Averaging of the Nonlinear Dynamics of Flapping Wing Micro Air Vehicles for Symmetrical Flapping

Orlowski, Christopher T.; Girard, Anouck

doi:10.2514/6.2011-1228

Cited by 8 publications

(10 citation statements)

References 13 publications

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“…Taha et al (2012) noted in their review paper that the averaging of the dynamic forcing from the flapping wings may omit important aspects, such as the possible energy transfer from the highfrequency modes to the low-frequency modes of the body motions. Further, Orlowski and Girard (2011b) showed that the wingbeat-cycle-averaging of the flapping wing aerodynamics resulted in a flight trajectory different from the numerical solution of the full equations. For the numerical flight simulations in this study, we performed a direct time integration of the fully coupled 6-DOF nonlinear multibody dynamics equations of motion.…”

Section: Introductionmentioning

confidence: 99%

A multibody approach for 6-DOF flight dynamics and stability analysis of the hawkmothManduca sexta

Kim¹,

Han²

2014

Bioinspir. Biomim.

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This paper investigates the six degrees of freedom (6-DOF) flight dynamics and stability of the hawkmoth Manduca sexta using a multibody dynamics approach that encompasses the effects of the time varying inertia tensor of all the body segments including two wings. The quasi-steady translational and unsteady rotational aerodynamics of the flapping wings are modeled with the blade element theory with aerodynamic coefficients derived from relevant experimental studies. The aerodynamics is given instantaneously at each integration time step without wingbeat-cycle-averaging. With the multibody dynamic model and the aerodynamic model for the hawkmoth, a direct time integration of the fully coupled 6-DOF nonlinear multibody dynamics equations of motion is performed. First, the passive damping magnitude of each single DOF is quantitatively examined with the measure of the time taken to half the initial velocity (thalf). The results show that the sideslip translation is less damped approximately three times than the other two translational DOFs, and the pitch rotation is less damped approximately five times than the other two rotational DOFs; each DOF has the value of (unit in wingbeat strokes): thalf,forward/backward = 7.10, thalf,sideslip = 17.95, thalf,ascending = 7.13, thalf,descending = 5.77, thalf,roll = 0.68, thalf,pitch = 2.39, and thalf,yaw = 0.25. Second, the natural modes of motion, with the hovering flight as a reference equilibrium condition, are examined by analyzing fully coupled 6-DOF dynamic responses induced by multiple sets of force and moment disturbance combinations. The given disturbance combinations are set to excite the dynamic modes identified in relevant eigenmode analysis studies. The 6-DOF dynamic responses obtained from this study are compared with eigenmode analysis results in the relevant studies. The longitudinal modes of motion showed dynamic modal characteristics similar to the eigenmode analysis results from the relevant literature. However, the lateral modes of motion revealed more complex behavior, which is mainly due to the coupling effect in the lateral flight states and also between the lateral and longitudinal planes of motion. The main sources of the flight instability of the hovering hawkmoth are examined as either the longitudinal instability grown from the coupled forward/backward velocity and the pitch rate, or the lateral instability grown from the coupled sideslip velocity and the roll rate.

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Section: Introductionmentioning

confidence: 99%

A multibody approach for 6-DOF flight dynamics and stability analysis of the hawkmothManduca sexta

Kim¹,

Han²

2014

Bioinspir. Biomim.

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“…This approach has been used by Dietl and Garcia (2008) Averaging theory, on the other hand, predicts the behavior of the original time varying system 'on an average'. Averaging technique is the more popular choice for analyzing the system as opted by Oppenheimer et al (2011), Deng et al (2006a, Khan and Agrawal (2007), Orlowski and Girard (2011a), Karásek and Preumont (2012). Averaging for flapping wing MAVs have been dealt with rigorously in Deng et al (2006a).…”

Section: Literature Reviewmentioning

confidence: 99%

“…In this thesis we have discussed averaging method, as applied to the MAV system. Since the idea of averaging is to get a time invariant model for control purposes, it is unsure how quarter cycle averaging proposed in Orlowski and Girard (2011a) is useful for purpose of control.…”

Section: Introductionmentioning

confidence: 99%

Modeling and control of flapping wing micro aerial vehicles

2019

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Research in robots that emulate insect flight or micro aerial vehicles (MAV) has gained significant momentum in the past decade owing to the vast number of fields they could be employed in. In this paper, key modeling and control aspects of a flapping wing MAV in hover have been discussed. Models of varying complexity have been developed by previous researchers. Here, we examine the validity of key assumptions involved in some of these models in a closed-loop control setting. Every model has limitations and with proper design of feedback control these limitations can be overcome up to a certain degree. Three nonlinear models with increasing complexity have been developed. Model I includes only the rigid body dynamics while ignoring the wing dynamics while model II includes the rigid body dynamics along with the wing kinematics. Lastly, model III encompasses the complete rigid body and the rigid wing dynamics. To ensure these higher fidelity models can be rendered unnecessary with a suitably designed controller, a method is presented wherein the controller is designed for the simplest model and tested for its robustness on the more complex models. Linear quadratic regulator (LQR) is used as the main control system design methodology. A nonlinear parameter optimization algorithm is employed to design a family of LQR control systems for the MAV. Additionally, critical performance trade-offs are illuminated, and properties at both the plant output and input are examined. Lastly, we also provide specific rules of thumb for the control system design.

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“…While flapping-wing dynamics are highly complex, warranting investigation into multi-body modelling, 37,11,38,39 several studies have demonstrated that for basic considerations, e.g. in the context of design and control work, the conventional fixed-wing aircraft equations of motion represent a suitable description for many insects and FWMAVs.…”

Section: Iiia Local Model Estimationmentioning

confidence: 99%

“…Particularly low-order models of flapping-wing dynamics and aerodynamics typically have a limited applicability range and/or have not been validated in different conditions with free-flight data. 7,8,9,10,11,12,13,14 However, it is essential to know how a system behaves in all its operating conditions, in order to ensure an effective operation and maximise its performance. Furthermore, accurate global models are highly valuable and often indispensable to provide more realistic and comprehensive simulation possibilities, support the development and testing of new controllers and allow for the application of more advanced control approaches.…”

Section: Introductionmentioning

confidence: 99%

Global LPV model identification of flapping-wing dynamics using flight data

Armanini

Karásek

Visser

2018

2018 AIAA Modeling and Simulation Technologies Conference

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Biologically-inspired flapping-wing micro aerial vehicles are characterised by nonlinear, unsteady aerodynamics and complex dynamics, both highly challenging to model. To take full advantage of the flight capabilities of such vehicles, it is necessary to obtain insight into their dynamics in the different flyable conditions, and to provide adequate control in all of these conditions. Nonetheless, the dynamics are typically only considered in a single flight regime, and controllers are frequently tuned for a particular flight condition. Due the high complexity of flapping flight and limited availability of accurate free-flight data, global models are not yet readily available, particularly models based on free-flight data and suitable for practical applications. This paper demonstrates an approach to obtain a global dynamic model for a flapping-wing micro aerial vehicle. To allow for standard linear control and systems theory to be applied, the nonlinear dynamics are approximated using a linear parameter-varying (LPV) approach based on a set of local linear models. The scheduling parameters, and the parameters in the underlying local models, are determined using system identification methods applied to free-flight data collected on a real test platform, and covering a significant part of the flight envelope. The proposed approach allows for modelling of the vehicle and prediction of the dominant dynamic properties across the considered part of the flight envelope, using a total of 16 parameters, as opposed to the starting point of 46 local models with 12 parameters each. The use of a single model adapting to the flight condition provides flexibility and continuous coverage, and is therefore highly useful for simulation and control applications. While in the explored part of the flight envelope the nonlinearity was found to be limited, such that a weighted average model may be sufficient for some applications, the LPV model provides a higher accuracy and more consistent performance across the conditions considered. Additionally, the approach is shown to be promising and is expected to be adaptable to cover more significant variation. Improvements could be obtained through more extensive flight envelope coverage, more accurate measurement and more informative identification data.

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Averaging of the Nonlinear Dynamics of Flapping Wing Micro Air Vehicles for Symmetrical Flapping

Cited by 8 publications

References 13 publications

A multibody approach for 6-DOF flight dynamics and stability analysis of the hawkmothManduca sexta

A multibody approach for 6-DOF flight dynamics and stability analysis of the hawkmothManduca sexta

Modeling and control of flapping wing micro aerial vehicles

Global LPV model identification of flapping-wing dynamics using flight data

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