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

Computing Forward Reachable Sets for Nonlinear Adaptive Multirotor Controllers