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Computing Forward Reachable Sets for Nonlinear Adaptive Multirotor Controllers
In multirotor systems, guaranteeing safety while considering unknown
disturbances is essential for robust trajectory planning. Computing the forward
reachable set (FRS), the set of all possible states with bounded disturbances,
can be a viable solution to find robust and collision-free trajectories.
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 mitigate
these problems by applying a nonlinear disturbance observer (NDOB) and an
adaptive controller to the multirotor system. We formulate the FRS of the
closed-loop system combined with the adaptive controller in augmented state
space by exploiting the Hamilton-Jacobi reachability analysis and then present
the ellipsoidal approximation in a closed-form expression to compute the small
FRS in real time. Moreover, tighter disturbance bounds in the prediction
horizon are inferred from the NDOB so that a much smaller FRS can be generated.
Numerical examples validate the computational efficiency and the smaller scale
of the proposed FRS compared to the baseline.Comment: 7 pages, 3 figures, submitted to ACC 202
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