Abstract
A method for controlling the angular orientation with respect to the horizon plane of the platform of a uniaxial wheeled module moving without slippage over the underlying surface is considered. For a module involving a one-axis gyroscope, a compensating flywheel, and a stabilizing weight, equations of motion are derived, which describe the module as a nonholonomic system due to the absence of slippage of its wheels over the underlying surface. The conditions for the “force of undisturbability” of the platform by the inertial forces upon its arbitrary translational-rotational motion and the conditions for “informational undisturbability” by the inertial forces of the accelometric sensor of the deviation of the platform from the horizon plane are determined. The analytical relationships determining the conditions for the absence of slippage of the wheels are found. By numerical simulation, rational values of the coefficient in the laws governing the moments of forces developed by the control elements of the structure are obtained. The effectiveness of these laws is confirmed by the results of simulating the control processes over the angular motion of the platform of the module along a typical trajectory of its motion over the underlying surface.
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References
V. N. Belotelov and Yu. G. Martynenko, “Control of spatial motion of an inverted pendulum mounted on a wheel pair,” Mech. Solids 41 (6), 6–21 (2006).
S. Agrawal, J. Franch, and K. Pathak, “Velocity control of a wheeled inverted pendulum by partial feedback linearization,” in Proceedings of the 43th IEEE Conference on Decision and Control, Univ. of Delaware, Newark, USA, 2004.
F. Grasser, A. D’Arrigo, S. Colombi, and A. C. Rufer, “JOE: a mobile, inverted pendulum,” IEEE Trans. Ind. Electron. 49, 107–114 (2002).
V. N. Maksimov and A. I. Chernomorskii, “Control system of nonholonomic uniaxial wheeled module for monitoring geometry parameters of airfield pavements,” J. Comput. Syst. Sci. Int. 54, 483 (2015).
A. V. Lenskii and A. M. Formal’skii, “Gyroscopic stabilization of a two-wheeled robot bicycle,” Dokl. Math. 70, 993–997 (2004).
A. V. Lenskii and A. M. Formal’skii, “Two-wheel robot–bicycle with a gyroscopic stabilizer,” J. Comput. Syst. Sci. Int. 42, 482 (2003).
G. P. Sachkov, S. V. Feshchenko, and A. I. Chernomorskii, “Stabilization of translational–rotational motion of uniaxial wheeled platform along a linear trajectory,” J. Comput. Syst. Sci. Int. 49, 823 (2010).
V. V. Dobronravov, Principles of Nonholonomic System Mechanics (Vysshaya Shkola, Moscow, 1970) [in Russian].
B. S. Aleshin, A. I. Chernomorskii, S. V. Feshchenko, et al., Orientation, Navigation and Stabilization of Uniaxial Wheeled Modules, Ed. by B. S. Aleshin and A. I. Chernomorskii (Mosk. Aviats. Inst., Moscow, 2012) [in Russian].
Ya. N. Roitenberg, Hyroscopes (Nauka, Moscow, 1975) [in Russian].
A. Yu. Ishlinskii, “Full compensation of external disturbances caused by maneuvering in gyroscopic systems,” in The Invariance Theory and Its Application to Automatic Devices, Collection of Articles of Academy of Science of Ukr. SSR (Moscow, 1959), pp. 81–92 [in Russian].
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Original Russian Text © B.S. Aleshin, E.D. Kuris, K.S. Lel’kov, V.N. Maksimov, A.I. Chernomorskii, 2017, published in Izvestiya Akademii Nauk, Teoriya i Sistemy Upravleniya, 2017, No. 1, pp. 150–159.
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Aleshin, B.S., Kuris, E.D., Lel’kov, K.S. et al. Control of the angular orientation of the platform of a uniaxial wheeled module moving without slippage over an underlying surface. J. Comput. Syst. Sci. Int. 56, 146–156 (2017). https://doi.org/10.1134/S1064230717010026
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DOI: https://doi.org/10.1134/S1064230717010026