Steering a Chaplygin Sleigh Using Periodic Impulses

Tallapragada, Phanindra; Fedonyuk, Vitaliy

doi:10.1115/1.4036117

Cited by 18 publications

(19 citation statements)

References 7 publications

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“…Various generalizations of the problem of the Chaplygin sleigh were considered by many authors [20,21,22,23,24,25,26,27,28]. In particular, attention was given to problems of the motion of the sleigh in the presence of periodic impulse impacts [20,21], with periodic switchovers of the nonholonomic constraint to different locations [23,24], and with periodic transfers of the massive load placed on the sleigh [25,26]. Analysis was also made of the motion of the sleigh under the action of random forces which model a fluctuating continuous medium [28], when, according to the authors, the motion resembles random walks of bacterial cells with a diffusion component.…”

Section: Introductionmentioning

confidence: 99%

The Chaplygin sleigh with friction moving due to periodic oscillations of an internal mass

2018

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For a Chaplygin sleigh moving in the presence of weak friction, we present and investigate two mechanisms of arising acceleration due to oscillations of an internal mass. In certain parameter regions, the mechanism induced by small oscillations determines acceleration which is on average one-directional. The role of friction is that the velocity reached in the process of the acceleration is stabilized at a certain level. The second mechanism is due to the effect of parametric excitation of oscillations, when the internal moving particle is comparable in mass with the main platform, and, as occurs, a necessary condition for the acceleration is presence of friction. The parametric instability and the resulting acceleration of the sleigh turn out to be bounded if the line of oscillations of the moving mass is displaced from the center of mass. The steady-state regime of motion is in many cases associated with a chaotic attractor; accordingly, the motion of the sleigh turns out to be similar to the process of random walk on a plane.

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Section: Introductionmentioning

confidence: 99%

The Chaplygin sleigh with friction moving due to periodic oscillations of an internal mass

2018

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“…The equations of motion of the Chaplygin sleigh without the internal rotor, [6,12,18] can be obtained from (13) and (14) by setting ε = 0,…”

Section: Simulation Resultsmentioning

confidence: 99%

“…3 Equations (22) and (25) represent the leading order equations for the evolution of the velocity of the sleigh. These equations are the same as those that describe the motion of the Chaplygin sleigh without an internal rotor, (17), (18). The leading order solutions u 0 and Ω 0 are shown in Fig.…”

Section: Transient Dynamics Of the Sleigh And Regular Perturbation Exmentioning

confidence: 99%

Chaotic dynamics of the Chaplygin sleigh with a passive internal rotor

Fedonyuk

Tallapragada

2018

Nonlinear Dyn

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The Chaplygin sleigh is a classic example of a nonholonomically constrained mechanical system. The sleigh's motion always converges to a straight line whose slope is entirely determined by the initial configuration and velocity of the sleigh. We consider the motion of a modified Chaplygin sleigh that contains a passive internal rotor. We show that the presence of even a rotor with small inertia modifies the motion of the sleigh dramatically. A generic trajectory of the sleigh in a reduced velocity space exhibits two distinct transient phases before converging to a chaotic attractor. We demonstrate this through numerics. In recent work the dynamics of the Chaplygin sleigh have also been shown to be similar to that of a fish like body in an inviscid fluid. The influence of a passive degree of freedom on the motion of the Chaplygin sleigh points to several possible applications in controlling the motion of the nonholonomically constrained terrestrial and aquatic robots.

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“…On the other hand, if n < N − m then the system's motion involves dynamics, and is governed by interaction between the nonholonomic constraints and balance of generalized momentum variables. Examples of such systems are the snakeboard [9,10], roller racer [11,12], and several actuated variants of Chaplygin's sleigh [13,14,15]. There have been many works on dynamics and control of nonholonomic locomotion systems, exploiting their geometric structure for analyzing periodic control inputs [16,17].…”

Section: Scientific Backgroundmentioning

confidence: 99%

Nonholonomic Dynamics of the Twistcar Vehicle: Asymptotic Analysis and Hybrid Dynamics of Frictional Skidding

Halvani

2021

Preprint

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The Twistcar vehicle is a classic example of a nonholonomic dynamical system. The vehicle model consists of two rigid links connected by an actuated rotary joint and supported by wheeled axles, where nonholonomic constraints are assumed to impose no skidding of the wheels. Recent experimental measurements conducted with a robotic Twistcar prototype have shown disagreements with previous theoretical analyses. In particular, significant skidding has been observed, in addition to discrepancies with respect to theoretical predictions of divergence in oscillations of the vehicle’s speed and orientation, as well as direction reversal depending on the vehicle’s structure. The goal of our research is to resolve this disagreement by generalizing the theoretical analysis. First, we extend previous asymptotic analysis by incorporating the effects of links’ inertia and oscillation amplitude of the input angle on the direction of net motion. Next, we formulate the vehicle’s hybrid dynamics under frictional bounds and skid-state transitions. Using numerical analysis, we obtain optimal values for the vehicle’s mean speed and energetic cost-of-transport as a function of the input frequency. Our results improve the agreement between theory and experiments and suggest directions for further experimental investigation.

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Steering a Chaplygin Sleigh Using Periodic Impulses

Cited by 18 publications

References 7 publications

The Chaplygin sleigh with friction moving due to periodic oscillations of an internal mass

The Chaplygin sleigh with friction moving due to periodic oscillations of an internal mass

Chaotic dynamics of the Chaplygin sleigh with a passive internal rotor

Nonholonomic Dynamics of the Twistcar Vehicle: Asymptotic Analysis and Hybrid Dynamics of Frictional Skidding

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