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Research Papers

Prediction of Wheel Slipping Limits for Mobile Robots

[+] Author and Article Information
Alan Whitman, Garrett Clayton

Center for Nonlinear Dynamics and Control,
Villanova University,
Villanova, PA 19085

Hashem Ashrafiuon

Center for Nonlinear Dynamics and Control,
Villanova University,
Villanova, PA 19085
e-mail: hashem.ashrafiuon@villanova.edu

1Corresponding author.

Contributed by the Dynamic Systems Division of ASME for publication in the JOURNAL OF DYNAMIC SYSTEMS, MEASUREMENT,AND CONTROL. Manuscript received June 17, 2018; final manuscript received October 4, 2018; published online November 22, 2018. Assoc. Editor: Richard Bearee.

J. Dyn. Sys., Meas., Control 141(4), 041002 (Nov 22, 2018) (9 pages) Paper No: DS-18-1289; doi: 10.1115/1.4041664 History: Received June 17, 2018; Revised October 04, 2018

In this paper, we present a method to accurately predict the wheel speed limits at which mobile robots can operate without significant slipping. The method is based on an asymptotic solution of the nonlinear equations of motion. Using this approach, we can predict wheel slipping limits of both the inside and outside wheel when the robot is in a constant circular motion of any radius. The analytical results are supported by experiments, which show that the inside wheel slipping limits for circular motions of various radii occur very close to the predicted values. The method is then applied to predict wheel speed profiles for general motion without slipping and experimentally verified for a sinusoidal path.

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References

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Figures

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Fig. 1

The mobile robot and its model

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Fig. 4

Theoretical and experimental slipping speed limits as a function of circular path radii using wheels with tires (top) and without tires (bottom). The solid lines indicate the inside (left) and the dashed line the outside (right) wheel theoretical slip speed limits.

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Fig. 2

Static friction coefficient test results with and without tires

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Fig. 5

Mobile robot using wheels with tires achieving circular paths of radius 0.3 m using wheel speeds of ψ˙±=200,100 rpm (top) and ψ˙±=220,110 rpm (bottom)

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Fig. 3

Theoretical and experimental wheel speed ratios as a function of circular path radii using wheels with tires (top) and without tires (bottom)

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Fig. 7

Sinusoidal trajectory position tracking errors (top) and orientation error (bottom) with a speed scale factor of 0.3

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Fig. 8

Sinusoidal trajectory position tracking errors (top) and orientation error (bottom) with a speed scale factor of 0.6

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Fig. 9

The paths achieved by the robot using various speed scale factors

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Fig. 6

Sinusoidal path wheel speed profiles as determined by Eq. 48 (top) and by using Eqs. (35)(37) (bottom) subject to maximum of 250 rpm.

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