Publications (53)19.35 Total impact
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ABSTRACT: The motion of a chain of three identical bodies along a straight line in a dryfriction medium is studied. The motion is excited and controlled by changing the distances between the bodies of the chain. An undulatory excitation mode is proposed, in which the distances between the adjacent bodies of the chain change periodically and the time histories of the distances in the pairs of adjacent bodies consecutively repeat each other with a constant time shift. It looks like a wave is running along the chain. The necessary and sufficient conditions for the system to be able to move from rest are established. For a specific excitation mode, in which the time histories of the distances between the bodies of the chain are defined as piecewise quadratic functions, a steadystate motion of the system is studied for the case where the friction force is small in comparison with the force necessary for a body of the chain to be moved from a state of rest through a distance characterizing the amplitude of oscillations of adjacent bodies during the excitation period.ZAMM Journal of applied mathematics and mechanics: Zeitschrift für angewandte Mathematik und Mechanik 12/2013; 93(12). · 0.95 Impact Factor  [Show abstract] [Hide abstract]
ABSTRACT: Optimal controls are constructed for two types of mobile systems propelling themselves due to relative oscillatory motions of their parts. The system of the first type is modelled by a rigid body (main body) to which two links are attached by revolute joints. All three bodies interact with the environment with the forces depending on the velocity of motion of these bodies relative to the environment. The system is controlled by highfrequency periodic angular oscillations of the links relative to the main body. The system of the other type consists of two bodies, one of which (the main body) interacts with the environment and with the other body (internal body), which interacts with the main body but does not interact with the environment. The system is controlled by periodic oscillations of the internal body relative to the main body. For both systems, the motions with the main body moving along a horizontal straight line are considered. Optimal control laws that maximize the average velocity of the main body are found.Regular and Chaotic Dynamics 01/2013; 18(12). · 0.93 Impact Factor  [Show abstract] [Hide abstract]
ABSTRACT: A mechanical system consisting of a movable base and an object (rigid body) connected to the base by means of a twodegreeoffreedom gimbal with mutually perpendicular axes is considered. The possibility to eliminate the projection of the apparent acceleration of a given object point on the plane perpendicular to an objectfixed axis by controlling the rotation of the gimbal frames is investigated. The apparent acceleration of a given object point is the difference between the absolute acceleration vector and the gravitational acceleration vector at this point. Sufficient conditions under which this goal is attainable in principle are formulated. Equations governing the rotation of the gimbal frames are derived. This problem is related to the development of control systems for gravitysensitive technologies in spacecraft.Journal of Computer and Systems Sciences International 05/2012; 51(3). · 0.27 Impact Factor  [Show abstract] [Hide abstract]
ABSTRACT: The rectilinear motion of a twobody system is considered. One of the bodies (the main body) interacts with a resistive environment, while the other body (the internal body) interacts with the main body but does not interact with the environment. The force applied to the internal body leads to a reaction that acts on the main body and produces a change in its velocity, which causes a change in the resistance of the environment to the motion of the main body. Thus, by controlling the motion of the internal body, one can control the external force acting on the main body and, as a consequence, the motion of the entire system. A periodic motion of the internal body relative to the main body, which generates the motion of the main body with periodically changing velocity and the maximum displacement for the period, is constructed for a wide class of laws of resistance of the environment to the motion of the main body.The principle of motion considered is appropriate for mobile mini and microrobots. The body (housing) of such robots can be hemetically sealed and smooth, without protruding parts, which enables these robots to be used for the nondestructive inspection of miniature engineering structures such as thin pipelines, as well as in medicine. Problems of optimizing the control modes for such systems are of interest both to researchers in the field of optimal control and to specialists in applied mechanics and robotics.Journal of Applied Mathematics and Mechanics 01/2012; 76(1):1–14. · 0.31 Impact Factor  [Show abstract] [Hide abstract]
ABSTRACT: tuilmenau.de Abstract. The paper deals with nontraditional vibration driven locomotion systems. In the first part, the motion of a chain of interconnected bodies (mass points) along a straight line on a rough surface is considered. The system is subjected to kinematic constraints modeling the excitation mode. It is assumed that there is dry (Coulomb's) friction acting between the plane and each body. The magnitude of the friction force depends on the direction of the motion. The expression for the average velocity of the steadystate motion of the system as a whole is found. In the second part, the motion of two bodies (mass points) connected by a linear spring is studied for the case, where the coefficient of friction is independent of the direction of the motion. The system is driven by two unbalanced rotors attached to the bodies. It is shown, that the direction of motion can be reversed without changing the direction of rotation of the rotors.01/2011;  [Show abstract] [Hide abstract]
ABSTRACT: The motion of a finite chain of identical bodies along a straight line in a resistive medium is studied. The major aim of this study is to investigate the fundamental properties of such systems, in particular, their ability to move from a state of rest and sustain the motion at constant average velocity in media with different resistance properties and the influence of the control strategy on the motion. The motion is excited and controlled by changing the distances between the bodies of the chain. For a given friction law, the necessary and sufficient conditions for the system to be able to move from rest are established.ZAMM Journal of applied mathematics and mechanics: Zeitschrift für angewandte Mathematik und Mechanik 12/2010; 91(4):259  275. · 0.95 Impact Factor  [Show abstract] [Hide abstract]
ABSTRACT: Design of mobile robots that can move without wheels or legs is an important engineering and technological problem. Selfpropelling mechanisms that consist of a body that has contact with a rough surface and internal masses are considered. Asymmetry in friction that is necessary for the robot to move can be provided in several ways. First, the robot can be equipped with specific contact devises that provide anisotropy for the coefficient of friction, i.e., the coefficient of friction depends on the direction of motion. For example, the contact surface of the robot can be covered with needles. Second, this asymmetry can be provided for isotropic friction by changing the normal pressure of the robot on supporting surface. A number of mathematical models of such systems are presented in the paper. KeywordsDesignInpipe robotsModellingVibrationdriven robots03/2010: pages 465477;  [Show abstract] [Hide abstract]
ABSTRACT: A rectilinear motion of a system of two bodies connected by a spring on a rough horizontal plane is studied. The motion of the system is excited by two identical unbalanced rotors based on the respective bodies. Major attention is given to the steadystate motion. A nearlyresonant excitation mode, when the angular velocities of the rotor are close to the natural frequency of the system, is considered. A set of algebraic equations for determining an approximate value of the average steadystate velocity of the entire system is obtained for the case of small friction. It is shown that control of the steadystate motion can be provided by changing the phase shift between the rotations of the rotors and the sign of the resonant detuning measured by the difference between the angular velocity of the rotors and the natural frequency of the system. By varying the phase shift one can control the magnitude of the average velocity, and varying the detuning enables one to change the direction of the motion.Multibody System Dynamics 09/2009; 22(2):199219. · 1.75 Impact Factor  [Show abstract] [Hide abstract]
ABSTRACT: A limiting performance of shock isolation is studied for an object modeled by two rigid bodies connected by a viscoelastic element with a linear characteristic. The object is attached to a movable base by means of a shock isolator, which is regarded as a device that produces a control force between the base and the object. The base and the object move along the same straight line. The base is subject to an external shock excitation that is characterized by the time history of the acceleration of the base. A control law is defined for the shock isolator to minimize the maximum magnitude of the displacement of the object relative to the base, provided that the force of interaction between the components of the object does not exceed a prescribed value. An algorithm for constructing the exact solution of the problem under certain assumptions is presented. A technique for constructing an approximate solution for an object having high stiffness is described. The optimal control is shown to have impulse components. Examples are given. The twocomponent model considered in the paper is known to have been utilized to describe the mechanical response of a human body to a shock load along the spine or from thorax to back. Therefore, the problem under consideration can be regarded as a benchmark optimal control problem for a system that protects from injuries cased by shock loads. Solution of such problems is highly topical for development of safety systems for vehicles.Journal of Computer and Systems Sciences International 04/2009; 48(2):206219. · 0.27 Impact Factor  [Show abstract] [Hide abstract]
ABSTRACT: The motion of a body controlled by movable internal masses in a resistive environment along a horizontal straight line is considered. Optimal periodic modes of motion are constructed for the internal masses to maximize the average speed of the velocityperiodic motion of the body. The maximum displacement allowed for the internal masses inside the body, as well as the relative velocities or accelerations of these masses are subjected to constraints. Three types of the resistance laws — piecewise linear friction, quadratic friction, and Coulomb's dry friction — are considered.12/2008: pages 3140;  [Show abstract] [Hide abstract]
ABSTRACT: The problem of the optimal control of a rigid body moving along a rough horizontal plane due to motion of two internal masses is solved. One of the masses moves horizontally parallel to the line of motion of the main body, while the other mass moves in the vertical direction. Such a mechanical system models a vibrationdriven robot–a mobile device able to move in a resistive medium without special propellers (e.g., wheels, legs or caterpillars). Periodic motions are constructed for the internal masses to ensure velocityperiodic motion of the main body with maximum average velocity, provided that the period is fixed and the magnitudes of the accelerations of the internal masses relative to the main body do not exceed prescribed limits. Based on the optimal solution obtained for a fixed period without any constraints imposed on the amplitudes of vibration of the internal masses, a suboptimal solution that takes such constraints into account is constructed.Journal of Applied Mathematics and Mechanics 08/2008; 72(2):126135. · 0.31 Impact Factor  [Show abstract] [Hide abstract]
ABSTRACT: To improve the protection of a wheelchairseated person with disabilities traveling in a vehicle from injuries in a crash, it is proposed to attach the wheelchair to a movable platform separated from the vehicle body by means of a shock isolator. The control of the platform is designed to reduce the occupant's injury risk, as compared with the case of the attachment of the wheelchair directly to the vehicle. The isolator design is based on the minimization of the force transmitted to the wheelchair occupant, provided that the space allowed for the platform to move relative to the vehicle is constrained. The possibility of preacting control, when the isolator is engaged for a time prior to the crash, is discussed. Passive tiedown and restraint systems are studied, although it is recognized that active systems could provide even lower injury risks. A multibody model of the platformbased occupied wheelchair is utilized for fullscale simulation of the response of the system to a crash pulse. The simulation shows a noticeable reduction in the injury risk due to the platform and an even greater reduction of injury with preacting control.Medical Engineering & Physics 04/2008; 30(2):25867. · 1.84 Impact Factor  [Show abstract] [Hide abstract]
ABSTRACT: The limiting possibilities of the protection of the human head from impacts by means of helmets are analyzed. The shell (base) of the helmet is assumed to decelerate after an impact against an obstacle with constant acceleration during a given time interval. The minimum of the peak magnitude of the displacement of the head (the object to be protected) relative to the helmet shell is determined, provided that the injury risk index does not exceed a prescribed tolerable value, as well as the corresponding time history of the absolute acceleration of the head. The injury risk index is defined by the HIC functional. This functional is adopted as a standard measure for the head injury risk in crash tests of vehicles, as well as in the tests of shock protection equipment for industries and sports. The time history of the motion of the head and the peak magnitude of the displacement of the head relative to the helmet shell are studied as functions of the shock pulse duration (the deceleration time of the helmet shell). The case of the instantaneous shock, when the shell comes to an instantaneous stop after hitting the obstacle, was considered in [1].Journal of Computer and Systems Sciences International 01/2008; 47(1):93102. · 0.27 Impact Factor  [Show abstract] [Hide abstract]
ABSTRACT: An optimal control problem is solved for a rigid body that moves along a straight line on a rough horizontal plane due to the motion of two internal masses. One of the masses moves horizontally parallel to the line of motion of the system's main body and the other mass moves vertically. Such a mechanical system models a vibrationdriven robot able to move in a resistive medium without special propelling devices (wheels, legs or caterpillars). A periodic motion of the internal masses is constructed to ensure a velocityperiodic motion of the main body with a maximum average velocity, provided that the period is flxed and the accelerations of the internal masses relative to the main body lie within prescribed limits. This statement does not constrain the amplitude of vibrations of the internal masses. Based on the solution of the problem, a suboptimal control that takes this constraint into account is constructed.01/2007;  Journal of Dynamic Systems Measurement and Controltransactions of The Asme  J DYN SYST MEAS CONTR. 01/2007; 129(4).
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ABSTRACT: The rectilinear motion on a horizontal rough plane of a vibrationdriven system consisting of a carrying body, which interacts with the plane directly, and of internal masses that perform harmonic oscillations relative to the carrying body is considered. The vertical and horizontal oscillations of the internal masses have the same frequency, but are shifted in phase. It is shown that by controlling the phase shift of the horizontal and vertical oscillations and their frequencies, it is possible to change the direction and magnitude of the average velocity of the steady motion of the carrying body. A similar system may provide a model of a vibrationdriven robot that does not require special limbs (wheels, legs, or chain tracks)Journal of Computer and Systems Sciences International 09/2006; 45(5):831840. · 0.27 Impact Factor 
Article: Control of motion of an inhomogeneous cylinder with internal movable masses along a horizontal plane
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ABSTRACT: The controlled motion of a rigid inhomogeneous cylinder over a rough horizontal plane is considered. The control is provided by controlled motion of internal masses. Mathematical models are constructed that correspond to rolling without loss of contact or slippage. The conditions for the physical implementability of such a motion are derived. The case where the internal moving masses from a rigid flywheel the centre of inertia of which lies on the axis of the cylinder is investigated in detail. A neartimeoptimal feedback control that enables the total energy to be changed in a required way is constructed on the basis of an asymptotic approach. The main operating modes are simulated, namely, swinging up of the cylinder to a large angular amplitude, rotation with a prescribed energy, deceleration of rolling to a complete stop, and oscillations and rotations in the neighbourhood of the separatrix.Journal of Applied Mathematics and Mechanics 01/2006; · 0.31 Impact Factor  Journal of the Brazilian Society of Mechanical Sciences and Engineering 01/2006; 28(4). · 0.24 Impact Factor

Conference Paper: Optimal control problem for head injury criterion
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ABSTRACT: The optimal control of the deceleration of a particle moving along a straight line after an impact against a surface covered with an impact isolation coating is considered. The force applied to the particle by the surface is treated as the control variable, that is, the control force replaces the coating. The deceleration distance is minimized under the constrained value of the HIC functional  an integral criterion that is utilized in engineering biomechanics to evaluate the expected severity of impactinduced head injury of a human being. The solution indicates the limiting capabilities of the prevention from the head injuries in the case of traffic accidents, falling, or other occurrences by means of an appropriate coating of the surface against which impacts can occur.Physics and Control, 2005. Proceedings. 2005 International Conference; 09/2005  [Show abstract] [Hide abstract]
ABSTRACT: The optimal control of the deceleration of a particle moving along a straight line after an impact against a surface covered with an impact isolation coating is considered. The force applied to the particle by the surface is treated as the control variable. The deceleration distance is minimized under the constrained value on the HIC functional – an integral criterion that is utilized in engineering biomechanics to evaluate the expected severity of impactinduced head injury of a human being. The solution obtained provides indicates limiting capabilities of the prevention from the head injuries in the case of traffic accidents, falling, or other occurrences by means of an appropriate coating of the surface against which impacts can occur.Journal of Computer and Systems Sciences International 01/2005; 44(2). · 0.27 Impact Factor
Publication Stats
139  Citations  
19.35  Total Impact Points  
Top Journals
Institutions

1989–2013

Russian Academy of Sciences
 Institute of Problems in Mechanics
Moskva, Moscow, Russia


2003–2009

Nizhny Novgorod State University
 Research Institute of Applied Mathematics and Cybernetics
Gorkey, Nizjnij Novgorod, Russia
