# N.N. Bolotnik

Russian Academy of Sciences, Moskva, Moscow, Russia

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## Publications (68)28.93 Total impact

• ##### Article: On the motion of lumped-mass and distributed-mass self-propelling systems in a linear resistive environment
N. Bolotnik · M. Pivovarov · I. Zeidis · K. Zimmermann
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ABSTRACT: The motion of self-propelling limbless locomotion systems in a linear viscous environment is considered. The resistance (friction) force acting on an element of the systems is assumed to be proportional to the velocity of this element relative to the environment, the coefficient of proportionality (coefficient of friction) being constant. Two models of interaction of the locomotor with the environment are distinguished. In the first model, the coefficient of friction is constant for a mass element, whereas in the second model, this coefficient is constant for a length element. It is shown that progressive locomotion is impossible for the first model and is possible for the second model. This is explained by the fact that in the second model, the coefficient of friction for a mass element is in fact controlled by changing the length of this element due to deformation of the locomotor's body. The first model applies for lumped mass systems, while the second model is adequate for distributed mass limbless locomotors, like worms. For both models, the equations of motion of the system's center of mass are derived and analyzed.
No preview · Article · Sep 2015 · ZAMM Journal of applied mathematics and mechanics: Zeitschrift für angewandte Mathematik und Mechanik
• ##### Article: Quasi-optimal control of rotation of a rigid body about a fixed axis taking friction into account
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ABSTRACT: A mechanical system is considered that consists of a rotating base and a rigid body which can rotate with respect to the base around the axis coinciding with the axis of the base rotation. The control of the body’s motion with respect to the base is performed using a direct (high-torque) electric drive. The voltage applied across armature circuit terminals of the motor serves as a control variable. A dynamical model of the system is proposed that takes into account the friction moment in the rolling bearings with respect to the rotation axis. The rolling-friction moment is represented by an odd function of the angular velocity of body rotation that has a jump discontinuity at zero, as is the case for the dry-friction characteristic. An optimal control problem for bringing the body to the specified angular position in the absence of friction is solved. The time integral of a quadratic function of the control and phase variables is the functional to be minimized. For the system with friction, quasi-optimal feedback control laws are constructed, and sticking zones are estimated which are caused by sliding and rolling dry friction. Control modes are proposed with compensation for nonidealities and perturbation factors. Mathematical simulation is conducted and the dynamical characteristics of the process under control are determined.
No preview · Article · May 2015 · Journal of Computer and Systems Sciences International
• ##### Article: The motion of a two-body limbless locomotor along a straight line in a resistive medium
N. Bolotnik · M. Pivovarov · I. Zeidis · K. Zimmermann
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ABSTRACT: The behavior of a two-body self-propelling locomotion system in a resistive environment is studied. The motion of the system is excited and sustained by means of a periodic change in the distance between the bodies. A complete analysis of the motion of the system is performed for the case where the resistance forces applied by the environment to the bodies of the system are represented by linear functions of the velocities of these bodies relative to the environment. For the case where the resistance forces are nonlinear functions of the velocities of the bodies, a model based on the averaged equation of motion is used. This model assumes the forces of friction acting in the system to be small in comparison with the excitation force. The motion of the system along a horizontal straight line in an isotropic dry friction environment is investigated in detail for two particular types of excitation modes. The calculated results are compared with the experimental data.
No preview · Article · Apr 2015 · ZAMM Journal of applied mathematics and mechanics: Zeitschrift für angewandte Mathematik und Mechanik
• ##### Article: Design of mobile microrobots with thermomechanical actuators
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ABSTRACT: A design concept of a legged mobile microrobot that utilizes thermomechanical actuators is discussed. The forces and torques acting on the legs of the microrobot are identified and analyzed. The phases of motion, conditions of motion, and sequences of operations are defined; the performance characteristics of the robots are studied. A number of design schematics of the microrobot are presented and compared. The issues related to the mechanical structure of the robots, as well as the content and amount of information required by the measurement and control systems are considered. A modified thermomechanical actuator was developed for the microrobot leg. The structure of the actuator involves a feedback sensor. The design sketches of the inspector microrobot with an on-board micromanipulator based on the thermomechanical actuator are proposed. Possible applications of the microrobot for aerospace planet missions are discussed. This study was supported by the Russian Science Foundation (Grant # 14-19-00949).
No preview · Article · Jan 2015
• ##### Article: Physical characteristics of the sensing elements of feedback sensors combined with thermomechanical actuators for plant micromotion control systems
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ABSTRACT: The paper is devoted to extending the functionality and finding possible applications of microrobotic system components, i.e., actuators based on the thermomechanical effect and used in miniature plant motion control systems. A top metallization layer added to the actuator design creates in its structure a sensing element responsive to humidity, light, and motion. Thus, a single device combines active and sensitive elements and provides feedback thus simplifying the technology and reducing the cost of the multifunctional device.
No preview · Article · Jan 2015 · Journal of Computer and Systems Sciences International
• ##### Article: Dynamics and control of a two-module mobile robot on a rough surface
N. Bolotnik · M. Pivovarov · I. Zeidis · K. Zimmermann
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ABSTRACT: A two-module (two-body) locomotion system moving along a straight line on a rough horizontal plane is considered. The motion of the system is excited by a periodic change in the distance between the bodies. Friction between the bodies and the plane obeys Coulomb’s law. The conditions for the system to be able to start moving from a state of rest and the steady-state motion are studied. The friction force acting on the system is assumed to be small as compared with the excitation force, and the method of averaging is applied to the equation of motion of the system’s center of mass. On the basis of the averaged equation, necessary and sufficient conditions subject to which the system can start moving from a state of rest in a dry friction environment are obtained. The excitation law that implies a piecewise quadratic time history of the distance between the bodies is considered. For this excitation law, the system can start moving from a state of rest if the bodies have different masses and the times of increase and decrease of the distance between them do not coincide. Closed-form expressions for the steady-state velocity of the system’s center of mass are obtained and investigated as a function of the parameters of the system and the excitation law. The maximum magnitudes of the steady-state velocities and the respective values of the parameters are found. An experimental prototype of the robot under consideration was built. The experimental results demonstrate qualitative agreement with the theoretical predictions.
No preview · Article · Jan 2014
• ##### Article: Optimal control of vibrationally excited locomotion systems
Felix L. Chernousko · Nikolai N. Bolotnik · Tatiana Yu. Figurina
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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 high-frequency 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.
No preview · Article · Jan 2013 · Regular and Chaotic Dynamics
• ##### Article: Optimal control of the rectilinear motion of a two-body system in a resistive medium
N.N. Bolotnik · T.Yu. Figurina · F.L. Chernous’ko
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ABSTRACT: The rectilinear motion of a two-body 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 micro-robots. The body (housing) of such robots can be hemetically sealed and smooth, without protruding parts, which enables these robots to be used for the non-destructive inspection of miniature engineering structures such as thin pipe-lines, 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.
No preview · Article · Dec 2012 · Journal of Applied Mathematics and Mechanics
• ##### Article: Control of the apparent acceleration of a rigid body attached to a movable base by means of a two-degree-of-freedom gimbal
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ABSTRACT: A mechanical system consisting of a movable base and an object (rigid body) connected to the base by means of a two-degree-of-freedom 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 object-fixed 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 gravity-sensitive technologies in spacecraft.
No preview · Article · May 2012 · Journal of Computer and Systems Sciences International
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##### Article: The undulatory motion of a chain of particles in a resistive medium
N. Bolotnik · M. Pivovarov · I. Zeidis · K. Zimmermann
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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.
Full-text · Article · Apr 2011 · ZAMM Journal of applied mathematics and mechanics: Zeitschrift für angewandte Mathematik und Mechanik
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##### Article: Optimal periodic motions of systems with internal masses in resistive media
Felix L. Chernousko · Nikolai Bolotnik

Preview · Article · Jan 2011
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##### Article: CONTROLLED MOTION OF MECHANICAL SYSTEMS INDUCED BY VIBRATION AND DRY FRICTION
Nikolai Bolotnik · Mikhail Pivovarov · Igor Zeidis · Klaus Zimmermann
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ABSTRACT: tu-ilmenau.de Abstract. The paper deals with non-traditional 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 steady-state 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.
Full-text · Article · Jan 2011
• ##### Chapter: Dynamics of Mobile Vibration-Driven Robots
K. Zimmerman · I. Zeidis · N. Bolotnik · S. Jatsun
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ABSTRACT: Design of mobile robots that can move without wheels or legs is an important engineering and technological problem. Self-propelling 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. KeywordsDesign-In-pipe robots-Modelling-Vibration-driven robots
No preview · Chapter · Mar 2010
• ##### Article: Injury Biomechanics and Control: Optimal Protection from Impact
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ABSTRACT: Structure of the BookRelated StudiesReferences
No preview · Article · Oct 2009
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##### Article: Dynamics of a two-module vibration-driven system moving along a rough horizontal plane
K. Zimmermann · I. Zeidis · N. Bolotnik · M. Pivovarov
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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 steady-state motion. A nearly-resonant 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 steady-state velocity of the entire system is obtained for the case of small friction. It is shown that control of the steady-state 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.
Full-text · Article · Sep 2009 · Multibody System Dynamics
• ##### Article: Optimal shock isolation of a two-component viscoelastic object
D. V. Balandin · N. N. Bolotnik
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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 two-component 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.
No preview · Article · Apr 2009 · Journal of Computer and Systems Sciences International
• ##### Chapter: Control of Vibration-Driven Systems Moving in Resistive Media
Nikolai N. Bolotnik · Felix L. Chernousko · Tatiana Yu. Figurina
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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 velocity-periodic 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 — piece-wise linear friction, quadratic friction, and Coulomb's dry friction — are considered.
No preview · Chapter · Dec 2008
• ##### Article: Optimal control of the rectilinear motion of a rigid body on a rough plane by means of the motion of two internal masses
N.N. Bolotnik · T. Yu. Figurina
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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 vibration-driven 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 velocity-periodic 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.
No preview · Article · Aug 2008 · Journal of Applied Mathematics and Mechanics
• ##### Article: Concept of a platform-based impact isolation system for protection of wheelchair occupants from injuries in vehicle crashes
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ABSTRACT: To improve the protection of a wheelchair-seated 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 pre-acting 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 platform-based occupied wheelchair is utilized for full-scale 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 pre-acting control.
No preview · Article · Apr 2008 · Medical Engineering & Physics
• ##### Article: Limiting performance analysis of the protection of the human head from impact-induced injuries taking into account the duration of the shock pulse
D. V. Balandin · A. S. Belozerov · N. N. Bolotnik
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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].
No preview · Article · Feb 2008 · Journal of Computer and Systems Sciences International

#### Publication Stats

 293 Citations 28.93 Total Impact Points

#### Top co-authors View all

• ##### Leonid D Akulenko   (16)
A. Ishlinsky Institute for Problems in Mechanics of the Russian Academy of Sciences
• ##### Thomas Roßmann   (2)
ASM Assembly Systems GmbH & Co. KG

#### Institutions

• ###### Russian Academy of Sciences
• Institute of Problems in Mechanics
Moskva, Moscow, Russia
• ###### Nizhny Novgorod State University
• Research Institute of Applied Mathematics and Cybernetics
Gorkey, Nizjnij Novgorod, Russia