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Rectilinear Periodic Motions of Systems with Internal Bodies

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Dynamics of Mobile Systems with Controlled Configuration

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Abstract

In this chapter, we consider rectilinear motions of mobile systems that move in resistive media without external propelling devices (legs, wheels, caterpillars, fins, screw propellers, etc.) due to the motion of internal bodies. Such systems consist of a rigid housing and internal bodies that can move relative to the housing under the action of drives. The drives implement the interaction of the internal bodies with the housing of the locomotion system. The housing interacts also with the environment, whereas the internal bodies do not interact with the environment. A force applied by the drive to an internal body causes a reaction force applied to the housing, as a result of which the velocity of the housing relative to the environment changes. The change in the velocity of the housing leads to a change in the resistance (friction) force applied by the environment to the housing. The forces generated by the drives are internal forces for the mechanical system under consideration (the housing plus the internal bodies), while the environment resistance force is an external force. Thus, by controlling the motion of the internal bodies due to internal forces one can control the external force applied to the locomotion system and thereby the motion of the system as a whole. Mobile robots that move due to the motion of internal bodies are frequently called capsule robots (capsubots). The capsule robots have a number of advantages over mobile systems of other types. The capsule robots are simple in design, do not need complex mechanisms to transmit the motion from the drives to the propelling devices, are easy to miniaturize, and their housings can be made hermetic and geometrically smooth, without protruding pieces. The last circumstance enables the capsule robots to be used in vulnerable environments, in particular, in medicine for diagnosis inspections inside a human body or for precise delivery of a drug to an affected area. Capsule robots can be used also for motion inside thin tubes, for example, for their technical inspection, or in narrow slots. A number of control and optimization problems for capsule robots are solved.

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References

  1. Nagaev RF, Tamm EA (1980) Vibration-induced motion in a medium with quadratic-law resistance. Mach Sci (Mashinovedenie) (4):3–8. (In Russian)

    Google Scholar 

  2. Gerasimov SA (2003) Vibrational displacement in a gravity field. J Appl Mech Techn Phys 44(6):786–789

    Article  Google Scholar 

  3. Chernousko FL (2005) On the motion of a body containing a movable internal mass. Doklady Phys 50(11):593–597

    Article  Google Scholar 

  4. Chernousko FL (2006) Analysis and optimization of the motion of a body controlled by a movable internal mass. J Appl Math Mech 70(6):915–941

    MathSciNet  Google Scholar 

  5. Chernousko FL (2008) The optimal periodic motions of a two-mass system in a resistant medium. J Appl Math Mech 72(2):116–125

    Article  MathSciNet  Google Scholar 

  6. Fang HB, Xu J (2011) Dynamic analysis and optimization of a three-phase control mode of a mobile system with an internal mass. J Vib Control 17(1):19–26

    Article  MathSciNet  Google Scholar 

  7. Li H, Furuta K, Chernousko FL (2005) A pendulum-driven cart via internal force and static friction. In: Proceedings of international conference on “Physics and Control”. St.-Petersburg, Russia (pp 15–17)

    Google Scholar 

  8. Li H, Furuta K, Chernousko FL (2006) Motion generation of the capsubot using internal force and static friction. In Proceedings of 45th IEEE conference on decision and control, San Diego, CA, USA, 13–15 Dec 2006 (pp 6575–6580)

    Google Scholar 

  9. Bolotnik NN, Figurina TYu (2008) 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 72(2):126–135

    Article  MathSciNet  Google Scholar 

  10. Bolotnik NN, Zeidis I, Zimmermann K, Yatsun SF (2006) Dynamics of controlled motion of vibration-driven systems. J Comput Syst Sci Int 45(5):481–496

    Article  Google Scholar 

  11. Chekina EA (2021) Periodic body motions along a horizontal rough surface by moving two internal masses. J Phys Conf Ser 1959:012014

    Google Scholar 

  12. Sorokin KS (2009) Motion of a mechanism along a rough inclined plane using the motion of internal oscillating masses. J Comput Syst Sci Int 48(6):993–1001

    Article  MathSciNet  Google Scholar 

  13. Bardin BS, Panev AS (2018) On periodic motions of a body with a movable internal mass along a horizontal surface. Trudy MAI (Transactions of the Moscow Aviation Institute) No 84. https://trudymai.ru/upload/iblock/6a2/bardin_panev_rus.pdf?lang=ru &issue=84. (in Russian)

  14. Golitsyna MV (2018) Periodic regime of motion of a vibratory robot under a control constraint. Mech Solids 45(Suppl. 1):49–59

    Article  MathSciNet  Google Scholar 

  15. Golitsyna MV (2018) Optimal choice of the acceleration of a pendulum in problems of control of a vibration-driven robot. Mechatron Autom Control (Mekhatronika. Avtomatizatsiya. Upravlenie)19(1):31–39. (In Russian)

    Google Scholar 

  16. Golitsyna MV, Samsonov VA (2018) Estimating the domain of admissible parameters of a control system of a vibratory robot. J Comput Syst Sci Int 57(2):255–272

    Article  MathSciNet  Google Scholar 

  17. Sobolev NA, Sorokin KS (2007) Experimental investigation of a model of a vibration-driven robot with rotating masses. J Comput Syst Sci Int 46(5):826–835

    Article  Google Scholar 

  18. Bardin BS, Rachkov AA (2021) On periodic motions of a body with an internal moving mass on a rough horizontal plane in the case of anisotropic friction. J Phys Conf Ser 1959:012005

    Google Scholar 

  19. Figurina T, Glazkov T (2021) Optimization of the rectilinear motion of a capsule system along a rough plane. ZAMM 101(3)

    Google Scholar 

  20. Borisov AV, Vetchanin EV, Kilin AA (2017) Control of the motion of a triaxial ellipsoid in a fluid using rotors. Math Notes 102(3–4):455–464

    Article  MathSciNet  Google Scholar 

  21. Vetchanin EV, Tenenev VA (2011) Modeling of control of the motion of a body with variable mass geometry in a viscous fluid. Comput Res Model (Komp’yuternye Issledovaniya i Modelirovanie) 3(4):371–381. (In Russian)

    Google Scholar 

  22. Vetchanin EV, Kilin AA (2016) Free and controlled motion of a body with a moving internal mass through a fluid in the presence of circulation around the body. Doklady Phys 61(1):32–36

    Article  Google Scholar 

  23. Kilin AA, Vetchanin EV (2015) The control of the motion through an ideal fluid of a rigid body by means of two moving masses. Russ J Nonlinear Dyn 11(4):633–645. (In Russian)

    Google Scholar 

  24. Kozlov VV, Onishchenko DA (2003) The motion in a perfect fluid of a body containing a moving point mass. J Appl Math Mech 67(4):553–564

    Google Scholar 

  25. Kozlov VV, Ramodanov SM (2012) On the motion of a body with a rigid shell and variable mass geometry in a perfect fluid. Doklady Phys 47:132–135

    Article  Google Scholar 

  26. Rmodanov SM, Tenenev VA (2011) The motion of a body with a variable mass geometry in an unbounded viscous fluid. Russ J Nonlinear Dyn 7(3):635–647. (In Russian)

    Google Scholar 

  27. Vetchanin EV, Karavaev YL, Kalinkin AA, Klekovkin AV, Pivovarov EN (2015) A model of a screwless underwater robot. Bull Udmurt Univ Math Mech Comput Sci (Vestnik Udmurtskogo Universitsta. Matematika. Mekhanika. Komp’yuternye nauki) 25(4):544–553. (In Russian)

    Google Scholar 

  28. Klekovkin AV (2020) Simulation of the motion of a propellerless mobile robot with an unchanged shape of the hull by means of rotation of an internal rotor. Bull Udmurt Univ Math Mech Comput Sci (Vestnik Udmurtskogo Universitsta. Matematika. Mekhanika. Komp’yuternye nauki) 30(4):645–656. (In Russian)

    Google Scholar 

  29. Karavaev YL, Kilin AA, Klekovkin AV (2016) Experimental investigations of the controlled motion of a screwless underwater robot. Regul Chaotic Dyn 21(7–8):918–926

    Article  MathSciNet  Google Scholar 

  30. Karavaev YL, Klekovkin AV, Mamaev IS, Tenenev VA, Vetchanin EV (2022) A simple physical model for control of a propellerless aquatic robot. J Mech Robot 14(1)

    Google Scholar 

  31. Tahmasian S, Jafaryzad A, Bulzoni NL, Staples AE (2020) Dynamic analysis and design optimization of a drag-based vibratory swimmer. Fluids 5(1). https://doi.org/10.3390/fluids5010038

  32. Figurina TYu (2007) Optimal control of the motion of a two-body system along a straight line. J Comput Syst Sci Int 46(2):227–233

    Article  MathSciNet  Google Scholar 

  33. Podosinnikova AA (2012) Optimal control of dual-mass system motion in a medium with a piecewise linear resistance. J Comput Syst Sci Int 51(6):849–858

    Article  MathSciNet  Google Scholar 

  34. Bolotnik NN, Figurina TYu, Chernousko FL (2012) Optimal control of the rectilinear motion of a two-body system in a resistive medium. J Appl Math Mech 76(1):1–14

    Article  MathSciNet  Google Scholar 

  35. Egorov AG, Zakharova OS (2010) The energy-optimal motion of a vibration-driven robot in a resistive medium. J Appl Math Mech 74(4):443–451

    Article  MathSciNet  Google Scholar 

  36. Egorov AG, Zakharova OS (2012) The optimal quasi-stationary motion of a vibration-driven robot in a viscous medium. Russ Math 56(2):50–55

    Google Scholar 

  37. Egorov AG, Zakharova OS (2015) The energy-optimal motion of a vibration-driven robot in a medium with a inherited law of resistance. J Comput Syst Sci Int 54(3):495–503

    Article  MathSciNet  Google Scholar 

  38. Tahmasian S (2021) Dynamic analysis and optimal control of drag-based vibratory systems using averaging. Nonlinear Dyn 104:2201–2217

    Article  Google Scholar 

  39. Bolotnik NN, Nunuparov AM, Chashchukhin VG (2016) Capsule-type vibration-driven robot with an electromagnetic actuator and an opposing spring: Dynamics and control of motion. J Comput Syst Sci Int 55(6):986–1000

    Article  MathSciNet  Google Scholar 

  40. Nunuparov A, Becker F, Bolotnik N, Zeidis I, Zimmermann K (2019) Dynamics and motion control of a capsule robot with an opposing spring. Arch Appl Mech 89(4):2193–2208

    Article  Google Scholar 

  41. Liu Y, Pavlovskaia E, Hendry D, Wiercigroch M (2013) Vibro-impact responses of capsule system with various friction models. Int J Mech Sci 72:39–54

    Article  Google Scholar 

  42. Liu Y, Pavlovskaia E, Wiercigroch M, Peng ZK (2015) Forward and backward motion control of a vibro-impact capsule system. Int J Nonlinear Mech 70:30–46

    Article  Google Scholar 

  43. Liu Y, Wiercigroch M, Pavlovskaia E, Yu Y (2013) Modelling of a vibro-impact capsule system. Int J Mech Sci 66:2–11

    Article  Google Scholar 

  44. Liu Y, Pavlovskaya E, Wiercigroch M (2016) Experimental verification of the vibro-impact capsule model. Nonlinear Dyn 83:1029–1041

    Article  Google Scholar 

  45. Liu Y, Islam S, Pavlovskaya E, Wiercigroch M (2016) Optimization of the vibro-impact capsule system. J Mech Eng 62:430–439

    Google Scholar 

  46. Yan Y, Liu Y, Liao M (2015) A comparative study of the vibro-impact capsule systems with one-sided and two-sided constraints. Nonlinear Dyn 89:1063–1087

    Article  Google Scholar 

  47. Fang HB, Xu J (2011) Dynamics of a mobile system with an internal acceleration-controlled mass in a resistive medium. J Sound Vib 330:4002–4018

    Article  Google Scholar 

  48. Fang H, Xu J (2014) Stick-slip effect in a vibration-driven system with dry friction: sliding bifurcations and optimization. J Appl Mech 81(5):051001–1–051001–10

    Google Scholar 

  49. Kugushev EI, Popova TV, Sazonov SV (2020) On the motion of a rigid body with a movable internal mass along a straight line with a viscous friction. In: Stability and oscillations of nonlinear control systems (Pyatnitskii Conference): materials of the 15th international scientific conference (June 3–5, 2020) Ustoichivost’ i kolebaniya nelineinykh sistem upravleniya (konferentsiya Pyatnitskogo): Materialy XV mezhdunarodnoi nauchnoi konferentsii. Inst Control Sci Moscow 2020:239–241. (In Russian)

    Google Scholar 

  50. Makhmudov PK, Samsonov VA, Dosaev MZ, Klimina LA, Vershinin YA (2020) The motion of a wheeled inertially excited robot due to the motion of internal masses. In: Stability and oscillations of nonlinear control systems (Pyatnitskii Conference): materials of the 15th international scientific conference (June 3–5, 2020) Ustoichivost’ i kolebaniya nelineinykh sistem upravleniya (konferentsiya Pyatnitskogo): Materialy XV mezhdunarodnoi nauchnoi konferentsii. Inst Control Sci Moscow 2020:298–300. (In Russian)

    Google Scholar 

  51. Fang HB, Xu J (2012) Controlled motion of a two-module vibration-driven system induced by internal acceleration-controlled masses. Arch Appl Mech 82:461–477

    Article  Google Scholar 

  52. Ivanov AP (2020) Analysis of an impact-driven capsule robot. Int J Nonlinear Mech 119. (March)

    Google Scholar 

  53. Vartholomeos P, Papadopoulos E (2006) Dynamics, design and simulation of a novel microrobotic platform employing vibration microactuators. Trans ASME J Dyn Syst Meas Control 128(1):122–133

    Google Scholar 

  54. Yan Y, Liu Y, Manfredi L, Prasad S (2019) Modelling of the self-propelled vibro-impact capsule in small intestine. Nonlinear Dyn 96(1):123–144

    Article  Google Scholar 

  55. Huda MN, Yu H (2015) Trajectory tracking control of an underactuated capsubot. Auton Robots 39(2):183–198

    Article  Google Scholar 

  56. Huda MN, Yu H, Cang S (2015) Behavior-based control approach for the trajectory tracking of an underactuated planar capsule robot. IET Control Theory Appl 9:163–175

    Article  MathSciNet  Google Scholar 

  57. Ivanov AP, Sakharov AV (2012) Dynamics of a rigid body with movable internal masses and a rotor on a rough plane. Russ J Nonlinear Dyn 8(4):763–772. (In Russian)

    Google Scholar 

  58. Sakharov AV (2015) Rotation of a body with two movable internal masses on a rough plane. J Appl Math Mech 79(2):132–141

    Article  MathSciNet  Google Scholar 

  59. Fang H, Wang KW (2017) Piezoelectric vibration-driven locomotion systems—exploiting resonance and bistable dynamics. J Sound Vib 391:153–169

    Google Scholar 

  60. Sendoh M, Ishiyama K, Arai K-I (2003) Fabrication of magnetic actuator for use in a capsule endoscope. IEEE Trans Magnet 39(5):3232–3234

    Article  Google Scholar 

  61. Xu J, Fang H (2019) Improving performance: recent progress on vibration-driven locomotion systems. Nonlinear Dyn 98(4):2651–2669

    Article  MathSciNet  Google Scholar 

  62. Zhan X, Xu J, Fang H (2016) Planar locomotion of a vibration-driven system with two internal masses. Appl Math Model 40(2):871–885

    Article  MathSciNet  Google Scholar 

  63. Zhan X, Xu J, Fang H (2018) A vibration-driven planar locomotion robot-Shell. Robotica 36(9):1402–1420

    Article  Google Scholar 

  64. Chernousko FL (2016) Motion of a body along a plane under the influence of movable internal masses. Doklady Phys 61(10):494–498

    Article  Google Scholar 

  65. Arnold VI (1992) Ordinary differential equations. Springer, Berlin, Heidelberg

    Google Scholar 

  66. Pontryagin LS, Boltyanskii VG, Gamkrelidze RF, Mishchenko EF (1964) The mathematical theory of optimal processes. Pergamon Press, Oxford

    Google Scholar 

  67. Blekhman II, Dzhanelidze GYu (1964) Vibrational transportation. Nauka, Moscow (In Russian)

    Google Scholar 

  68. Blekhman II (2000) Vibrational mechanics. World Scientific, Singapore, p 509

    Book  Google Scholar 

  69. Lavendel EE, Liepinsh IY (1963) To the optimization of inseparable vibratory transportation modes. Bull Higher Educ Inst Mech Eng (Izvestiya Vuzov. Mashinostroenie) (4):5–9. (In Russian)

    Google Scholar 

  70. Troitskii VA (1963) On the optimization of a vibration transporter process. J Appl Math Mech 27(6):1715–1726

    Article  MathSciNet  Google Scholar 

  71. Troitskii VA (1976) Optimal oscillatory processes in mechanical systems. Mashinostroenie, Leningrad (In Russian)

    Google Scholar 

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  1. Institute for Problems in Mechanics, Russian Academy of Sciences, Moscow, Russia

    Felix Chernousko & Nikolay Bolotnik

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  1. Felix Chernousko
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  2. Nikolay Bolotnik
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Correspondence to Felix Chernousko .

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Chernousko, F., Bolotnik, N. (2024). Rectilinear Periodic Motions of Systems with Internal Bodies. In: Dynamics of Mobile Systems with Controlled Configuration. Springer, Singapore. https://doi.org/10.1007/978-981-97-1825-2_5

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  • DOI: https://doi.org/10.1007/978-981-97-1825-2_5

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