Felix L. Chernousko

Motion Generation of the Capsubot Using Internal Force and Static Friction

In this paper, a capsule type robot is designed. The motion is described. The robot has no moving part outside its body, no legs, no wheel. Its motion is purely based on its internal force and friction with the environments. A four step motion pattern is proposed. A minimal energy solution is derived. A prototype capsule robot, consisting a plastic tube with a copper coil and a NiFeB magnet rod which can slide inside the tube, is built. It is essentially a motion magnet linear motor. The motion generation results are verified experimentally

Decomposition and suboptimal control in dynamical systems

Abstract A non-linear controllable dynamical system described by Lagrange equations is considered. The problem of constructing bounded controlling forces which steer the system to a given state in a finite time is investigated. Sufficient conditions are indicated for the problem to be solvable. Under these conditions, the initial system splits into subsystems, each with the degree of freedom. On the basis of this decomposition, using a game-theoretic approach, a feedback control law is proposed which solves the problem posed above and is nearly time-optimal. It is shown that the control must be constructed with proper allowance for the maximum values of the non-linear terms and perturbations in the equations of motion. The perturbations may be ignored only if the ratio of the maximum level of the perturbation to that of the control does not exceed the “golden section”.

Modelling of snake-like locomotion

Locomotion of snakes and other limbless animals and insects have been studied in biomechanics and have stimulated research and development of biologically inspired crawling robots. In the paper, snake-like locomotion of multilink mechanisms is investigated. Plane multibody systems are considered that consist of two, three, or many links connected by revolute joints and can move along a horizontal plane. Dry friction forces obeying Coulombs law act between the linkage and the plane. Control torques are created by actuators installed at the joints. It is shown that the multilink mechanism can perform various periodic and wavelike motions and reach any position and configuration in the plane. The proposed motions of two-link and three-link mechanisms consist of alternating slow and fast phases. For multilink mechanisms with more than four links, slow quasi-static motions are possible. The dynamics of periodic snake-like locomotion is analyzed, and the respective control algorithms are proposed. Displacements, the average speed of locomotion, and the required magnitudes of control torques are evaluated for different types of multilink systems. Optimal values of geometrical and mechanical parameters are determined that correspond to the maximum speed of motion. The results of computer simulation confirm the obtained theoretical results. Due to the simplicity of snake-like mechanisms, they are of interest for the design of mobile robots, especially for mini-robots.

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 perturbations

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.

Regular motions of a tube-crawling robot: simulation and optimization

The tube-crawling robot is an eight-legged walking machine that moves inside pipe-lines and can be used for inspection, maintenance, and repair. Optimization of structural parameters and possible gaits of the robot is discussed. The results obtained by computer simulation show a considerable sensitivity of operation characteristics of the robot with respect to its geometrical and kinematic parameters.

Regular motion of a tube-crawling robot in a curved tube

ABSTRACT The motion of an eight-legged tube-crawling robot through a curved (toroidal) tube is investigated in terms of kinematics. A class of regular gaits implementing such a motion is defined. In these gaits, the center of mass of the robot body moves by the same distance during each step, and, at the beginning and the end of each step, the center of mass of the robot body lies on the axis of the tube and, moreover, the axis of the robot is tangential to that of the tube. Each step consists of two half-steps. During each half-step the robot body performs a plane-parallel motion in the plane where the feet of the supporting legs lie. The parameters of the gait are calculated, and some qualitative features of the motion of the robot are analyzed. Computer simulation results are presented. The analysis of the motion of the robot in a toroidal tube is important for planning and control of the passage of the robot through turns of a pipeline. *Communicated by W. Book.

Perturbed Motions of a Rigid Body Close to Lagrange’s Case

In Sect. 11.1, we describe an averaging procedure for slow variables of a perturbed motion of a rigid body, where the motion is close to Lagrange’s case in the first approximation [1]. It turns out that a number of applied problems admit averaging over the nutation angle θ.

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.