Motion Control of a Spherical Robot with a Pendulum Actuator for Pursuing a Target

Abstract

The problem of controlling the rolling of a spherical robot with a pendulum actuator pursuing a moving target by the pursuit method, but with a minimal control, is considered. The mathematical model assumes the presence of a number of holonomic and nonholonomic constraints, as well as the presence of two servo-constraints containing a control function. The control function is defined in accordance with the features of the simulated scenario. Servo-constraints set the motion program. To implement the motion program, the pendulum actuator generates a control torque which is obtained from the joint solution of the equations of motion and derivatives of servo-constraints. The first and second components of the control torque vector are determined in a unique way, and the third component is determined from the condition of minimizing the square of the control torque. The system of equations of motion after reduction for a given control function is reduced to a nonautonomous system of six equations. A rigorous proof of the boundedness of the distance function between a spherical robot and a target moving at a bounded velocity is given. The cases where objects move in a straight line and along a curved trajectory are considered. Based on numerical integration, solutions are obtained, graphs of the desired mechanical parameters are plotted, and the trajectory of the target and the trajectory of the spherical robot are constructed.

Control of a Spherical Robot with a Nonholonomic Omniwheel Hinge Inside

“…In the case of controlling the spherical pendulum-type robot, due to the appropriate torque control of an unbalanced axisymmetric pendulum, trajectory control is quite possible. This is confirmed by the results of [13,16].…”

“…The problem of controlling the spherical robot (spherical shell) using various mechanisms that set it in motion is one of the urgent problems of nonholonomic mechanics and robotics. These are rotary mechanisms [7][8][9][10][11][12], pendulum mechanisms [13][14][15][16][17], mechanisms with omniwheels [18][19][20] and some others [21,22]. In these works, the equations of motion of the studied mechanical systems are given and control actions for the realization of motion are obtained.…”

“…Speaking about the control of the spherical robot, first of all we assume trajectory control, which is carried out by setting two (in the case of two omniwheels) or three (in the case of three omniwheels) servo-constraints [16,23]. In this paper, trajectory control will be understood as motion control along a given smooth curve with a given velocity, that is, with a given law of motion.…”

“…In this paper, trajectory control will be understood as motion control along a given smooth curve with a given velocity, that is, with a given law of motion. Motion control along a given smooth curve can also be the basis of an algorithm for the spherical robot pursuing some moving object [16]. Therefore, the problem of trajectory control of the spherical robot with certain design features is relevant and important.…”