Capturing 3D Gaussian Splatting (3DGS) objects using drones presents a significant challenge in selecting suitable input views from candidate poses to ensure high-quality synthesized novel views. This challenge is compounded by the inherent limitations of drone resources, such as battery life and network bandwidth. In this paper, we employ uncertainty to quantify the contributions of individual candidate poses so as to optimize the computed drone trajectories. More specifically, we introduce optimal and efficient algorithms to compute drone trajectories on the fly, which, to the best of our knowledge, has never been done in the literature. Our extensive experiments revealed that, compared to the previous studies, our solution can: (i) incrementally construct good-quality 3DGS objects while following the computed trajectories, (ii) deliver final 3DGS objects with superior quality, and (iii) achieve the above goals with fewer input views captured at selected poses.