Tatiana Yu. Figurina

Quasi-Static Motion of a Two-Link System along a Horizontal Plane

Quasi-static motion of a two-link system along a rough horizontal plane is considered. Dry friction acts between the links of the system and the plane. During the motion, the configuration of the linkage changes, whereas the points of contact of the linkage and the plane remain the same. The control torque applied at the joint of the linkage is chosen so as to provide equilibrium condition for each of the links. It is shown that the quasi-static motion of the two-link system is uncontrollable and the uniqueness of this motion is proved for given initial position of the linkage. The trajectories of the vertices are found, depending on the parameters of the system.

Optimal control of vibrationally excited locomotion systems

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.

Optimal Control of a Two-Body System Moving in a Viscous Medium

Abstract A two-body system moving along a horizontal line in a nonlinear viscous medium is considered. One of the bodies (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. A periodic optimal motion of the internal body relative to the main body, which sustains the velocity-periodic motion of the main body and maximizes its average velocity, is defined by solving an optimal control problem.

OPTIMAL CONTROL OF PERIODIC MOTIONS OF VIBRATION-DRIVEN SYSTEMS

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 systems main body and the other mass moves vertically. Such a mechanical system models a vibration-driven 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 velocity-periodic motion of the main body with a maximum average velocity, provided that the period is fixed 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.

Optimal Control of Motion of a Robot Driven by a Movable Internal Body in a Resistive Environment

Abstract A two-body system moving along a horizontal line in a nonlinear viscous medium is considered. One of the bodies (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. A periodic optimal motion of the internal body relative to the main body, which sustains the motion of the main body with periodically changing velocity and maximizes its average speed, is defined by solving an optimal control problem.

Control of Vibration-Driven Systems Moving in Resistive Media

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 Coulombs dry friction — are considered.