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Grasping Force Optimization for Multi-fingered Robotic Hands Using Projection and Contraction Methods

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Abstract

Grasping force optimization of multi-fingered robotic hands can be formulated as a convex quadratic circular cone programming problem, which consists in minimizing a convex quadratic objective function subject to the friction cone constraints and balance constraints of external force. This paper presents projection and contraction methods for grasping force optimization problems. The proposed projection and contraction methods are shown to be globally convergent to the optimal grasping force. The global convergence makes projection and contraction methods well suited to the warm-start techniques. The numerical examples show that the projection and contraction methods with warm-start version are fast and efficient.

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References

  1. Cutkosky, M.R.: On grasp choice, grasp model, and design of hands for manufacturing task. IEEE Trans. Robot. Autom. 5, 269–279 (1989)

    Article  Google Scholar 

  2. Ko, C.H., Chen, J.K.: Grasping force based manipulation for multifingered hand-arm robot using neural networks. Numer. Algebra Control Optim. 4, 59–74 (2014)

    Article  MathSciNet  MATH  Google Scholar 

  3. Cheng, F., Orin, D.: Efficient algorithms for optimal force distribution the compact dual LP method. IEEE Trans. Robot. Autom. 6, 178–187 (1990)

    Article  Google Scholar 

  4. Liu, Y.: Qualitative test and force optimization of 3-D frictional forceclosure grasps using linear programming. IEEE Trans. Robot. Autom. 15, 163–173 (1999)

    Article  Google Scholar 

  5. Buss, M., Faybusovich, L., Moore, J.: Dikin-type algorithms for dexterous grasping force optimization. Int. J. Robot. Res. 17, 831–839 (1998)

    Article  Google Scholar 

  6. Han, L., Trinkle, J., Li, Z.: Grasp analysis as linear matrix inequality problems. IEEE Trans. Robot. Autom. 16, 663–674 (2000)

    Article  Google Scholar 

  7. Helmke, U., Huper, K., Moore, J.: Quadratically convergent algorithms for optimal dextrous hand grasping. IEEE Trans. Robot. Autom. 18, 138–146 (2002)

    Article  Google Scholar 

  8. Lobo, M.S., Vandenberghe, L., Boyd, S., Lebret, H.: Application of second order cone programming. Linear Algebra Appl. 284, 193–228 (1998)

    Article  MathSciNet  MATH  Google Scholar 

  9. Boyd, S., Wegbreit, B.: Fast computation of optimal contact forces. IEEE Trans. Robot. 23, 1117–1132 (2007)

    Article  Google Scholar 

  10. Ko, C.H., Chen, J.S.: Optimal grasping manipulation for multifingered robots using semismooth Newton method. Math. Probl. Eng. 2013, 1–9 (2013)

    Article  MathSciNet  Google Scholar 

  11. Bai, Y.Q., Gao, X.R., Yu, C.J.: A primal-dual interior-point method for optimal grasping manipulation of multi-fingered hand-arm robots. J. Oper. Res. Soc. China 5, 1–16 (2017)

    Article  MathSciNet  MATH  Google Scholar 

  12. Zhou, J.C., Chen, J.S.: Properties of circular cone and spectral factorization associated with circular cone. J. Nonlinear Convex A. 214, 807–816 (2013)

    MathSciNet  MATH  Google Scholar 

  13. Outrata, J.V., Sun, D.F.: On the coderivative of the projection operator onto the second-order cone. Set-Valued Var. Anal. 16, 999–1014 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  14. Kanzow, C., Ferenczi, I., Fukushima, M.: On the local convergence of semismooth Newton methods for linear and nonlinear second-order cone programs without strict complementarity. SIAM J. Optim. 20, 297–320 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  15. He, B.S.: A new method for a class linear variational inequalities. Math. Program. 66, 137–144 (1994)

    Article  MathSciNet  MATH  Google Scholar 

  16. Luenberger, D.G.: Introduction to Linear and Nonlinear Programming. Addison-wesley, Boston (1973)

    MATH  Google Scholar 

  17. He, B.S., Wang, X., Yang, J.F.: A comparison of different contraction methods for monotone variational inequalities. J. Comput. Math. 27, 459–473 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  18. Demmel, J.W.: Applied Numerical Linear Algebra. SIAM Publications, Philadelphia (1997)

    Book  MATH  Google Scholar 

  19. Sturm, J.F.: Using SeDuMi 1.02, a MATLAB toolbox for optimization over symmetric cones. Optim. Methods Softw. 11—-12, 625–653 (1999)

    Article  MathSciNet  MATH  Google Scholar 

  20. Sturm, J.F.: Central region method. In: Frenk, J.B.G., Roos, C., Terlaky, T., Zhang, S. (eds.) High Performance Optimization, pp. 157–194. Kluwer Academic Publishers, Dordrecht (2000)

    Google Scholar 

  21. Ye, Y., Todd, M.J., Mizuno, S.: An \(O(\sqrt{n}log\epsilon )\)-iteration homogeneous and self dual linear programming algorithm. Math. Oper. Res. 19, 53–67 (1994)

    Article  MathSciNet  MATH  Google Scholar 

  22. Zhao, X.Y.: A semismooth Newton-CG augmented Lagrangian method for large scale linear and convex quadratic SDPs. Ph.D. Thesis, National University of Singapore (2009)

Download references

Acknowledgements

We would like to thank the editor and the anonymous reviewers for their constructive comments, and we benefit much from the suggestions. This work was supported by the National Science Foundations for Young Scientists of China (11101320), the National Science Basic Research Plan in Shaanxi Province of China (2015JM1031), and the Fundamental Research Funds for the Central Universities (JB150713).

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Authors and Affiliations

  1. School of Mathematics and Statistics, Xidian University, Xi’an, 710071, China

    Xuewen Mu & Yaling Zhang

  2. School of Computer Science, Xi’an Science and Technology University, Xi’an, 710054, China

    Yaling Zhang

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  1. Xuewen Mu
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  2. Yaling Zhang
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Correspondence to Xuewen Mu.

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Mu, X., Zhang, Y. Grasping Force Optimization for Multi-fingered Robotic Hands Using Projection and Contraction Methods. J Optim Theory Appl 183, 592–608 (2019). https://doi.org/10.1007/s10957-019-01540-9

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  • DOI: https://doi.org/10.1007/s10957-019-01540-9

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