This paper addresses the problem of computing robust trajectories against uncertainties in the robot model. Based on the notion of closed-loop state sensitivity introduced in [1], [2] for identifying deviations of the closed-loop trajectories of any robot/controller pair against variations of uncertain parameters in the robot model, uncertainty tubes can be derived for bounded parameter variations [3]. Such tubes were integrated within a motion planner named SAMP [4] to produce robust global plans, emphasizing the generation of low sensitivity trajectories. However, a bottleneck of this method remains the very high computational cost of the uncertainty tubes. In this paper, we mitigate this problem by proposing a novel framework that first incorporates a Long Short-Term Memory [5] (LSTM) neural network (NN) to provide fast and accurate uncertainty tubes estimation, and then reduces tracking errors at given points on the trajectory. We validate our framework on a full 3D-quadrotor UAV model performing a 'ring-recovering' task requiring high accuracy. Our results show the computational gain of the LSTM-based robust planning and that the subsequent optimization stage significantly improves the accuracy of the trajectory execution.