In the present work, it is described a fast motion-planner for mobile robots moving on natural terrains. The planner is very flexible: it can be use on a wide class of vehicles with different kinematics, and with generic shapes (even with concavity and holes). Because of these characteristics, it could be applied for the assembly planning in the manufacturing industry, as in the piano mover's problems. Considering robots moving with smoothed trajectories on variable terrains, we have developed this algorithm based on an anisotropic propagation of attraction potentials on a non-Euclidean manifold. The optimal collision-free trajectories are found following the minimum valley of a potential hypersurface embedded in a 4D space. Thanks to the underlying multilayered cellular automata architecture, it is a distributed approach. This planner turn out to be very fast, allowing to react to the dynamics of the environment, evolving toward new solutions every time the obstacles positions changes