Joong-Kwan Kim

Longitudinal Flight Dynamics of Bioinspired Ornithopter Considering Fluid-Structure Interaction

This paper addresses the flapping frequency-dependent trim flight characteristics of a bioinspired ornithopter. An integrative ornithopter flight simulator including a modal-based flexible multibody dynamics solver, a semiempirical reduced-order flapping-wing aerodynamic model, and their loosely coupled fluid―structure interaction are used to numerically simulate the ornithopter flight characteristics. The effect of the fluid―structure interaction of the main wing is quantitatively examined by comparing the wing deformations in both spanwise and chordwise directions, with and without aerodynamic loadings, and it shows that the fluid―structure interaction created a particular phase delay between the imposed wing motion and the aeroelastic response of the main wing and tail wing. The trimmed level flight conditions of the ornithopter model are found to satisfy the weak convergence criteria, which signifies that the longitudinal flight state variables of ornithopters need to be bounded and that the mean value of the variables are converged to the finite values. Unlike conventional fixed-wing aerial vehicles, the longitudinal flight state variables, such as forward flight speed, body pitch attitude, and tail-wing angle of attack in trimmed level flight, showed stable limit-cycle oscillatory behaviors with the flapping frequency as the dominant oscillating frequency. The mean body pitch attitude and tail-wing angle, and the root-mean-square value of the body pitch attitude, decreased as the flapping frequency increased. In addition, the mean forward flight speed is found to almost linearly increase with the flapping frequency.

Passive Longitudinal Stability in Ornithopter Flight

T HIS work investigates the effect of aeroelastic interaction between flexible ornithopter wings and the surrounding airflow on overall flight dynamics and stability. Typical ornithopter wings are composed of carbon rod stiffeners with a nylon fabric skin, providing anisotropic flexibility distribution to the wings. High speed camera images of ornithopter flights reveal that the wings undergo passive deformation both in chordand spanwise directions, and this aeroelastic phenomenon is known to heavily affect aerodynamic forces andmoments of the entirewing [1–6]. However, no studies have adequately addressed whether or not flexibility of wings is favorable to flight stability. Generally, for the analysis of flight dynamics and stability of ornithopters, a complex nonlinear flexible multibody configuration of an ornithopter is simplified to a linear rigid-body dynamics model with a quasisteady aerodynamic model. In particular, the passive deformation of a flexible-wing structure is oftentimes not considered or at best assumed to have a prescribed form to guarantee enough lift and thrust to propel the vehicle aloft [7–11]. Among these relevant studies, Dietl et al. [7] focused on the flight stability of an ornithopter using a single rigid-body model with prescribed sinusoidal twist angle distribution profile of the wings and concluded that the system had an unstable limit-cycle trim condition. This paper addresses the issue of the effect of passive deformation in local twist angles of flexible ornithopter wings and how it influences longitudinal flight stability. Two different ornithopter models were constructed based on the ornithopter flight simulation framework used in previous studies [12,13], which can account for flexiblemultibody dynamics andfluid-structure interaction ofwings. Both models were identical except for the wing structure; the reference model has rigid wings with prescribed sinusoidal local twist angle change as in [7], whereas the other hasflexiblewingswith aeroelastically varying local twist angles resulting from fluidstructure interaction. Longitudinal trimmed level flight and transient response to a pitch directional moment disturbance were compared between the two ornithopter models to ascertain the effect of aeroelasticity. II. Modeling and Simulation Methodology

Stroke Plane Control for Longitudinal Stabilization of Hovering Flapping Wing Air Vehicles

I N CONTRAST to the tailed flapping-wing micro air vehicles (MAVs), which possess inherent longitudinal static stability from the tail wing [1], unstable dynamic characteristics have been reported for the tailless flapping-wing MAVs [2–6]. Even though there exist flapping counterforces and torques [7,8] that provide each isolated degree of freedom (DOF) with stable damped dynamics, the coupled translational motion with pitching motion causes unstable longitudinal dynamics of the tailless flapping-wing MAVs [6,9,10]. Many studies have been conducted on the stabilization and control of flapping-wing MAVs [11–20]. Based on Doman et al. [11], Oppenheimer et al. [12] used the split-cycle constant-period frequency modulation with wing bias to control all the 6-DOF of an aircraft concept driven by two bimorph piezoelectric actuators. Bhatia et al. [20] used several sets of wing kinematic parameters for the stabilization of the vehicle in a gusty environment. Most previous studies have also controlled mathematically parameterized wing kinematics, which demand complex articulation mechanisms when they come to an actual hardware implementation [11–20]. Besides the controllability of the system, the control parameters of artificial flapping-wingMAVs need to consider actual implementation issues; a smaller number of control inputs is also intuitively preferable. This study presents the stabilization of all the six longitudinal flight state variables using two control parameters, which are the stroke plane angle and the wingbeat frequency. Within a limited range, the wingbeat frequency is one of the easily adjustable control parameters; virtually all the commercial toy flappers employ it as one of the control inputs. Instead of modulating the entire wing kinematics as proposed in [11–20], we propose to control the stroke plane angle for the stabilization of longitudinal flight dynamics. The effects of controlling the stroke plane angle and the wingbeat frequency to the flight dynamic stability are mainly characterized by establishing a flight simulator [21] of a hovering insect (i.e., the hawkmothManduca sexta). The flight trajectory of themodel vehicle is obtained by directly integrating the longitudinal nonlinear equations of rigid-body motion with time-varying wing inertia, which is coupled with a quasi-steady blade-element aerodynamic model. Linearization of the full nonlinear equations of the hovering flapping-wing MAV is conducted; the linear time-invariant system model is obtained by applying both small perturbation theory and cycle-averaging theory. The full-state feedback controller of the flapping-wing MAV is designed by minimizing a quadratic performance and is implemented on the longitudinal nonlinear equations of motion to confirm the effectiveness of the controller. Also, we found a very simple control strategy for a longitudinal stabilization: maintaining the stroke plane angle constant with respect to the global coordinates, based on an investigation in the designed optimal control inputs and consequent pitching dynamics of the flapping-wing MAV model. The effectiveness of this simple control strategy is verified using a high-fidelitymultibody simulation environment [1,6].

Periodic Tail Motion Linked to Wing Motion Affects the Longitudinal Stability of Ornithopter Flight

During slow level flight of a pigeon, a caudal muscle involved in tail movement, the levator caudae pars vertebralis, is activated at a particular phase with the pectoralis wing muscle. Inspired by mechanisms for the control of stability in flying animals, especially the role of the tail in avian flight, we investigated how periodic tail motion linked to motion of the wings affects the longitudinal stability of ornithopter flight. This was achieved by using an integrative ornithopter flight simulator that included aeroelastic behaviour of the flexible wings and tail. Trim flight trajectories of the simulated ornithopter model were calculated by time integration of the nonlinear equations of a flexible multi-body dynamics coupled with a semi-empirical flapping-wing and tail aerodynamic models. The unique trim flight characteristics of ornithopter, Limit-Cycle Oscillation, were found under the sets of wingbeat frequency and tail elevation angle, and the appropriate phase angle of tail motion was determined by parameter studies minimizing the amplitude of the oscillations. The numerical simulation results show that tail actuation synchronized with wing motion suppresses the oscillation of body pitch angle over a wide range of wingbeat frequencies.

Role of Trailing-Edge Vortices on the Hawkmothlike Flapping Wing

A time-course force measurement and time-resolved particle image velocimetry study were conducted to investigate the unsteady characteristics of an insect wing. In most cases, the tendencies of the aerodynamic forces in the stroke phase were extremely similar to the stroke velocity profiles, which indicated the appositeness of the steady aerodynamic model. The time-course forces showed that the wing–wake interaction appeared in temporally and spatially restricted sections right after the stroke reversal. The time-resolved particle image velocimetry taken near the stroke reversal demonstrated the vortex-dominated flowfields including the leading-edge vortex and the trailing-edge vortices. This was in contrast to the middle of the stroke, which only had a stable leading-edge vortex. The results showed that the unsteadiness was highly associated with the trailing-edge vortex structures. In particular, the wing–wake interaction were substantially influenced by the behavior of the number 2 trailing-edge vortex...

Hovering and forward flight of the hawkmoth Manduca sexta: trim search and 6-DOF dynamic stability characterization.

We show that the forward flight speed affects the stability characteristics of the longitudinal and lateral dynamics of a flying hawkmoth; dynamic modal structures of both the planes of motion are altered due to variations in the stability derivatives. The forward flight speed u e is changed from 0.00 to 1.00 m s(-1) with an increment of 0.25 m s(-1). (The equivalent advance ratio is 0.00 to 0.38; the advance ratio is the ratio of the forward flight speed to the average wing tip speed.) As the flight speed increases, for the longitudinal dynamics, an unstable oscillatory mode becomes more unstable. Also, we show that the up/down (w(b)) dynamics become more significant at a faster flight speed due to the prominent increase in the stability derivative Z(u) (up/down force due to the forward/backward velocity). For the lateral dynamics, the decrease in the stability derivative L(v) (roll moment due to side slip velocity) at a faster flight speed affects a slightly damped stable oscillatory mode, causing it to become more stable; however, the t(half) (the time taken to reach half the amplitude) of this slightly damped stable oscillatory mode remains relatively long (∼12T at u(e) = 1 m s(-1); T is wingbeat period) compared to the other modes of motion, meaning that this mode represents the most vulnerable dynamics among the lateral dynamics at all flight speeds. To obtain the stability derivatives, trim conditions for linearization are numerically searched to find the exact trim trajectory and wing kinematics using an algorithm that uses the gradient information of a control effectiveness matrix and fully coupled six-degrees of freedom nonlinear multibody equations of motion. With this algorithm, trim conditions that consider the coupling between the dynamics and aerodynamics can be obtained. The body and wing morphology, and the wing kinematics used in this study are based on actual measurement data from the relevant literature. The aerodynamic model of the flapping wings of a hawkmoth is based on the blade element theory, and the necessary aerodynamic coefficients, including the lift, drag and wing pitching moment, are experimentally obtained from the results of previous work by the authors.

Limit-Cycle Oscillation Suppression of Ornithopter Longitudinal Flight Dynamics

This paper investigates an effective control strategy for reducing the pitch limit-cycle oscillation (LCO) of an ornithopter in trimmed level flight condition. Using a nonlinear flight model of the ornithopter including structural dynamics, aerodynamics, and their mutual interaction, a numerical flight test with a continuous main wing motion and a step input of the tail wing is performed to acquire the input/output datasets for ornithopter system identification. The Prediction-Error Method is successfully applied to obtain the closed-form system equations, and a Linear-Quadratic-Gaussian regulator is designed for optimal output feedback control. The designed LQG regulator is implemented in the nonlinear flight model to evaluate the pitch LCO suppression, and the effect of the modeling fidelity of the PEM models is also discussed. The resulting optimal tail control input for LCO suppression is found to be synchronized to the main wing motion. In addition, a preshaped simple harmonic tail motion is also examined to simply realize the LCO suppression of the ornithopter.

Extended Unsteady Vortex-Lattice Method for Insect Flapping Wings

An extended unsteady vortex-lattice method is developed to study the aerodynamics of insect flapping wings while hovering and during forward flight. Leading-edge suction analogy and vortex-core growth models are used as an extension, which is incorporated into a conventional unsteady vortex-lattice method in an effort to overcome the challenges that arise when simulating insect aerodynamics such as wing–wake interaction and leading-edge effects. A convergence analysis was carried out to derive an optimal aerodynamic mesh and a time-step size for flapping-wing models. A parallel computing technique was used to reduce computational time. The aerodynamics of hawkmoth (Manduca sexta) wing models was simulated, and the results were validated against previous numerical and experimental data.

Experimental Study on the Unsteady Aerodynamics of a Robotic Hawkmoth Manduca sexta model

Time-course force measurement and time-resolved PIV studies were conducted in order to investigate unsteady aerodynamic characteristics. A dynamically scaled-up robotic wing model was operated underwater within the Reynolds number range of 7.4×10 – similar to a hovering hawkmoth. In the stroke section, the tendencies of each CL were substantially obeyed to the translational velocity profiles. This indicated the appositeness of the quasisteady estimation in the stroke phase. Also, the CL traces in the rotational phase showed that the wing-wake interaction was a localized phenomenon that appeared in a temporally and spatially narrow section right after the stroke reversal. It was found that the wing-wake interaction was impacted by the rotational profiles, i.e. the level of the rotational velocity rather than the change of the translational profiles. The PIV results demonstrated that the vortical structures near the stroke reversal, which were clearly described the LEV of the previous stroke, the TEVs due to the wing rotation, and the LEV of the next stroke. Timeline vorticity distributions showed that the TEV1 was generated by the impulsive start of the wing rotation. Such structures pointed out that the characteristics of the wing-wake interaction were not associated with the LEV of the next stroke, but substantially related with the TEV2.

The effect of the abdomen deformation on the longitudinal stability of flying insects

In this paper, we derive longitudinal nonlinear equations of motion of a hovering insect with deformable abdomen to investigate the effect of the abdominal motion to the longitudinal dynamics. The blade-element theory, which is based on experimentally obtained aerodynamic coefficients, is used for the periodic force and moment excitation to the system. Here, we focus on the role of the deformable abdomen to investigate whether or not the flexible body is a decisive factor to the longitudinal flight dynamic stability. Three cases: 1) rigid connection between the thorax and abdomen, 2) flexible connection, and 3) active connection with a feedback control, are compared to check the role of the abdomen deformation on the longitudinal flight dynamic stability, by examining eigenvalues of the linearized system model of each case. The results show that an active control of the abdominal angle can stabilize the longitudinal flight dynamics of the insect modeled in this study.