In the case of non-holonomic robot navigation, path planning algorithms such as Rapidly-exploring Random Tree (RRT) rarely provide feasible and smooth paths without the need of additional processing. Furthermore, in a transport context like power wheelchair navigation, passenger comfort should be a priority and influence path planning strategy. In this paper, we propose a local path planner which guarantees bounded curvature value and continuous Cubic Bézier piecewise curves connection. To simulate and test this Cubic Bézier local path planner, we developed a new RRT version (CBB-RRT*) which generates on-the fly comfortable path adapted to non-holonomic constraints.