  In multirotor systems, guaranteeing safety while considering unknown
disturbances is essential for robust trajectory planning. The Forward reachable
set (FRS), the set of feasible states subject to bounded disturbances, can be
utilized to identify robust and collision-free trajectories by checking the
intersections with obstacles. However, in many cases, the FRS is not calculated
in real time and is too conservative to be used in actual applications. In this
paper, we address these issues by introducing a nonlinear disturbance observer
(NDOB) and an adaptive controller to the multirotor system. We express the FRS
of the closed-loop multirotor system with an adaptive controller in augmented
state space using Hamilton-Jacobi reachability analysis. Then, we derive a
closed-form expression that over-approximates the FRS as an ellipsoid, allowing
for real-time computation. By compensating for disturbances with the adaptive
controller, our over-approximated FRS can be smaller than other ellipsoidal
over-approximations. Numerical examples validate the computational efficiency
and the smaller scale of our proposed FRS.
