Y. Yavin

Open loop strategies for the control of a disk rolling on a horizontal plane

The concept of feasible command strategies is introduced and their applicability is demonstrated by solving a guidance and control problem. This problem concerns the control of the motion of a rolling disk that has to be steered from a point A to a small neighbourhood of a point B, both of them in the (X, Y) plane. In addition, the motion of the rolling disk is subjected to state and control constraints.

On a horizontal version of the inverse pendulum problem

This work deals with the guidance and control of a system which is composed of a rolling disk and a slender rod that is freely pivoted, through its middle point, about the disks center. The motion of the disk-rod system is subjected to state and control constraints, of which one of them serves as a generalized, horizontal version, of the inverse pendulum problem. In this work two concepts are introduced. First the concept of feasible command strategies is introduced and their applicability is demonstrated by solving a guidance and control problem concerning the above-mentioned system. Second, the concept of path controllability is introduced and a condition is derived for the systems motion path controllability. The derivation of this condition enables one to design closed-loop control laws for the systemss motion.

On the motion of a disc rolling on a horizontal plane: Path controllability and feedback control

Abstract This work deals with the feedback control and guidance of the motion of a disc rolling, without slipping, on the horizontal ( X , Y )-plane. The concept of path controllability is introduced, and is used to establish a condition under which the discs motion is path controllable. The derivation of this condition is used to design a robust closed-loop control law for the discs motion, such that the disc will roll, during a finite time-interval, [0, t f ], from a point A to a small neighbourhood of B , where A and B are two given points in the ( X , Y )-plane.

Modelling and control of the motion of a rolling disk: effect of motor dynamics on the dynamical model

This work deals with the modelling and control of a system which is composed of a disk rolling on a plane, a controlled slender rod that is pivoted through its center of mass about the disks center and two overhead rotors with their axes fixed in the upper part of the rod (see Figs. 1 and 2). The rod is controlled in such a manner that it is always aligned along the line passing through the points O and C, where O denotes the center of the disk and C denotes the point of contact between the disk and the plane. Each of the rotors is being driven by a DC motor. In addition, a third DC motor, located at the center of the disk, is generating a pedalling torque applied to the disks motion. The aim of this work is first to obtain a set of dynamic equations of the disks motion that includes the motors dynamics. Then, a control strategy is proposed under which the disks inclination is stabilized about its vertical position and the disks motion is able asymptotically to track any given smooth ground trajectory.

Stabilization and control of the motion of an autonomous bicycle by using a rotor for the tilting moment

Abstract This work deals with the stabilization and control of a riderless bicycle. It is assumed here that the bicycle is controlled by a pedalling torque, a directional torque and by a rotor mounted on the crossbar that generates a tilting torque. A kind of an inverse control strategy is proposed under which the motion of the bicycle is stabilized and its rear wheel is able asymptotically to track any given smooth ground trajectory

Control of a rotary inverted pendulum

Abstract This work deals with the control of a rotary inverted pendulum (see Figure 1). This device is composed of the following: an arm rotating in the horizontal plane where one of its ends is mounted on a motor shaft and where a rod is mounted on its other end. The rods lower end is mounted on the arms free end in such a manner that, the rod is moving as an inverted pendulum in a plane that is at all times perpendicular to the rotating arm. The problem dealt with here is to find a control law to the motors output torque such that the inverted pendulum motion will be stabilized about a vertical axis.

Inclination control of the motion of a rolling disk by using a rotor

Abstract This work deals with the control and guidance of a system which is composed of a disk rolling on a plane, a controlled slender rod that is pivoted through its center of mass about the disks center, and a rotor with its axis fixed in the upper end of the rod (see Figs. 1 and 2). The rod is controlled in such a manner that it is always aligned along the line passing through the points O and C, where O denotes the center of the disk and C denotes the point of contact between the plane and the disk. The rotor rotates in a plane that is always perpendicular to the plane of the disk. Using the concept of path controllability, control laws are derived for the disks pedalling moment and the rotors torque, to steer the disks motion from a point P1 to a point P2, both of them in the plane, during a given time interval [0, tf].

Modelling of the motion of a disk rolling on a smooth rigid surface

This letter deals with the modelling of the motion of a disk rolling without slipping on a rigid surface.

Navigation and control of the motion of a riderless bicycle

This work deals with the guidance and control of a riderless bicycle. Given two points, p1 and P2, in the horizontal plane and a finite time interval [0, tf], denote by (x1,y1,z1) the coordinates of the center of the bicycles rear wheel. Based on a simplified dynamical model of the bicycle, and by using the concept of path controllability, control laws are derived for the bicycles pedalling moment and directional moment such that (x1,y1) will move from P1 to P2 during the time interval [0, tf].

Stabilization and control of the motion of a rolling disk by using two rotors fixed along its axis

Abstract This work deals with the stabilization and control of a system which is composed of a disk rolling on a plane, a slender rod that is fixed along the disks axis with its middle point fixed in the disks center, and two identical rotors fixed in the rod equally spaced along both sides of the disk. Each of the rotors is rotating in a plane that is perpendicular to the plane of the disk. In addition, these planes are perpendicular to each other (see Fig. 1). A kind of an inverse control strategy is proposed under which the motion of the disk is stabilized and is able asymptotically to track any given smooth ground trajectory.