Flowfield estimation in the wake of a pitching and heaving airfoil

Hinson, Brian T.; Morgansen, Kristi A.

doi:10.1109/acc.2012.6315288

Cited by 8 publications

(16 citation statements)

References 15 publications

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“…Calculating (10) analytically is often challenging for complex systems. Instead, it is possible to numerically estimate the observability Gramian, termed the empirical local observability Gramian, by simulating the system and comparing the outputs y for perturbations ±ε of the initial condition [26,27]. It can be shown that as ε → 0, the estimate converges to the result from (10).…”

Section: Discussionmentioning

confidence: 99%

“…Unfortunately, however, the observability Lie algebra calculation does not give any indication of what that control needs to be; only that it cannot be identically zero. To address this limitation, previous studies have developed methods that use the condition number of the observability Gramian to rank potential trajectories [27]. In this paper, we take a bio-inspired approach as described below.…”

Section: Discussionmentioning

confidence: 99%

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Monocular distance estimation from optic flow during active landing maneuvers

2014

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Vision is arguably the most widely used sensor for position and velocity estimation in animals, and it is increasingly used in robotic systems as well. Many animals use stereopsis and object recognition in order to make a true estimate of distance. For a tiny insect such as a fruit fly or honeybee, however, these methods fall short. Instead, an insect must rely on calculations of optic flow, which can provide a measure of the ratio of velocity to distance, but not either parameter independently. Nevertheless, flies and other insects are adept at landing on a variety of substrates, a behavior that inherently requires some form of distance estimation in order to trigger distance-appropriate motor actions such as deceleration or leg extension. Previous studies have shown that these behaviors are indeed under visual control, raising the question: how does an insect estimate distance solely using optic flow? In this paper we use a nonlinear control theoretic approach to propose a solution for this problem. Our algorithm takes advantage of visually controlled landing trajectories that have been observed in flies and honeybees. Finally, we implement our algorithm, which we term dynamic peering, using a camera mounted to a linear stage to demonstrate its real-world feasibility.

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Section: Discussionmentioning

confidence: 99%

Section: Discussionmentioning

confidence: 99%

Monocular distance estimation from optic flow during active landing maneuvers

2014

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“…24,30 Linearization may fail to adequately model the input/output relationship of the nonlinear system over a wide range of operating conditions. The empirical observability gramian does not require linearization but merely the ability to simulate the system.…”

Section: B Measures Of Leader Aircraft Observabilitymentioning

confidence: 99%

Wake Estimation and Optimal Control for Autonomous Aircraft in Formation Flight

DeVries

Paley

2013

AIAA Guidance, Navigation, and Control (GNC) Conference

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The continued development of sophisticated aircraft with high fidelity control systems will enable autonomous execution of challenging tasks such as aerial refueling and close formation flight. In order to achieve such tasks in autonomous flight, an aircraft must sense other aircraft in close proximity and position itself relative to them. For example, aerial refueling requires the follower aircraft to intercept the filling nozzle attached to the leader aircraft; also, formation-flying aircraft must position themselves strategically to realize benefits of aerodynamic efficiency. This paper uses lifting-line theory to represent a two-aircraft formation and presents a grid-based, recursive Bayesian filter for estimating the wake parameters of the leader aircraft using noisy pressure measurements distributed along the trailing aircraft's wing; the estimator also requires a binary, relative-altitude measurement to break the vertical symmetry. Optimal control strategies are presented to steer the follower aircraft to a desired position relative to the leader while simultaneously optimizing the observability of the leader's relative position. The control algorithms guide the follower aircraft along trajectories that maintain adequate observability, thereby guaranteeing estimator performance. Theoretical results are illustrated using numerical examples of two-aircraft formations.

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“…The results showed that vortex location and strength are observable using two velocity sensors, and that active motion of the airfoil (i.e., flapping) improves vortex observability, similar to the way that the dither signal in [13] improved estimator performance. An unscented Kalman filter (UKF) was used in simulation to estimate the location and strength of vortices in the wake of the flapping airfoil [14]. In this work, the goal is to find sensor locations that improve estimation accuracy.…”

mentioning

confidence: 99%

“…In previous work by the authors [14], an unsteady potential flow model of airfoil flapping was studied to determine the observability of vortices in the wake using velocity sensors on the surface of the airfoil. The results showed that vortex location and strength are observable using two velocity sensors, and that active motion of the airfoil (i.e., flapping) improves vortex observability, similar to the way that the dither signal in [13] improved estimator performance.…”

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confidence: 99%

Observability-Based Optimal Sensor Placement for Flapping Airfoil Wake Estimation

Hinson

Morgansen

2014

Journal of Guidance, Control, and Dynamics

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This work considers the optimal sensor placement problem for a general nonlinear system using the eigenvalues of the observability Gramian in the cost function. The problem is formulated as a mixed-integer convex optimization problem. Using the empirical observability Gramian, the input data to this optimization problem are computed from a simulation of the nonlinear system with no analytical model required. A piecewise linear approximation to the observability Gramian is proposed using special ordered sets of type two, allowing a coarser sensor location mesh and thus fewer binary variables and shorter solution times compared with standard gridded approaches. The solution methodology is applied to vortex estimation in the wake of a flapping airfoil using velocity sensors on the surface of the airfoil, which is modeled using unsteady potential flow and a Joukowski conformal mapping. Resulting optimal sensor sets are found near the trailing edge in pairs on the upper and lower surface. Although the observability Gramian is computed from the linearized system, the optimal sensor sets yield improved performance of an unscented Kalman filter estimating wake vortex structure on the nonlinear dynamics; the optimal sets outperform more than 99% of the sampled feasible sensor sets, thus validating the observability eigenvalues as a measure of nonlinear estimator performance. Nomenclature A, B, C = linearized system dynamics matrices a = Joukowski cylinder radius E = expectation operator F = Fisher information matrix f = nonlinear dynamics model H = linear measurement model h = nonlinear measurement model k = discrete time step k r = reduced frequency P = covariance matrix p = number of desired sensors r = number of candidate sensors s i = sensor location for sensor i u = control input u = control linearization deviation u 0 = control linearization trajectory v = measurement noise W = observability Gramiañ W = empirical observability Gramian W = interpolated observability Gramian W d = discrete-time observability Gramian w j = special ordered set weight vector for sensor j x = state vector x = state linearization deviation x 0 = state linearization trajectory

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Flowfield estimation in the wake of a pitching and heaving airfoil

Cited by 8 publications

References 15 publications

Monocular distance estimation from optic flow during active landing maneuvers

Monocular distance estimation from optic flow during active landing maneuvers

Wake Estimation and Optimal Control for Autonomous Aircraft in Formation Flight

Observability-Based Optimal Sensor Placement for Flapping Airfoil Wake Estimation

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