Although advance future avionics will enable full compliance with the given trajectory; there are many uncertainty sources that can deflect aircraft from their intended positions. In this article we investigate potential of robust trajectory planning, considered as an additional demand management action, as a mean to alleviate the en-route congestion in airspace. Robust trajectory planning (RTP) involves generation of congestion-free trajectories with minimum operating cost taking into account uncertainty of trajectory prediction and unforeseen event. The model decision variables include ground delay, change of horizontal route and vertical profile (flight level) to resolve congestion problem. The article introduces a novel approach for route generation (3D trajectory) based on homotopic feature of continuous functions. It is shown that this approach is capable of generating a large number of route shapes with a reasonable number of decision variables. RTP problem is modeled as a mixed-variable optimization problem and it is solved using stochastic optimization technique. The model is tested on a real-life example from the French airspace. The results indicate that, under certain conditions, with small increase of total planned costs, it is possible to increase robustness of the proposed solution providing a good alternative to the solutions given by existing conflict-free trajectory planning models.