This work addresses the problem of generating robust and accurate trajectories taking into account uncertainties in the robot dynamic model. Based on the notion of closedloop sensitivity, which quantifies deviations in the closed-loop trajectories of any robot/controller pair against uncertainties in the robot model parameters, uncertainty tubes can be derived for bounded parameter variations. In our prior work, such tubes were integrated within a motion planner named SAMP to produce robust global plans, emphasizing the generation of trajectories with low sensitivity to model uncertainty. However, the high computational cost of the uncertainty tubes is a bottleneck for this method. Here, we solve this problem by proposing a novel framework that first incorporates a Gated Recurrent Unit (GRU) neural network to provide fast and accurate estimation of uncertainty tubes and then minimizes these tubes at given points along the trajectory. We experimentally validate our framework on a 3D quadrotor in two challenging scenarios: a navigation through a narrow window, and an in-flight “ring catching” task that requires high accuracy.