Controlled Motion of a Spherical Robot with Feedback. I

Ivanova, Tatiana B.; Kilin, Alexander A.; Пивоварова, Е. Н.

doi:10.1007/s10883-017-9387-2

Cited by 25 publications

(6 citation statements)

References 37 publications

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“…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.…”

Section: Introductionmentioning

confidence: 99%

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

Putkaradze

Rogers

2018

Meccanica

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The motion of a rolling ball actuated by internal point masses that move inside the ball's frame of reference is considered. The equations of motion are derived by applying Euler-Poincaré's symmetry reduction method in concert with Lagrange-d'Alembert's principle, which accounts for the presence of the nonholonomic rolling constraint. As a particular example, we consider the case when the masses move along internal rails, or trajectories, of arbitrary shape and fixed within the ball's frame of reference. Our system of equations can treat most possible methods of actuating the rolling ball with internal moving masses encountered in the literature, such as circular motion of the masses mimicking swinging pendula or straight line motion of the masses mimicking magnets sliding inside linear tubes embedded within a solenoid. Moreover, our method can model arbitrary rail shapes and an arbitrary number of rails such as several ellipses and/or figure eights, which may be important for future designs of rolling ball robots. For further analytical study, we also reduce the system to a single differential equation when the motion is planar, that is, considering the motion of the rolling disk actuated by internal point masses, in which case we show that the results obtained from the variational derivation coincide with those obtained from Newton's second law. Finally, the equations of motion are solved numerically, illustrating a wealth of complex behaviors exhibited by the system's dynamics. Our results are relevant to the dynamics of nonholonomic systems containing internal degrees of freedom and to further studies of control of such systems actuated by internal masses.

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Section: Introductionmentioning

confidence: 99%

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

Putkaradze

Rogers

2018

Meccanica

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“…In the first problem, a homogeneous sphere rolls inside the shell, and in the second, a spherical pendulum is fastened at its center. Possible generalizations and special cases of the latter problem arise in considering the dynamics of spherical robots controlled by an internal pendulum mechanism [46][47][48][49][50][51][52][53]. Related problems concerning the dynamics of a rigid body with a spherical support can be found in [54][55][56][57].…”

Section: Introductionmentioning

confidence: 99%

The Integrable Problem of the Rolling Motion of a Dynamically Symmetric Spherical Top with One Nonholonomic Constraint

Kilin¹,

Ivanova²

2023

Nelin. Dinam.

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This paper addresses the problem of a sphere with axisymmetric mass distribution rolling on a horizontal plane. It is assumed that there is no slipping of the sphere as it rolls in the direction of the projection of the symmetry axis onto the supporting plane. It is also assumed that, in the direction perpendicular to the above-mentioned one, the sphere can slip relative to the plane. Examples of realization of the above-mentioned nonholonomic constraint are given. Equations of motion are obtained and their first integrals are found. It is shown that the system under consideration admits a redundant set of first integrals, which makes it possible to perform reduction to a system with one degree of freedom.

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“…Recently, many kinds of spherical mobile robots have been developed and several practical applications are being studied by research institutes and universities [2][3][4][5][6][7][8]. The robot makes contact to the ground with the help of the round shell at a single point, and is driven by the inner actuation mechanism.…”

Section: Introductionmentioning

confidence: 99%

Research on Motion Control for a Mobile Robot Using Learning Control Method

Zheng

2021

Applied Mathematics and Nonlinear Sciences

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Precise motion control is a challenging and important goal in the application of mobile robots. The mechanical structure of a novel mobile robot is presented. Using the support vector machine learning control method in statistical theory, the human control strategy is represented by the parametric model without knowledge of the actual robot mathematical model. Moreover, using the learning controller, the position motion control experiments of the robot are carried out. The results of the experiments show that this learning control method is feasible and valid for the precise position control of the mobile robot, and the maxim error is less than 32 cm in a 10 m linear movement.

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Controlled Motion of a Spherical Robot with Feedback. I

Cited by 25 publications

References 37 publications

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

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

The Integrable Problem of the Rolling Motion of a Dynamically Symmetric Spherical Top with One Nonholonomic Constraint

Research on Motion Control for a Mobile Robot Using Learning Control Method

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