Algorithms of Determination by the Trajectory of Robots in the Conditions of Interval Uncertainty of the Data
Keywords:
Mathematical modeling, obot, set of possible trajectories, condition of progressiveness of movement, interval values, generalized intervals, interval splines, error functionAbstract
In work the problem of bilateral approximation of possible trajectories of robot in the
conditions of interval uncertainty of the data is considered. The problem is reduced to construction
of interval splines, for cases of linear and cubic interval splines algorithms of their construction
and results of numerical experiments are described, the corresponding graphic interpretations are
presented.
References
1. Jaulin L., Kieffer M., Didrit O., Walter E. Applied Interval Analysis. Springer-Verlag London Limited, (2001)
2. Bahvalov N.S. Numerical methods. - Moskva: Science, (1973)
3. Kalmykov S.A., Shokin Yu.I. and Yuldashev Z.KH. Metods of interval analysis. Novosibirsk: Nauka, (1986)
4. Shary S.P. Finite-dimensional interval analysis. Publishing house "XYZ (2010)
5. Yuldashev Z.Kh., Ibragimov A.A., Tadjibaev Sh.Kh. Interval polynomial interpolation for bounded-error data,
15th GAMM-IMACS International Symposium on Scientific Computing, Computer Arithmetic and Verifed
Numerical Computations, Novosibirsk, pp. 190-191, (2012)
6. Shokin Yu.I., Yuldashev Z.Kh. Representability of interval value functions with real limited functions. –
Collection. "Numerical methods of continuum mechanics vol.4, №5, pp. 134-146, (1973)
7. Dobronets B.S., Shokin Yu.I., Yuldashev Z.Kh. Task of interpolation of the interval analysis. AN UzSSR.
"Questions of calculus mathematics Vol. 31, (1975)
8. Zavyalov Yu.S., Kvasov B.I., Miroshnichenko V.L. The methods of spline functions. – Moskva : Science, (1980)
9. Schroder G. Differentiation of interval functions. Proc. Amer. Math. Soc., Vol. 36, pp. 485-490, (1972)
10. Moore R.E. Interval Analysis. – Englewood Cliffs. N.J.: Prentice-Hall, (1966)
11. Yuldashev Z.Kh., Ibragimov A.A., Kalhanov P.J. The package of interval algorithms for wide usage. Registered
in state register of programs for PC of the Republic of Uzbekistan, Certificate of official registration of
programs for PC N DGU 02201, Tashkent city, (2011)
12. Yuldashev Z.Kh., Ibragimov A.A., Kalhanov P.J. The complex of programs for calculation of values of interval
algebraically admissible expressions within the limits of various interval arithmetics. Registered in state
register of programs for PC of the Republic of Uzbekistan, Certificate of official registration of programs for
PC N DGU 02202, Tashkent city, (2011)
13. Yuldashev Z.Kh., Ibragimov A.A. About analysis of full error in the method of interval marching and problem
of inversion of interval matrixes. Computational technologies. Novosibirsk, Russia. N 9(2), pp.235-240, (2004)
2. Bahvalov N.S. Numerical methods. - Moskva: Science, (1973)
3. Kalmykov S.A., Shokin Yu.I. and Yuldashev Z.KH. Metods of interval analysis. Novosibirsk: Nauka, (1986)
4. Shary S.P. Finite-dimensional interval analysis. Publishing house "XYZ (2010)
5. Yuldashev Z.Kh., Ibragimov A.A., Tadjibaev Sh.Kh. Interval polynomial interpolation for bounded-error data,
15th GAMM-IMACS International Symposium on Scientific Computing, Computer Arithmetic and Verifed
Numerical Computations, Novosibirsk, pp. 190-191, (2012)
6. Shokin Yu.I., Yuldashev Z.Kh. Representability of interval value functions with real limited functions. –
Collection. "Numerical methods of continuum mechanics vol.4, №5, pp. 134-146, (1973)
7. Dobronets B.S., Shokin Yu.I., Yuldashev Z.Kh. Task of interpolation of the interval analysis. AN UzSSR.
"Questions of calculus mathematics Vol. 31, (1975)
8. Zavyalov Yu.S., Kvasov B.I., Miroshnichenko V.L. The methods of spline functions. – Moskva : Science, (1980)
9. Schroder G. Differentiation of interval functions. Proc. Amer. Math. Soc., Vol. 36, pp. 485-490, (1972)
10. Moore R.E. Interval Analysis. – Englewood Cliffs. N.J.: Prentice-Hall, (1966)
11. Yuldashev Z.Kh., Ibragimov A.A., Kalhanov P.J. The package of interval algorithms for wide usage. Registered
in state register of programs for PC of the Republic of Uzbekistan, Certificate of official registration of
programs for PC N DGU 02201, Tashkent city, (2011)
12. Yuldashev Z.Kh., Ibragimov A.A., Kalhanov P.J. The complex of programs for calculation of values of interval
algebraically admissible expressions within the limits of various interval arithmetics. Registered in state
register of programs for PC of the Republic of Uzbekistan, Certificate of official registration of programs for
PC N DGU 02202, Tashkent city, (2011)
13. Yuldashev Z.Kh., Ibragimov A.A. About analysis of full error in the method of interval marching and problem
of inversion of interval matrixes. Computational technologies. Novosibirsk, Russia. N 9(2), pp.235-240, (2004)
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Published
2018-09-28
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Section
Mathematical modeling of technological processes
