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This paper presents a set of paths, called bi-elementary paths. These paths are smooth and feasible for a car-like robot (i.e. their tangent direction is continuous and they respect a minimum turning radius constraint), and they can be followed by a real vehicle without stopping (i.e. they have a continuous curvature profile)-which is not the case of Dubins' curves. These paths are composed of arcs of a clothoid (a clothoid is a curve whose curvature is a linear function of its arc length), and are used to define a simplified, i.e. non-complete, planner. This simplified planner is, in turn, used in two global planning schemes, namely the Ariadne's Clew algorithm and probabilistic path planning. This paper proves an important property of the bi-elementary paths, from which the completeness of the two global planners is deduced.
Scheuer et al. (Fri,) studied this question.