Abstract
This work considers the controlled movements of a rigid body along a horizontal plane in the presence of dry-friction forces between the body and the plane. Control is carried out by means of an auxiliary point mass, equipped with an actuator and capable of moving relative to the body. It is shown that under certain general conditions the system is completely controllable and can be transferred from an arbitrary initial state to any given terminal state. The considered setup simulates the dynamics of rotary movements of mobile capsule robots.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
REFERENCES
F. L. Chernous’ko, “Analysis and optimization of the motion of a body controlled by means of a movable internal mass,” J. Appl. Math. Mech. 70 (6), 819–842 (2006).
H. Li, K. Furuta, and F. L. Chernousko, “Motion generation of the capsubot using internal force and static friction,” in Proc. 45th IEEE Conf. on Decision and Control (San Diego, 2006), pp. 6575–6580.
F. L. Chernous’ko, “The optimal periodic motions of a two-mass system in a resistant medium,” J. Appl. Math. Mech. 72 (2), 116–125 (2008).
K. Zimmermann, I. Zeidis, N. Bolotnik, and M. Pivovarov, “Dynamics of a two-module vibration-driven system moving along a rough horizontal plane,” Multibody Syst. Dyn. 22, 199–219 (2009).
H. B. Fang and J. Xu, “Dynamic analysis and optimization of a three-phase control mode of a mobile system with an internal mass,” J. Vib. Control 74 (4), 443–451 (2011).
A. P. Ivanov and A. V. Sakharov, “Dynamics of rigid body, carrying moving masses and rotor, on a rough plane,” Nelineinaya Din. 8 (4), 763–772 (2012).
M. N. Huda and H. Yu, “Trajectory tracking control of an underactuated capsubot,” Auton. Robots 39 (2), 183–198 (2015).
N. N. Bolotnik, A. M. Nunuparov, and V. G. Chashchukhin, “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 (2016).
Y. Liu, E. Pavlovskaya, and M. Wiercigroch, “Experimental verification of the vibro-impact capsule model,” Nonlinear Dyn. 83, 1029–1041 (2016).
M. N. Huda, H. Yu, and S. Cang, “Behavior-based control approach for the trajectory tracking of an underactuated planar capsule robot,” IET Control Theory Appl. 9, 163–175 (2015).
F. L. Chernousko, “Motion of a body along a plane under the influence of movable internal masses,” Dokl. Phys. 61, 494–498 (2016).
F. L. Chernousko, “Two-dimensional motions of a body containing internal moving masses,” Meccanica 51 (12), 3203–3209 (2016).
F. L. Chernousko, “Optimal motions of bodies controlled by internal moving masses,” IFAC Paper-OnLine, No. 51–32, 1–6 (2018).
X. Zhan, J. Xu, and H. Fang, “A vibration-driven planar locomotion robot—Shell,” Robotica 36 (9), 1402–1420 (2018).
J. Xu and H. Fang, “Improving performance: recent progress on vibration-driven locomotion systems,” Nonlinear Dyn. 98 (4), 2651–2669 (2019).
Funding
This work is supported by the Russian Foundation for Basic Research (projects nos. 20-01-00378 and 21-51-12004).
Author information
Authors and Affiliations
Corresponding author
Additional information
Translated by L. Trubitsyna
About this article
Cite this article
Chernousko, F.L. Controlling the Planar Motions of a Rigid Body Using a Movable Mass. Mech. Solids 56, 1461–1470 (2021). https://doi.org/10.3103/S0025654421080057
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.3103/S0025654421080057