) Paper No: JMR-12-1195; doi: 10.1115/1.4025174 History: Received November 18, 2012; Revised July 07, 2013

This paper investigates a new robust optimization framework based on density-convex reliability model and applies it to the dimensional optimization of magnetic resonance (MR) compatible surgical robot. As a justified tool for assessing reliability, the density-convex model is proposed on account of the reality that available data information is always insufficient. Based on the density-convex model, reliability functions of structure are constructed and taken as constraint conditions. The Euclidean norm of the sensitivity Jacobian matrix is selected as robust index and stated as the ultimate objective function. By using finite element method and artificial neural network (FEM–ANN) method, the explicit functions of mechanical response are achieved effectively. The optimization is solved by a gradient-based optimization algorithm in the framework. As an application of the above optimization framework, a prototype robot is designed and manufactured. Finally, a test experiment verifies the high reliability of the robot and further proves the validity and effectiveness of this proposed method.

Copyright © 2013 by ASME
Your Session has timed out. Please sign back in to continue.


Gomes, P., 2011, “Surgical Robotics: Reviewing the Past, Analysing the Present, Imagining the Future,” Rob. Comput.-Integr. Manuf., 27(2), pp. 261–266. [CrossRef]
Vaida, C., Plitea, N., Pisla, D., and Gherman, B., 2013, “Orientation Module for Surgical Instrumentsła Systematical Approach,” Meccanica, 48(1), pp. 145–158. [CrossRef]
Thompson, J., and Supple, W., 1973, “Erosion of Optimum Designs by Compound Branching Phenomena,” J. Mech. Phys. Solids, 21(3), pp. 135–144. [CrossRef]
Lin, P. T., Gea, H. C., and Jaluria, Y., 2011, “A Modified Reliability Index Approach for Reliability-Based Design Optimization,” ASME J. Mech. Des., 133(8), p. 044501. [CrossRef]
Mashayekhi, M., Salajegheh, E., Salajegheh, J., and Fadaee, M. J., 2012, “Reliability-Based Topology Optimization of Double Layer Grids Using a Two-Stage Optimization Method,” Struct. Multidisc. Optim., 45(6), pp. 815–833. [CrossRef]
Saha, A., and Ray, T., 2011, “Practical Robust Design Optimization Using Evolutionary Algorithms,” ASME J. Mech. Des., 133(10), p. 101012. [CrossRef]
Diez, M., and Peri, D., 2010, “Robust Optimization for Ship Conceptual Design,” Ocean Eng., 37(11), pp. 966–977. [CrossRef]
Doltsinis, I., and Kang, Z., 2004, “Robust Design of Structures Using Optimization Methods,” Comput. Methods Appl. Mech. Eng., 193(23), pp. 2221–2237. [CrossRef]
Elishakoff, I., 1995, “Essay on Uncertainties in Elastic and Viscoelastic Structures: From AM Freudenthal's Criticisms to Modern Convex Modeling,” Comput. Struct., 56(6), pp. 871–895. [CrossRef]
Moens, D., and Vandepitte, D., 2006, “Recent Advances in Non-Probabilistic Approaches for Non-Deterministic Dynamic Finite Element Analysis,” Archiv. Comput. Methods Eng., 13(3), pp. 389–464. [CrossRef]
Venter, G., and Haftka, R., 1999, “Using Response Surface Approximations in Fuzzy Set Based Design Optimization,” Struct. Optim., 18(4), pp. 218–227. [CrossRef]
Carreras, C., and Walker, I. D., 2000, “Interval Methods for Improved Robot Reliability Estimation,” Proceedings of Reliability and Maintainability Symposium, Annual, IEEE, pp. 22–27.
Zhang, A. R., and Liu, X., 2012, “Research on the Non-Probabilistic Reliability Based on Interval Model,” Appl. Mech. Mater., 166, pp. 1908–1912. [CrossRef]
Ben-Haim, Y., 1995, “A Non-Probabilistic Measure of Reliability of Linear Systems Based on Expansion of Convex Models,” Struct. Saf., 17(2), pp. 91–109. [CrossRef]
Qiu, Z., Ma, L., and Wang, X., 2006, “Ellipsoidal-Bound Convex Model for the Non-Linear Buckling of a Column With Uncertain Initial Imperfection,” Int. J. Nonlinear Mech., 41(8), pp. 919–925. [CrossRef]
Ben-Haim, Y., 1994, “A Non-Probabilistic Concept of Reliability,” Struct. Saf., 14(4), pp. 227–245. [CrossRef]
Ben-Haim, Y., and Elishakoff, I., 1995, “Discussion on: A Non-Probabilistic Concept of Reliability,” Struct. Saf., 17(3), pp. 195–199. [CrossRef]
Lombardi, M., and Haftka, R. T., 1998, “Anti-Optimization Technique for Structural Design Under Load Uncertainties,” Comput. Methods Appl. Mech. Eng., 157(1–2), pp. 19–31. [CrossRef]
Qiu, Z., and Elishakoff, I., 2001, “Anti-Optimization Technique—A Generalization of Interval Analysis for Nonprobabilistic Treatment of Uncertainty,” Chaos, Solitons Fractals, 12(9), pp. 1747–1759. [CrossRef]
Kang, Z., Luo, Y., and Li, A., 2011, “On Non-Probabilistic Reliability-Based Design Optimization of Structures With Uncertain-but-Bounded Parameters,” Struct. Saf., 33(3), pp. 196–205. [CrossRef]
Kang, Z., and Luo, Y., 2009, “Non-Probabilistic Reliability-Based Topology Optimization of Geometrically Nonlinear Structures Using Convex Models,” Comput. Methods Appl. Mech. Eng., 198(41), pp. 3228–3238. [CrossRef]
Au, F., Cheng, Y., Tham, L., and Zeng, G., 2003, “Robust Design of Structures Using Convex Models,” Comput. Struct., 81(28), pp. 2611–2619. [CrossRef]
Jiang, C., Han, X., and Liu, G., 2007, “Optimization of Structures With Uncertain Constraints Based on Convex Model and Satisfaction Degree of Interval,” Comput. Methods Appl. Mech. Eng., 196(49), pp. 4791–4800. [CrossRef]
Jiang, C., Han, X., Lu, G., Liu, J., Zhang, Z., and Bai, Y., 2011, “Correlation Analysis of Non-Probabilistic Convex Model and Corresponding Structural Reliability Technique,” Comput. Methods Appl. Mech. Eng., 200(33), pp. 2528–2546. [CrossRef]
Pantelides, C. P., and Ganzerli, S., 1998, “Design of Trusses Under Uncertain Loads Using Convex Models,” J. Struct. Eng., 124(3), pp. 318–329. [CrossRef]
Jiang, C., Bi, R., Lu, G., and Han, X., 2013, “Structural Reliability Analysis Using Non-Probabilistic Convex Model,” Comput. Methods Appl. Mech. Eng., 254, pp. 83–98. [CrossRef]
Yanfang, Z., Yanlin, Z., and Yimin, Z., 2011, “Reliability Sensitivity Based on First-Order Reliability Method,” Proc. Inst. Mech. Eng., Part C: J. Mech. Eng. Sci., 225(9), pp. 2189–2197. [CrossRef]
Caro, S., Bennis, F., and Wenger, P., 2005, “Tolerance Synthesis of Mechanisms: A Robust Design Approach,” ASME J. Mech. Des., 127(1), p. 86–94. [CrossRef]
Lauzier, N., and Gosselin, C., 2012, “Performance Indices for Collaborative Serial Robots With Optimally Adjusted Series Clutch Actuators,” ASME J. Mech. Rob., 4(2), p. 021002. [CrossRef]
Jiang, S., Liu, S., and Feng, W., 2011, “PVA Hydrogel Properties for Biomedical Application,” J. Mech. Behav. Biomed. Mater., 4(7), pp. 1228–1233. [CrossRef] [PubMed]


Grahic Jump Location
Fig. 1

ECM for two-dimensional problem

Grahic Jump Location
Fig. 2

ECM for three-dimensional problem

Grahic Jump Location
Fig. 3

Relation curves between reliability and reliability index β in 2D

Grahic Jump Location
Fig. 4

Curves of differences between proposed DCM and PM, ECM

Grahic Jump Location
Fig. 5

3D Solid model of the surgical robot

Grahic Jump Location
Fig. 6

Setup of needle insertion experiment

Grahic Jump Location
Fig. 7

Curves for needle insertion into and removal from soft tissue

Grahic Jump Location
Fig. 8

FEM analysis of the surgical robot

Grahic Jump Location
Fig. 9

Simplified pitch/lift module

Grahic Jump Location
Fig. 10

Maximum equivalent stress on Long-rod1 versus positions of sliders

Grahic Jump Location
Fig. 11

Flowchart of the optimization

Grahic Jump Location
Fig. 12

Loading and boundary conditions of FEM analysis

Grahic Jump Location
Fig. 13

Schematic representation of BP-ANN architecture

Grahic Jump Location
Fig. 14

Response surface of maximum deformation at l = 150 mm

Grahic Jump Location
Fig. 15

Process of training ANN and error analysis to the response surface of maximum deformation

Grahic Jump Location
Fig. 16

Response surface of maximum stress at l = 150 mm

Grahic Jump Location
Fig. 17

Process of training ANN and error analysis to the response surface of maximum stress

Grahic Jump Location
Fig. 18

Flowchart of the optimization process: In DCM, sm denotes the MPP. In FDA, I={i|θi(u,v)=0} is the subscript set of effective constrains, SUP{·} denotes supremum function. Minimization problems (a), (b), and (c) are all linear programming problems which can be easily resolved. ‖v(k+1)-v(k)‖≤10-3 is taken as convergence condition of this optimization.

Grahic Jump Location
Fig. 19

Experimental platform

Grahic Jump Location
Fig. 20

Experimental robot based on optimization

Grahic Jump Location
Fig. 21

Comparison between measured strains and target strain




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