Estimating the Domain of Admissible Parameters of a Control System of a Vibratory Robot

  • M. V. Golitsyna
  • V. A. Samsonov
Control Systems of Moving Objects


We consider the rectilinear motion of a vibratory robot on a plane; the robot is presented by a rigid body and a pendulum inside it. The motion is carried out in the gravity field; the force of dry friction acts between the body and the plane. The robot is controlled by choosing the angular acceleration of the pendulum. Two modes of the robot’s control that correspond to various constraints on the choice of the control are investigated. Each of the studied control laws ensures a periodic displacement of the robot; here, the robot moves only in one direction (the motion is irreversible). We discuss the problem of finding the boundaries of the dry friction parameter and the control parameter; we find the boundaries with which the proposed control modes are feasible.


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  1. 1.
    A. N. Grankin and S. F. Yatsun, “Investigation of vibroimpact regimes of motion of a mobile microrobot with electromagnetic drive,” J. Comput. Syst. Sci. Int. 48, 155 (2009).MathSciNetCrossRefzbMATHGoogle Scholar
  2. 2.
    A. P. Ivanov and A. V. Sakharov, “Dynamics of rigid body, carrying moving masses and rotor, on a rough plane,” Nelin. Dinam. 8, 763–772 (2012).CrossRefGoogle Scholar
  3. 3.
    S. F. Jatsun, N. N. Bolotnik, K. Zimmerman, and I. Zeidis, “Modeling of motion of vibrating robots,” in Proceedings of the 12th IFToMM World Congress in Mechanism and Machine Science, Besançon, France, June 17–21, 2007, pp. 171–188.Google Scholar
  4. 4.
    C. F. Yatsun, V. N. Shevyakin, L. Yu. Volkova, and V. V. Serebrovskii, “Dynamics of operated movement of three-mass robot on a flat surface,” Izv. Samar. Nauch. Tsentra RAN 13, 1134–1138 (2011).Google Scholar
  5. 5.
    P. Vartholomeos and E. Papadopoulos, “Analysis, design and control of a planar micro-robot driven by two centripetal-force actuators,” in Proc. of the International Conference on Robotics and Automation (ICRA), Orlando, USA, 2006, pp. 649–654.Google Scholar
  6. 6.
    L. Yu. Volkova and S. F. Yatsun, “Control of the three-mass robot moving in the liquid environment,” Nelin. Dinam. 7, 845–857 (2011).CrossRefGoogle Scholar
  7. 7.
    X. Zhan and J. Xu, “Locomotion analysis of a vibration-driven system with three acceleration-controlled internal masses,” Adv. Mech. Eng. 7 (3) (2015).Google Scholar
  8. 8.
    N. N. Bolotnik and T. Yu. Figurina, “Optimal control of the rectilinear motion of a rigid body on a rough plane by means of the motion of two internal masses,” J. Appl. Math. Mech. 76, 126–135 (2008).CrossRefzbMATHGoogle Scholar
  9. 9.
    N. N. Bolotnik, I. M. Zeidis, K. Zimmermann, and S. F. Yatsun, “Dynamics of controlled motion of vibrationdriven systems,” J. Comput. Syst. Sci. Int. 45, 831 (2006).CrossRefzbMATHGoogle Scholar
  10. 10.
    F. L. Chernous’ko, “Analysis and optimization of a body motion controlled by a movable internal mass,” Prikl. Mat. Mekh. 70, 915–941 (2006).zbMATHGoogle Scholar
  11. 11.
    F. L. Chernous’ko, “The optimal periodic motions of a two-mass system in a resistant medium,” J. Appl. Math. Mech. 72, 116–125 (2008).MathSciNetCrossRefGoogle Scholar
  12. 12.
    F. L. Chernous’ko and N. N. Bolotnik, “Mobile robots controlled by internal bodies motion,” Tr. IMM UrO RAN 16 (5), 213–222 (2010).Google Scholar
  13. 13.
    S. A. Gerasimov, “Vibration drift with quadratic drag,” Mech. Solids 42, 184–189 (2007).CrossRefGoogle Scholar
  14. 14.
    M. V. Kulikovskaya, “Maximization of average velocity of vibration robot,” in Proceedings of the 29th International Conference on Mathematical Methods in Engineering and Technologies MMTT-29, St. Petersburg, Russia, 2016, Vol. 3, pp. 130–135.Google Scholar
  15. 15.
    K. S. Sorokin, “Motion of a mechanism along a rough inclined plane using the motion of internal oscillating masses,” J. Comput. Syst. Sci. Int. 48, 993 (2009).MathSciNetCrossRefzbMATHGoogle Scholar
  16. 16.
    P. Vartholomeos and E. Papadopoulos, “Dynamics, design and simulation of a novel microrobotic platform employing vibration microactuators,” J. Dyn. Sys., Meas., Control 128, 122–133 (2005).CrossRefGoogle Scholar
  17. 17.
    B. S. Bardin and A. S. Panev, “On periodic motions of a body with a movable inner mass along a horizontal surface,” Tr. MAI, No. 84, 5 (2015).Google Scholar
  18. 18.
    M. V. Golitsyna and V. A. Samsonov, “Maximization of average velocity of vibratory robot (with one restriction on acceleration),” Springer Proc. Math. Stat. 181, 221–332 (2016).MathSciNetCrossRefGoogle Scholar

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© Pleiades Publishing, Ltd. 2018

Authors and Affiliations

  1. 1.Moscow State UniversityMoscowRussia

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