Dynamics and Control of a Spherical Robot with an Axisymmetric Pendulum Actuator

Abstract

This paper investigates the possibility of the motion control of a ball with a pendulum mechanism with non-holonomic constraints using gaits -the simplest motions such as acceleration and deceleration during the motion in a straight line, rotation through a given angle and their combination. Also, the controlled motion of the system along a straight line with a constant acceleration is considered. For this problem the algorithm for calculating the control torques is given and it is shown that the resulting reduced system has the first integral of motion.

On the dynamics of a rolling ball actuated by internal point masses

“…In particular, [17] actuates the rolling ball by internal masses which reciprocate along spokes. Reference [7] actuates the rolling ball by a combination of internal rotors and sliders, [22] actuates the rolling ball by an internal gyroscopic pendulum as shown in Figure 1.3d, [29,30,31,32] actuate the rolling ball by an internal spherical pendulum as shown in Figure 1.3e, and [21] actuates the rolling ball by an internal pendulum and yoke. This paper considers a rolling ball actuated by internal point masses that move along arbitrarily-shaped rails fixed within the ball, such as depicted in Figure 1.3c.…”

On the control of a robot ball using two omniwheels

“…The acceleration of a ball carrying a pendulum was studied in [13]. In such a case the center of mass of the system does not coincide with the geometric center of the ball.…”

“…This type includes devices carrying pendulums or massive carts on wheels or runners [7][8][9][10][11][12][13][14];…”

The contol of the motion through an ideal fluid of a rigid body by means of two moving masses

“…траектория в пространстве позиционных переменных g (в нашем случае в E(2)). В теории управления замкнутые кривые в пространстве β, которые обеспечивают наиболее «удачные» элементарные движения (например, разворот на месте или почти поступательное движение в каком-то направлении) в пространстве g, принято называть гейтами (см., например, [8,10,11,16]). Найдя для конкретной задачи ряд удач-ных гейтов, можно из них конструировать более сложные движения, решая тем самым те или иные задачи управления и оптимизации [8].…”