This paper deals with path planning for car-like robot. Usual planners compute paths made of circular arcs tangentially connected by line segments, as these paths are locally optimal. The drawback of these paths is that their curvature profile is not continuous: to follow them precisely, a vehicle must stop and reorient its directing wheels at each curvature discontinuity (transition segment-circle).
To remove this limitation, a new path planning problem is proposed: two curvature constraints are added to the classical kinematic constraints taken into account. Thus, the curvature must remain continuous, and its derivative is bounded (as the car-like robot can reorient its directing wheels with a limited speed only). For this problem, the existence of solutions and the characterization of those of optimal length are shown. A method solving the forward-only problem (i.e. the problem for a car moving only forward) is then presented, and this method is compared to the classical one w.r.t. the complexity and computation time, the length of the generated paths and the quality of the tracking.