N. N. Bolotnik

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)

Optimal Control of Manipulation Robots

Abstract Optimal control of manipulation robots is considered. Problems of optimal control for robots are stated and solved by means of both analytical and numerical methods. Some optimal time motions of robots with two and three degrees of freedom are presented. Some of these regimes were realized experimentally for industrial robots. The obtained results show that optimal regimes require much less time than non-optimal “natural” ones. Practical applications of optimal regimes are discussed.

Quasi-optimal control of rotation of a rigid body about a fixed axis taking friction into account

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.

Dynamics and Control of a Two-Module Mobile Robot on a Rough Surface

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.

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.

Design of Mobile Microrobots with Thermomechanical Actuators

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).

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.

Simulation of Dynamics and Optimization of Robotic Systems

Abstract The paper is devoted to analysis simulation and optimization of dynamics of manipulation robots. Theory and method for calculating motions arc developed for robots with structure containing elastic elements - joints and/or links. Static and dynamic experiments are carried our in order to identify mechanical parameters of robots. as a result of simulation, the influence of elastic flexibility of structure on dynamics of robots is evaluated. Dynamic accuracy of robots in estimated, and some recommendations are Given for its improvement. For different kinematic types of robots, optimal control regimes are developed which require minimal operational time. Numerical calculations and experiments show that implementation of optimal regims gives essential rise to robots efficiency.

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.

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.