  This paper studies path synthesis for nonholonomic mobile robots moving in
two-dimensional space. We first address the problem of interpolating paths
expressed as sequences of straight line segments, such as those produced by
some planning algorithms, into smooth curves that can be followed without
stopping. Our solution has the advantage of being simpler than other existing
approaches, and has a low computational cost that allows a real-time
implementation. It produces discretized paths on which curvature and variation
of curvature are bounded at all points, and preserves obstacle clearance. Then,
we consider the problem of computing a time-optimal speed profile for such
paths. We introduce an algorithm that solves this problem in linear time, and
that is able to take into account a broader class of physical constraints than
other solutions. Our contributions have been implemented and evaluated in the
framework of the Eurobot contest.
