Dynamic Modeling and Simulation of a Wheeled Mobile Robot for Traversing Uneven Terrain Without Slip

[+] Author and Article Information
Nilanjan Chakraborty

 Department of Mechanical Engineering, Indian Institute of Science, Bangalore, Karnatake 560012, India

Ashitava Ghosal1

 Department of Mechanical Engineering, Indian Institute of Science, Bangalore, Karnatake 560012, Indiaasitava@mecheng.iisc.ernet.in


To whom correspondence should be addressed.

J. Mech. Des 127(5), 901-909 (Oct 13, 2004) (9 pages) doi:10.1115/1.1867503 History: Received February 28, 2004; Revised October 13, 2004

It is known in literature that a wheeled mobile robot (WMR), with fixed length axle, will undergo slip when it negotiates an uneven terrain. However, motion without slip is desired in WMR’s, since slip at the wheel-ground contact may result in significant wastage of energy and may lead to a larger burden on sensor based navigation algorithms. To avoid slip, the use of a variable length axle (VLA) has been proposed in the literature and the kinematics of the vehicle has been solved depicting no-slip motion. However, the dynamic issues have not been addressed adequately and it is not clear if the VLA concept will work when gravity and inertial loads are taken into account. To achieve slip-free motion on uneven terrain, we have proposed a three-wheeled WMR architecture with torus shaped wheels, and the two rear wheels having lateral tilt capability. The direct and inverse kinematics problem of this WMR has been solved earlier and it was shown by simulation that such a WMR can travel on uneven terrain without slip. In this paper, we derive a set of 27 ordinary differential equations (ODE’s) which form the dynamic model of the three-wheeled WMR. The dynamic equations of motion have been derived symbolically using a Lagrangian approach and computer algebra. The holonomic and nonholonomic constraints of constant length and no-slip, respectively, are taken into account in the model. Simulation results clearly show that the three-wheeled WMR can achieve no-slip motion even when dynamic effects are taken into consideration.

Copyright © 2005 by American Society of Mechanical Engineers
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Figure 1

Torus-shaped wheel on uneven terrain

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Figure 2

Uneven terrain used for simulations

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Figure 3

Variation of parameters for single wheel moving on uneven terrain

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Figure 4

Locus of wheel center and ground contact point for single wheel moving on uneven terrain

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Figure 5

Components of slip velocity at the wheel ground contact point

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Figure 6

Conversation of energy and the variation of potential and kinetic energy

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Figure 7

Equivalent instantaneous mechanism for the 3-DOF WMR

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Figure 8

Variation of δ1, δ2

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Figure 9

Constraint satisfaction for the 3-wheeled WMR moving on uneven terrain

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Figure 10

Locus of wheel-ground contact point, wheel center and platform center of the 3-wheeled WMR on uneven terrain

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Figure 11

Verification of no-slip constraints at wheel-ground contact point



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