Properties of the Time-Optimal Feedback Control for a Pendulum-Like System

A time-optimal control problem for a pendulum-like system is considered. The system describes the dynamics of an inertial object under the action of a bounded control force and an external force which is periodic in coordinate. The terminal set consists of points on the abscissa axis of the phase plane, and the distance between two neighboring points is equal to the period of the external force. In the general case, the solution can be obtained only numerically. An estimate is found for the amplitude of the control for which the time-optimal feedback control has the simplest structure: the number of switchings is not greater than one for any initial conditions. For the estimated interval of the control constraints, we analyze the feedback control pattern.     

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.     

Plane Motions of Rigid Body Controlled by Means of Movable Mass

Doklady Physics - The plane motions of a rigid body controlled by means of an auxiliary movable point mass are considered. Dry friction forces act between the body and the horizontal plane. It is...     

Optimization of the motion in a resistant medium of a body with a movable internal mass

The motion, in a resistant medium, of a system consisting of a rigid body and movable internal mass is considered. The external medium acts on the body by a force that piecewise linearly depends on its speed. The class of periodic motions of the internal mass for which the speed of this mass relative to the body is piecewise constant is studied. It is shown that, under certain conditions, the forward movement of the whole system in the medium is possible. The average speed of this movement over a period is determined. Optimal parameters of the motion of the internal mass for which the average speed of the system movement is maximal are found.     

Static analysis of a two-member linkage interacting with a given surface

Summary The static interaction of a two-member linkage with a given surface is investigated. Dry friction acts at the point of contact of the linkage with the surface. The linkage has two drives generating torques at its joints. The optimal distribution of the joint torques is determined to maximize the friction force at the point of contact. The dependence of this maximal force on the lengths of the links and on the linkage configuration is investigated. The results obtained can be applied to the analysis and optimization of various robotic systems, in particular, manipulators interacting with rough surfaces and walking machines, especially tube-crawling robots. Received 21 December 1998; accepted for publication 25 February 1999     

Control of the Body Orientation by Means of Several Movable Masses

Doklady Physics - The problem of controlling the orientation of a rigid body by means of several auxiliary point masses moving with respect to a body is considered. The algorithm of reorientation...     

Properties of the Optimal Ellipsoids Approximating the Reachable Sets of Uncertain Systems

The ellipsoidal estimation of reachable sets is an efficient technique for the set-membership modelling of uncertain dynamical systems. In the paper, the optimal outer-ellipsoidal approximation of reachable sets is considered, and attention is paid to the criterion associated with the projection of the approximating ellipsoid onto a given direction. The nonlinear differential equations governing the evolution of ellipsoids are analyzed and simplified. The asymptotic behavior of the ellipsoids near the initial point and at infinity is studied. It is shown that the optimal ellipsoids under consideration touch the corresponding reachable sets at all time instants. A control problem for a system subjected to uncertain perturbations is investigated in the framework of the optimal ellipsoidal estimation of reachable sets.     

Ellipsoidal Bounds on Reachable Sets of Dynamical Systems with Matrices Subjected to Uncertain Perturbations1

Linear dynamical systems described by finite-difference or ordinary differential equations are considered. The matrix of the system is uncertain or subject to disturbances, and only the bounds on admissible perturbations of the matrix are known. Outer ellipsoidal estimates of reachable sets of the system are obtained and equations describing the evolution of the approximating ellipsoids are derived. An example is presented.