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Research Papers

Asymptotic Solution and Trajectory Planning for Open-Loop Control of Mobile Robots

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

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 March 19, 2016; final manuscript received October 25, 2016; published online March 10, 2017. Assoc. Editor: Davide Spinello.

J. Dyn. Sys., Meas., Control 139(5), 051004 (Mar 10, 2017) (9 pages) Paper No: DS-16-1150; doi: 10.1115/1.4035169 History: Received March 19, 2016; Revised October 25, 2016

A novel open-loop control method is presented for mobile robots based on an asymptotic inverse dynamic solution and trajectory planning. The method is based on quantification of sliding by a small nondimensional parameter. Asymptotic expansion of the equations yields the dominant nonslip solution along with a first-order correction for sliding. A trajectory planning is then introduced based on transitional circles between the robot initial states and target reference trajectory. The transitional trajectory ensures smooth convergence of the robot states to the target reference trajectory, which is essential for open-loop control. Experimental results with a differential drive mobile robot demonstrate the significant improvement of the controller performance when the first-order correction is included.

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Figures

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Fig. 1

The mobile robot and its model

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Fig. 2

Transitional and target circular paths

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Fig. 3

Experimental results for case 1 circular motion only; top to bottom: path, tracking errors, and wheel speed commands

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Fig. 4

Experimental results for case 1 circular and straight line motions; top to bottom: path, tracking errors, and wheel speed commands

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Fig. 5

Experimental results for case 2 circular motion only: paths (top) and tracking errors (bottom)

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Fig. 6

Experimental results for case 2 circular and straight line motions: paths (top) and tracking errors (bottom)

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Fig. 7

Experimental results for case 3 circular motion only: paths (top) and tracking errors (bottom)

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Fig. 8

Experimental results for case 3 circular and straight line motions: paths (top) and tracking errors (bottom)

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Fig. 9

Experimental results with varying ϵ values: paths (top) and tracking errors (bottom)

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