The use of a feedback motion plan instead of the decoupled scheme consisting of separate plan and control phases can facilitate the task of proving the properties of an autonomous system. The advantage of using a feedback motion plan is the possibility to validate the whole plan offline before its execution, which means that trajectories having different initial states can be tested simultaneously. In this paper, we formulate a feedback motion plan based on the extension of the \emph{wavefront expansion} to the case of vehicles having bounded curvature. Additionally, the use of a transition function and a Gaussian filter limits undesired oscillations in the resultant trajectories. The method is suitable for both single goal missions and path following. The paper illustrates the algorithm for the generation of the plan and presents simulation data containing example trajectories and analysis of tuning parameters. Finally, future developments are discussed.