Spherical robot of combined type: Dynamics and control

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

doi:10.1134/s1560354715060076

Cited by 48 publications

(22 citation statements)

References 18 publications

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“…More recently, [13] provides a detailed analysis of the trajectory of the Chaplygin sphere's contact point, and it has been shown that the dynamics of the Chaplygin top exhibit a strange attractor [14] and the phenomenon of reversal [15]. The dynamics of the rolling ball with dynamic internal structure is also an active topic in the nonholonomic mechanics literature [16,17,7,18,19,20,21,22,23].…”

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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“…This often makes them useless in practice. In [36], the motion of the ball is controlled using a pendulum-type mechanism, which can lead to an unbounded acceleration.…”

Section: Introductionmentioning

confidence: 99%

The Chaplygin Sleigh with Parametric Excitation: Chaotic Dynamics and Nonholonomic Acceleration

2017

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This paper is concerned with the Chaplygin sleigh with timevarying mass distribution (parametric excitation). The focus is on the case where excitation is induced by a material point that executes periodic oscillations in a direction transverse to the plane of the knife edge of the sleigh. In this case, the problem reduces to investigating a reduced system of two first-order equations with periodic coefficients, which is similar to various nonlinear parametric oscillators. Depending on the parameters in the reduced system, one can observe different types of motion, including those accompanied by strange attractors leading to a chaotic (diffusion) trajectory of the sleigh on the plane. The problem of unbounded acceleration (an analog of Fermi acceleration) of the sleigh is examined in detail. It is shown that such an acceleration arises due to the position of the moving point relative to the line of action of the nonholonomic constraint and the center of mass of the platform. Various special cases of existence of tensor invariants are found.

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“…More recently, [12] provides a detailed analysis of the trajectory of the Chaplygin sphere's contact point, and it has been shown that the dynamics of the Chaplygin top exhibit a strange attractor [13] and the phenomenon of reversal [14]. The dynamics of the rolling ball with dynamic internal structure is also an active topic in the nonholonomic mechanics literature [15,16,6,17,18,19,20,21,22].…”

Section: Introductionmentioning

confidence: 99%

“…by using the direct method. Reference [21] investigates the trajectory tracking control of a rolling ball actuated by an internal gyroscopic pendulum by piecing together special gaits, each of whose motion is determined analytically. To contrast with previous work, this paper investigates the optimal control (in the sense of the variational Pontryagin's minimum principle) of a rolling ball actuated by internal point masses for very general performance indexes and mass trajectories.…”

Section: Introductionmentioning

confidence: 99%

On the Optimal Control of a Rolling Ball Robot Actuated by Internal Point Masses

Putkaradze

Rogers

2020

Journal of Dynamic Systems, Measurement, and Control

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The controlled motion of a rolling ball actuated by internal point masses that move along arbitrarily-shaped rails fixed within the ball is considered. Application of the variational Pontryagin's minimum principle yields the ball's controlled equations of motion, a solution of which obeys the ball's uncontrolled equations of motion, satisfies prescribed initial and final conditions, and minimizes a prescribed performance index.

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Spherical robot of combined type: Dynamics and control

Cited by 48 publications

References 18 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 Chaplygin Sleigh with Parametric Excitation: Chaotic Dynamics and Nonholonomic Acceleration

On the Optimal Control of a Rolling Ball Robot Actuated by Internal Point Masses

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