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Geometric Control of a Quadrotor Unmanned Aerial Vehicle in Wind Fields Open Access

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This dissertation focuses on geometric modeling and control of a quadrotor unmannedaerial vehicle (UAV) in wind fields. Wind deteriorates stability and performance of smallaerial vehicles, and even may result in complete failure. To overcome this issue, thisdissertation concerns three topics, namely an identification method to understand the effectsof wind on the quadrotor UAV, and a mathematical framework to estimate wind in real-time,and a geometric adaptive controller to compensate wind disturbances.First, a computational approach for system identification for the attitude dynamics of arigid body is proposed. This is to identify unknown parameters of the system by investigatingits dynamic response. System identification or estimation for a rigid body is particularlychallenging as they evolve on the compact nonlinear manifold, referred to as the specialorthogonal group. Current methods based on local parameterizations or quaternions sufferfrom inherent singularities or ambiguities associated with them. The proposed methodaddresses these issues by formulating the system identification problem as an optimizationproblem on the special orthogonal group. It is solved by a geometric numerical integrator thatyields numerical trajectories that are consistent with the geometric structures of Hamiltoniansystems on a Lie group. As a result, the proposed method is particularly useful to handlelarge initial estimation errors that may cause substantial discrepancies between the targetattitude trajectories and the initial estimate of them.Second, the above technique is extended to a computational framework to identify theeffects of wind on the dynamics of a quadrotor UAV. Then, using the identified model,the strength and the direction of the wind are estimated without direct measurements fromanemometers. The proposed approach is based on the geometric numerical integratoron the special Euclidean group, referred to as a Lie group variational integrator suchthat singularities or complexities associated with the local coordinates or quaternions are completely avoided. Numerical examples illustrate that the presented methods successfullyidentify the effects of wind even for the challenging case of large initial estimation errors.Also, numerical results support that the presented method can be implemented for real-timewind estimation during flight.Finally, a geometric adaptive control scheme for a quadrotor UAV is developed, where theeffects of unknown, unstructured disturbances are mitigated by multilayer neural networksthat are adjusted online. The stability of the proposed controller is analyzed with Lyapunovstability theory on the special Euclidean group, and it is shown that the tracking errors areuniformly ultimately bounded with an ultimate bound that can be abridged arbitrarily. Amathematical model of wind disturbance on the quadrotor dynamics is presented, and itis shown that the proposed adaptive controller is capable of rejecting the effects of winddisturbances successfully. The efficacy of the proposed approach is illustrated by numericalexamples and indoor flight experiments.

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