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Global Optimization of Robot Control System Via Generalized Geometric Programming

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Intelligent Robotics and Applications (ICIRA 2008)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 5314))

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Abstract

A model of the robot control system can be described as a generalized geometric programming problem. The objection is to minimize the error subject to stability and torque constraints. A global optimization approach of generalized geometric programming has been used for solving the model. The relationships of sampling time versus the proportional gain (K p ), integral gain K i , and the derivative gain K v are studied. It is showed that the values of the control parameters (K p , K i , K v ) decrease as the sampling time increases before becoming flat. It is also concluded that generalized geometric programming is an efficient mathematical technique for the nonlinear control of robotic system.

This research was supported by Doctor Scientific Research Foundation of Northeast Dianli University, BSJXM-200702.

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References

  1. Duffin, R.J., Peterson, E.L.: Geometric programming with signomial. Journal of Optimization Theory and Applications 1(11), 3–35 (1973)

    Article  MathSciNet  Google Scholar 

  2. Fu, K.S., Gonzalez, R.C., Lee, C.S.: Robtics: Control, Sensing, Vision Intelligence. McGraw-Hill, New York (1987)

    Google Scholar 

  3. Sherali, H.D.: Global optimization of nonconvex polynomial programming problems having ratilnal exponents. Journal of Global optimization 12, 267–283 (1998)

    Article  MathSciNet  MATH  Google Scholar 

  4. Jha, N.K.: A discrete data base multiple objective optimazation of milling operation through geometric programming. J. Eng. ASM Trans. 112, 368–374 (1990)

    Article  Google Scholar 

  5. Jha, N.K.: Unified theory of automation in process planning utilizing multiobjectives under real world constraints. Appl. Math. Modelling 16, 58–69 (1992)

    Article  MATH  Google Scholar 

  6. Jha, N.K.: Computer aided formulation and optimal control of an integrated production system for competetive products. Production Panning Control 5, 47–58 (1994)

    Article  Google Scholar 

  7. Jha, N.K.: Geometric programming based robot control design. Computers ind. Engng. 29, 631–635 (1995)

    Article  MathSciNet  Google Scholar 

  8. Khatib, O., Burdick, J.: Optimization of dynamics in manipulator in design: the operational space formulation. Int. J. Robotics Automation 2 (1987)

    Google Scholar 

  9. Luh, J.Y.S., Walker, M.W., Paul, R.P.: On-line computational scheme for mechanical manipulator. Trans. ASME J. Dynamic Syst. Measurements Control 120, 69–76 (1980)

    Article  MathSciNet  Google Scholar 

  10. Maranas, C.D., Floudas, C.A.: Global optimization in generalized geometric programming. Computers chem. Engng. 21(4), 351–369 (1997)

    Article  MathSciNet  Google Scholar 

  11. Shin, K.G., Mckay, N.D.: A dynamic programming approch to trajectory planning of robotic manipulators. IEEE Trans. Automatic Control Ac-31 (1986)

    Google Scholar 

  12. Vijoykumar, R., Waldron, K.: Geometric optimization of manipulator structures for working volume and dexerity. Int. J. Robotics Res. 5 (1986)

    Google Scholar 

  13. Michalska, H., Torres-Torriti, M.: A geometric approach to feedback stabilization of nonlinear systems with drift. Systems and control letters 50, 303–318 (2003)

    Article  MathSciNet  MATH  Google Scholar 

  14. Yazarel, H., Pappas, G.J.: Proceeding of the 2004 American Control Conference, Boston, Massachusetts, June 30-July 2, pp. 553–559 (2004)

    Google Scholar 

  15. Wang, Y.J., Lan, Y.: Global optimization for special reverse convex programming. Computers & Mathematics with Applications 55(6), 1154–1163 (2008)

    Article  MathSciNet  MATH  Google Scholar 

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© 2008 Springer-Verlag Berlin Heidelberg

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Gong, J., Jia, R. (2008). Global Optimization of Robot Control System Via Generalized Geometric Programming. In: Xiong, C., Huang, Y., Xiong, Y., Liu, H. (eds) Intelligent Robotics and Applications. ICIRA 2008. Lecture Notes in Computer Science(), vol 5314. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-88513-9_47

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  • DOI: https://doi.org/10.1007/978-3-540-88513-9_47

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-88512-2

  • Online ISBN: 978-3-540-88513-9

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