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Performance of Low-Cost Air-Data Sensors for Airspeed and Angle of Attack Measurements in a Flapping-Wing Robot
Abstract
Air-data measurements are one of the essential observations for system identification of flapping-wing unmanned aerial vehicles (UAVs). The effects of intensive high-amplitude oscillations of ornithopters on air-data measurements were studied in detail. The movements of an average-sized ornithopter were simulated through a two-degree-of-freedom (2-DOF) mechanism in a wind tunnel, and measurements of an air-data system (pitot and air vane) attached to the mechanism were studied. pitot tests were conducted at different airspeeds and angles of attack (AoAs) using three pitot tubes. The same experimental conditions were created for air-vane measurements. Results revealed that within certain limits, the average measured airspeed was close to the true airspeed values. Two filters were proposed and used for real-time airspeed estimation. Based on the measurements, the oscillation amplitude of the air vane was almost twice that of the real AoA oscillations. However, the mean values of air-vane measurements and real AoAs coincided over one flapping period. For real-time estimation of AoA, which varies very fast with flapping, an estimator based on the least-squares method was implemented.
Similarities and differences of a large-scale flapping-wing robot with fixed-wing UAVs in equations of motion, trim curves, and aerodynamic forces in forward flight are discussed in this paper and a simplified model for flapping flight is presented. Due to the high Wing to Total Weight (WTW) ratio of large-scale ornithopters, simple rigid body dynamics is not accurate enough for flight dynamics modeling. On the other hand, the multi-body dynamics associated with flapping gives little insight into the behavior of the resulting model due to complexity of equations. It is also difficult to design proper controllers for such complicated models. In this paper, the effects of different terms of multi-body equations of ornithopter on the estimated aerodynamic forces are studied via experimental flight data. A simpler but yet accurate set of equations is obtained by removing less effective terms from original relations. The presented model is in the form of normal aircraft equations plus some additional terms which can be used in different control and estimation processes. In addition, trim conditions of forward flight are extracted using several flight tests, and corresponding periodic behavior of states and forces are studied. These studies are applicable for identifying time-periodic models.
Bioinspired flapping-wing robots allow for unprecedented manoeuvrability and versatility, and increasingly small and light designs, with significant potential for flight in tight or cluttered spaces. For efficient design, operation and control of such vehicles, fully exploiting their potential and allowing for flight in a wide range of conditions, it is paramount to explore and model their dynamics across their intended flight envelope. However, due the complex flapping-flight mechanisms and limited availability of free-flight data, global models are not yet available, particularly models based on real flight data and simple enough to be applicable in practice. This paper discusses a set of free-flight tests conducted with an ornithopter to, firstly, investigate its dynamics in a range of different flight conditions, and, secondly, provide a basis for global model identification, important for advanced controller development, simulation and performance evaluations. The obtained results are presented and system identification is used to provide insight into the dynamics of the ornithopter in different flight conditions. Additionally, the flight testing process is discussed, focusing on acquiring data suitable for identification and analysis of flapping-wing vehicles, specifically. This includes fusing on-board IMU and off-board optical tracking data, to obtain not only a higher quality and reliability, but also accurate high-frequency measurements that can be used to analyse time-resolved flapping effects in free flight and during manoeuvres.
A time-varying model for the forward flight dynamics of a flapping-wing micro aerial vehicle is determined from free-flight optical tracking data using system identification. Based on timescale separation, the aerodynamic forces and moments are each formulated as a linear addition of decoupled time-averaged and time-varying sub-models. The aerodynamic models are incorporated in linearised equations of motion, resulting in an accurate and simulation-capable dynamic model. The time-averaged component is assumed to be linear; the time-varying component is represented as a third-order Fourier series, which effectively approximates the flapping dynamics. Combining both components yields a more complete and realistic simulation. The model is used to assess the validity of the widely-applied timescale separation assumption and results suggest that while in steady flight the assumption applies well, during manoeuvres the time-varying dynamics are not fully captured. More accurate modelling of flapping-wing flight during manoeuvres may require more advanced models that consider coupling between the time scales. Nomenclature f = frequency, Hz F = aerodynamic forces, N , and moments, N m g = acceleration due to gravity, ms −2 I x , I z , I xz = body moments of inertia, kg · m 2 J = cost function L, M, N = aerodynamic moments around x b , y b and z b axis, N m m = mass, kg n k = number of measurement points n u , n x , n y = number of inputs u, states x, outputs y p, q, r = turn rates in body-fixed coordinates, rad · s −1 R = measurement error covariance matrix u, v, w = velocities in body-fixed coordinates ms −1 u = model input x b , y b , z b = body-fixed coordinate system x = state vector y = model-predicted system output z = measured system output X, Y, Z = aerodynamic forces along x b , y b and z b axis, N α, β = angle of attack, angle of sideslip, rad δ e , δ r = elevator deflection, rudder deflection, radˆΘ = parameter estimates Φ, Θ, Ψ = Euler angles, rad
There is currently a large effort underway to understand the flight dynamics of avian-based flapping-wing vehicles, or ornithopters, as they represent a critical intersection between existing biological flyers and the need for small aerial robots to conduct a variety of mission scenarios. Efforts to model the flight dynamics of these vehicles for feedback control have been complicated by a number of factors including nonlinear flight motions, unsteady aerodynamics at low Reynolds numbers, and limited sensor payload capacity. This paper presents data for a 0.45 kg ornithopter research platform, flown in straight and level mean flight. A visual tracking system was employed to follow retroreflective markers on the ornithopter and reconstruct state measurements. A multibody model of the flight dynamics was used to investigate the spatial distribution of kinematic variables over the duration of a wing stroke, and system identification techniques were employed to extract models for the lift, thrust, and pitching moment coefficients. Two methods of parameter estimation showed good results for relatively simple aerodynamic models that can be used for feedback control.
Several formulations have been proposed to model the dynamics of or-nithopters, with inconclusive results regarding the need for complex kine-matic formulations. Furthermore, the impact of assumptions made in the collected results was never assessed by comparing simulations with real flight data. In this study two dynamic models of a Flapping Wing Micro Aerial Vehicle (FWMAV) were derived and compared: a) single rigid body aircraft equations of motion and b) Virtual Work Principle derivation for multiple rigid body flapping kinematics. The aerodynamic forces and mo-ments were compared by feeding the states that were reconstructed from the position and attitude data of a 17 gram free flying FWMAV into the dynamic equations of both formulations. To understand the applicability of rigid body formulations to FWMAVs, six wing-to-body mass ratios and two wing configurations were studied using real flight data. The results show that rigid body models are valid for the aerodynamic reconstruction of FWMAVs with four wings in 'X' configuration and two-winged FWMAV ¶ Ph.D. candidate,
This paper presents an approach to the system identification of the Delfly II Flapping Wing Micro Air Vehicle (FWMAV) using flight test data. It aims at providing simple FWMAV aerodynamic models that can be used in simulations as well as in nonlinear flight control systems. The undertaken methodology builds on normal aircraft system identification methods and extends these with techniques that are specific to FWMAV model identification. The entire aircraft model identification cycle is discussed covering the set-up and automatic execution of the flight test experiments, the aircraft states, the aerodynamic forces and moments' reconstruction, the aerodynamic model structure selection, the parameter estimation and finally, the model validation. In particular, a motion capturing facility was used to record the flapper's position in time and from there compute the states and aerodynamic forces and moments that acted on it, assuming flapaveraged dynamics and linear aerodynamic model structures. It is shown that the approach leads to aerodynamic models that can predict the aerodynamic forces with high accuracy. Despite less accurate, the predictions of the aerodynamic moments still follow the general trend of the measured moments. Dynamic simulations based on the identified aerodynamic models show flight trajectories that closely match the ground truth spanning a number of flapping cycles. Finally, the dimensional aerodynamic forces and moments' coefficients of two of the identified aerodynamic models are presented.
This is an ideal book for graduate students and researchers interested in the aerodynamics, structural dynamics and flight dynamics of small birds, bats and insects, as well as of micro air vehicles (MAVs), which present some of the richest problems intersecting science and engineering. The agility and spectacular flight performance of natural flyers, thanks to their flexible, deformable wing structures, as well as to outstanding wing, tail and body coordination, is particularly significant. To design and build MAVs with performance comparable to natural flyers, it is essential that natural flyers' combined flexible structural dynamics and aerodynamics are adequately understood. The primary focus of this book is to address the recent developments in flapping wing aerodynamics. This book extends the work presented in Aerodynamics of Low Reynolds Number Flyers (Shyy et al. 2008).
Flapping-wing flight is a challenging system integration problem for designers due to tight coupling between propulsion and flexible wing subsystems with variable kinematics. High fidelity models that capture all the subsystem interactions are computationally expensive and too complex for design space exploration and optimization studies. A combination of simplified modeling and validation with experimental data offers a more tractable approach to system design and integration, which maintains acceptable accuracy. However, experimental data on flapping-wing aerial vehicles which are collected in a static laboratory test or a wind tunnel test are limited because of the rigid mounting of the vehicle, which alters the natural body response to flapping forces generated. In this study, a flapping-wing aerial vehicle is instrumented to provide in-flight data collection that is unhindered by rigid mounting strategies. The sensor suite includes measurements of attitude, heading, altitude, airspeed, position, wing angle, and voltage and current supplied to the drive motors. This in-flight data are used to setup a modified strip theory aerodynamic model with physically realistic flight conditions. A coupled model that predicts wing motions is then constructed by combining the aerodynamic model with a model of flexible wing twist dynamics and enforcing motor torque and speed bandwidth constraints. Finally, the results of experimental testing are compared to the coupled modeling framework to establish the effectiveness of the proposed approach for improving predictive accuracy by reducing errors in wing motion specification.
Flapping wing flight is a challenging system integration problem for designers due to tight coupling between propulsion and flexible wing subsystems with variable kinematics. Due to the fluid-structure interactions present in such a system, models must be tailored to a particular design instantiation to provide high accuracy and a clear picture of underlying physical phenomena. However, a practical design approach requires an extensible model that enables exploration of several design alternatives. The difficulty of generating models that are both highly accurate and extensible suggest a combined experimental and simplified modeling approach may offer a more tractable approach to system design and integration. However, experimental data on flapping wing air vehicles that is collected in a static laboratory test or a wind tunnel test is limited because of the rigid mounting of the vehicle, which alters the natural body response to flapping forces generated. Therefore, we undertake the design of a flapping wing air vehicle system that is instrumented to provide data that may be used to create and validate a simplified aerodynamics model that is capable of freely flying. The sensor suite includes measurements of attitude, heading, altitude, position, wing angle, as well as voltage and current supplied to the drive motors. With this approach, a complete energetic picture of flight is constructed, and by varying the parameters of the vehicle, the envelope of feasible performance is investigated. Finally, the results of the experimental testing are compared to a simplified aerodynamic model to establish the effectiveness of the proposed approach to system design.
Copyright © 2016 by ASME Country-Specific Mortality and Growth Failure in Infancy and Yound Children and Association With Material Stature
Use interactive graphics and maps to view and sort country-specific infant and early dhildhood mortality and growth failure data and their association with maternal
The purpose of this paper is to identify a longitudinal linear model of an ornithopter by automated flight tests. Flight tests were conducted outdoors, and an avionic board with sensors was installed on-board for measuring angular rates, Euler angles, and a total velocity. For accurate flight test, automated signal input is designed for elevator deflection: doublet and multi-step 3211 maneuver. During a cruise flight, the ornithopter normally had oscillation which is generated by flapping motion of the main wings. Fast Fourier transform (FFT) is used for analyzing flight data in a frequency domain, and a Butterworth filter is designed to filter the corrupted data by the flapping motion. The structure of the ornithopter linear model is assumed to be similar to a fixed-wing aircraft which has a periodic oscillation because it has similar control surfaces except the flapping motions. For system identification, unknown parameters are estimated by unconstrained nonlinear optimization.
Indoor flight testing of a bioinspired ornithopter is conducted in this study and the dominant flight state variables such as body pitch angle, forward flight speed, altitude, wings and tail motions of the freely flying ornithopter are simultaneously measured by using a three-dimensional visual tracking system. A control-oriented system model of the ornithopter in trimmed level flight is established based on the recorded inputs and outputs dataset and the system matrices are fitted in a least-squares sense. To reduce the amplitude of the ornithopter body oscillations, the identified linear time-invariant system model is formulated to a disturbance-rejection problem and an optimal controller minimizing the quadratic performance index is designed. The continuous wing motion defined as the known disturbance deteriorates the pitch balance with respect to the center of gravity; however, the designed feedforward and feedback controller periodically activates the ornithopter tail and successfully reduces the magnitudes of the body oscillations.
* Introduction * Elements of System Theory * Mathematical Model of an Aircraft * Outline of Estimation Theory * Regression Methods * Maximum Likelihood Methods * Frequency Domain Methods * Real-Time Parameter Estimation * Experiment Design * Data Compatibility * Data Analysis * MATLAB[registered] Software * Appendices * Index.
Wind vane motion constants (damping ratio, natural wavelength and decay
distance) are derived in a way which can accomodate both mechanical
friction and the presence of a propeller. The motion is shown to be
insufficiently described by a second order equation because of the way
in which the aerodynamic torque changes with angle of attack. This
implies that any measurements of vane constants made in the wind tunnel
at initial angles of attack above 20° are not representative for the
vane. Simple relations between easily measured vane dimensions and
motion constants are derived, and vane motion is proved to be
independent of the fin area.The WMO requirement for wind vanes is
translated into motion constants and shown to be fulfilled for any vane
with a damping ratio of 0.30. For turbulence measurements a certain
short-wavelength reliability limit for vane-measured spectra is
proposed. Experimental comparison of basic fin configurations shows the
inferiority of streamlined and splayed fins.General vane design rules
are given and are applied in the construction of an operational wind
vane with a damping ratio of 0.30 and of a fast propeller bivane with an
annular fin.
This valuable volume offers a systematic approach to flight vehicle system identification and covers exhaustively the time-domain methodology. It addresses in detail the theoretical and practical aspects of various parameter estimation methods, including those in the stochastic framework and focusing on nonlinear models, cost functions, optimization methods, and residual analysis. A pragmatic and balanced account of pros and cons in each case are provided. The book also presents data gathering and model validation and covers both large-scale systems and high-fidelity modeling.
Real world problems dealing with a variety of flight vehicle applications are addressed and solutions are provided. Examples encompass such problems as estimation of aerodynamics, stability, and control derivatives from flight data, flight path reconstruction, nonlinearities in control surface effectiveness, stall hysteresis, unstable aircraft, and other critical considerations.
Beginners, as well as practicing researchers, engineers, and working professionals who wish to refresh or broaden their knowledge of flight vehicle system identification, will find this book highly beneficial. Based on years of experience, the book also provides recommendations for overcoming problems likely to be faced in developing complex nonlinear and high-fidelity models and can help the novice negotiate the challenges of developing highly accurate mathematical models and aerodynamic databases from experimental flight data.
Software that runs under MATLAB® and sample flight data are provided to assist the reader in reworking the examples presented in the text. The software can also be adapted to the reader’s own interests.
Modeling and system identification of an ornithopter flight dynamics model
- J Grauer