Trajectory Planning with Safety Guaranty for a Multirotor based on the Forward and Backward Reachability Analysis

Seo, Ho Seong; Son, Clark Youngdong; Lee, Dongjae; Kim, H. Jin

doi:10.1109/icra40945.2020.9196760

Cited by 4 publications

(14 citation statements)

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“…We aim to approximate E Y (t) ∩ Prop Y (D P (t)) to an ellipsoid in a way similar to that in [17], [18]. Suppose that E Y (t) is the sub-zero level set of the value function V (e y , t) ∈ R:…”

Section: B Coordinate Transformation and Hamilton-jacobi Reachability...mentioning

confidence: 99%

“…All of these studies require an offline phase for the FRS computation. On the other hand, [17], [18] compute the FRSs of the nominal trajectories of the multirotor in real time. These studies approximate the FRS to an ellipsoid in an analytical expression by exploiting a generalized Hopf formula [19].…”

Section: Introductionmentioning

confidence: 99%

“…These studies approximate the FRS to an ellipsoid in an analytical expression by exploiting a generalized Hopf formula [19]. Although [17], [18] compute the high dimensional approximation of the FRS in real time unlike [10], [11], [12], the approximated FRS is too conservative to be applied to agile trajectory planning.…”

Section: Introductionmentioning

confidence: 99%

“…Our research aims to compute small FRSs in a receding horizon using a nonlinear disturbance observer (NDOB) and a nonlinear adaptive controller for a multirotor in real time. To achieve this objective, we extend earlier work [17], [18] by applying the adaptive controller as a feedback controller with the assumption that the disturbance is differentiable and that its time derivative is bounded. The NDOB and the adaptive controller for the multirotor are presented and the stability is proven to justify their use in the first step of this paper.…”

Section: Introductionmentioning

confidence: 99%

“…• the approximated FRSs are computed in real time and are much smaller than a baseline [18] when tightening future possible disturbances and adding the NDOB and the adaptive controller to the multirotor system.…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

Computing Forward Reachable Sets for Nonlinear Adaptive Multirotor Controllers

Han¹,

Choi²

2022

Preprint

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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.

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Section: B Coordinate Transformation and Hamilton-jacobi Reachability...mentioning

confidence: 99%