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Our contribution in this article is twofold. First, we identify the regularity properties of the trajectories of planar wheeled mobile robots. By regularity properties of a trajectory we mean whether this trajectory, or a function computed from it, belongs to a certain class <i>C<sup>n</sup></i> (the class of functions that are differentiable <i>n</i> times with a continuous <i>n</i><sup>th</sup> derivative). We show that, under some generic assumptions about the rotation and steering velocities of the wheels, any non-degenerate wheeled robot belongs to one of the two following classes. Class I comprises those robots whose admissible trajectories in the plane are <i>C</i><sup>1</sup> and piecewise <i>C</i><sup>2</sup>; and class II comprises those robots whose admissible trajectories are <i>C</i><sup>1</sup>, piecewise <i>C</i><sup>2</sup> and, in addition, curvature-continuous. Second, based on this characterization, we derive new feedback control and gap filling algorithms for wheeled mobile robots using the recently-developed affine trajectory deformation framework.
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