Abstract
Typically, the deformation of the tire in contact with the road has been neglected, thus a constant contact area A <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">c</inf> with a fixed infinitesimal pressure contact point P <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">c</inf> is assumed. However, wheel shows lateral and radial deformation, resulting in a non-constant contact area A <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">vc</inf> with a P <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">vc</inf> (t)≠P <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">c</inf> . Consequently, there arises endogenous forces when pivoting w.r.t. P <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">vc</inf> that may provoke skidding and/or slipping phenomena for nonholonomic (NH) vehicles, such as a car or a wheeled mobile robot (WMR). This phenomena may compromise tracking tasks of NH-WMR. Given the difficulty of measuring P <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">vc</inf> , these endogenous unmodelled forces have been cast wrongly as exogenous forces that appears as disturbances at a dynamic level, hence neglecting them as kinematic disturbances, which may lead to further contradiction in the models. In this paper, a Barrier Lyapunov Function (BLF) approach is addressed to handle robust velocity tracking for an affine differential kinematic NH-WMR model subject to unmatched disturbances, which arises when considering P <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">vc</inf> (t) at dynamic level. The closed-loop system yields convergence to an invariant set within the imposed barriers around a nominal desired reference provided by a smooth fuzzy velocity field. Representative simulations show that the mobile robot remains within the barriers width wich stands for the tolerance region of lateral disturbance velocity.
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