We address the problem of motion planning for aerial drones to allow them to fly through confined spaces and narrow gaps between obstacles. Finding safe and feasible trajectories for steering multiple drones towards some desired positions in tight spaces or guiding them through gaps smaller in width than their diameters is impossible without taking the drones’ orientations into account. To incorporate the orientation into the motion planning problem we employ an ellipsoid model of the drone body, and utilize the separating hyperplane theorem for convex sets to derive constraints that guarantee collision avoidance between the ellipsoid-shaped drone and obstacles modeled as ellipsoids, spheres, or polygons. The resulting set of constraints is seamlessly integrated into the motion planning method based on Bézier curve whose properties are exploited for efficient evaluation of the constraints. The efficacy of the proposed method in generating feasible and collision-free trajectories is demonstrated via different simulations involving single and multiple drones.