Dynamics of controlled motion of vibration-driven systems

The rectilinear motion on a horizontal rough plane of a vibration-driven 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 vibration-driven robot that does not require special limbs (wheels, legs, or chain tracks)     

Control of impact interaction of docking spacecraft

An impact interaction between spacecraft docking to one another by means of a probe-and-cone (probe-and-drogue) docking system is considered, a substantial difference of the spacecraft in mass being assumed. The most important parameters of the relative motion of the spacecraft influencing the impact force are identified. It is shown that in the case of uncontrolled impact, the realization of these parameters depends to a large extent on accidental occurrences during the docking process. Quantitative relations between the impact force and the aforementioned parameters are obtained. These relations reveal the potentials for feedback control of the impact force.     

Limiting performance analysis of the protection of the human head from impact-induced injuries taking into account the duration of the shock pulse

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].     

Control of the apparent acceleration of a rigid body attached to a movable base by means of a two-degree-of-freedom gimbal

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.     

Shock Isolation with Anticipating Control for External Disturbances of Various Shapes

Limiting performance analysis is performed for isolation of an object on a movable base from short-duration impact excitations by means of an active shock isolator with anticipating control. The external disturbance (excitation) is modeled by the time history of the absolute acceleration of the base. The control is performed by a force that acts between the base and the object to be protected. The absolute value of the control force is subject to a constraint. A procedure is proposed for constructing optimal anticipating controls that minimize the peak magnitude of the displacement of the object relative to the base for external disturbances from a certain class. For a number of types of external disturbances, the solution of the optimal control problem is obtained in closed form. The controls that are constructed in closed form are modified to be applicable for the disturbances for which closedform solutions are absent.     

Dynamics of a two-module vibration-driven system moving along a rough horizontal plane

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. This study was partly supported by the German Research Society (DFG) (projects Zi 540-12/1 and SFR 622) and the Russian Foundation for Basic Research (project 09-01-91330). An erratum to this article can be found at     

Orientation Control of an Object on a Rotating Base by Using a Two-Stage Electric Drive

Journal of Computer and Systems Sciences International - In this paper, we study the process of controlling the rotation of an object relative to a rotating base using a two-stage electric drive...     

Capsule-type vibration-driven robot with an electromagnetic actuator and an opposing spring: Dynamics and control of motion

A model of a mobile capsule robot that consists of the housing and internal body is considered. The internal body can move relative to the housing along a straight line. The internal body is attached to the housing by a spring. The system motion is excited by a force that acts between the housing and the internal body. The force changes in a pulse-width periodic mode. The robot’s motion along a straight line on a rough horizontal plane is investigated. It is assumed that the dry Coulomb friction acts between the housing and the plane. The dependence of the average steady state robot velocity on excitation parameters is analyzed. It is established that it is possible to control the magnitude and direction of the robot motion by changing the period and the duty cycle of the pulse-width excitation signal. The effect of the variation in the direction of the robot motion due to changing the excitation period is observed. This effect is associated with the phenomenon of resonance.     

Optimal shock isolation of a two-component viscoelastic object

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.     

Simulation and Optimization of Regular Motions of a Tube-Crawling Robot

The paper is devoted to issues associated with thetube-crawling robot designed at the Munich Technical University. Wefocus on the simulation of the robot dynamics and the optimization ofstructural parameters of the machine and characteristics of its gait.The mathematical model of the eight-legged tube-crawling robotperforming regular motions at a constant speed along a cylindrical tubeis described. On the basis of this model we investigate the influence ofthe machine design and gait parameters on the robot velocity and findtheir optimal values providing the maximal velocity under givenparametric and drive constraints. Numerical examples are presented anddiscussed.