Experimental Characterization of the Structural Dynamics and Aero-Structural Sensitivity of a Hawkmoth Wing Toward the Development of Design Rules for Flapping Wing Micro Air Vehicles

A case is made for why the structures discipline must take on a more central role in the research and design of flapping-wing micro-air-vehicles, especially if research trends continue toward bio-inspired, insect-sized flexible wing designs. In making the case, the eigenstructure of the wing emerges as a key structural metric for consideration. But with virtually no structural dynamic data available for actual insect wings, both engineered and computational wing models that have been inspired by biological analogs have no structural truth models to which they can be anchored. An experimental framework is therefore developed herein for performing system identification testing on the wings of insects. This framework is then utilized to characterize the structural dynamics of the forewing of a large sample of hawkmoth (Manduca Sexta) for future design and research consideration. The research also weighs-in on a decade-long debate as to the relative contributions that the inertial and fluid dynamic forces acting on a flapping insect wing have on its deformation (expression) during flight. Ultimately the findings proves that both affect wing expression significantly, casting serious doubt on the longstanding and most frequently cited research that indicates fluid dynamic forces have minimal or negligible effect

Closed-Loop Control of Constrained Flapping Wing Micro Air Vehicles

Micro air vehicles are vehicles with a maximum dimension of 15 cm or less, so they are ideal in confined spaces such as indoors, urban canyons, and caves. Considerable research has been invested in the areas of unsteady and low Reynolds number aerodynamics, as well as techniques to fabricate small scale prototypes. Control of these vehicles has been less studied, and most control techniques proposed have only been implemented within simulations without concern for power requirements, sensors and observers, or actual hardware demonstrations. In this work, power requirements while using a piezo-driven, resonant flapping wing control scheme, Bi-harmonic Amplitude and Bias Modulation, were studied. In addition, the power efficiency versus flapping frequency was studied and shown to be maximized while flapping at the piezo-driven system\u27s resonance. Then prototype hardware of varying designs was used to capture the impact of a specific component of the flapping wing micro air vehicle, the passive rotation joint. Finally, closed-loop control of different constrained configurations was demonstrated using the resonant flapping Bi-harmonic Amplitude and Bias Modulation scheme with the optimized hardware. This work is important in the development and understanding of eventual free-flight capable flapping wing micro air vehicle

Design and Control of Flapping Wing Micro Air Vehicles

Flapping wing Micro Air Vehicles (MAVs) continues to be a growing field, with ongoing research into unsteady, low Re aerodynamics, micro-fabrication, and fluid-structure interaction. However, research into flapping wing control of such MAVs continues to lag. Existing research uniformly consists of proposed control laws that are validated by computer simulations of quasi-steady blade-element formulae. Such simulations use numerous assumptions and cannot be trusted to fully describe the flow physics. Instead, such control laws must be validated on hardware. Here, a novel control technique is proposed called Bi-harmonic Amplitude and Bias Modulation (BABM) which can generate forces and moments in 5 vehicle degrees of freedom with only two actuators. Several MAV prototypes were designed and manufactured with independently controllable wings capable of prescribing arbitrary wing trajectories. The forces and moments generated by a MAV utilizing the BABM control technique were measured on a 6-component balance. These experiments verified that a prototype can generate uncoupled forces and moments for motion in five degrees of freedom when using the BABM control technique, and that these forces can be approximated by quasi-steady blade-element formulae. Finally, the prototype performed preliminary controlled flight in constrained motion experiments, further demonstrating the feasibility of BABM

DESIGN AND CONTROL OF A HUMMINGBIRD-SIZE FLAPPING WING MICRO AERIAL VEHICLE

Flying animals with flapping wings may best exemplify the astonishing ability of natural selection on design optimization. They evince extraordinary prowess to control their flight, while demonstrating rich repertoire of agile maneuvers. They remain surprisingly stable during hover and can make sharp turns in a split second. Characterized by high-frequency flapping wing motion, unsteady aerodynamics, and the ability to hover and perform fast maneuvers, insect-like flapping flight presents an extraordinary aerial locomotion strategy perfected at small size scales. Flapping Wing Micro Aerial Vehicles (FWMAVs) hold great promise in bridging the performance gap between engineered flying vehicles and their natural counterparts. They are perfect candidates for potential applications such as fast response robots in search and rescue, environmental friendly agents in precision agriculture, surveillance and intelligence gathering MAVs, and miniature nodes in sensor networks

Roll, Pitch and Yaw Torque Control for a Robotic Bee

In the last decade, the robotics community has pushed to develop increasingly small, autonomous flapping-wing robotic vehicles for a variety of civilian and military applications. The miniaturization of these vehicles has pushed the boundaries of technology in many areas, including electronics, artificial intelligence, and mechanics; as well as our understanding of biology. In particular, at the insect scale, fabrication, actuation, and flight control of a flapping-wing robot become especially challenging. This thesis addresses these challenges in the context of the “RoboBee” project, which has the goal of creating an autonomous swarm of at-scale robotic bees. A 100mg robot with a 3cm wingspan capable of generating roll, pitch and yaw torques in the range of $\pm 1\mu Nm$ by using a large, central power actuator to flap the wings and smaller control actuators to steer is presented. A dynamic model is used to predict torque generation capabilities, and custom instrumentation is developed to measure and characterize the vehicle’s control torques. Finally, controlled flight experiments are presented, and the vehicle is capable of maintaining a stable pitch and roll attitude during ascending vertical flight. This is the first successful controlled flight of a truly insect-scale flapping-wing robot.Engineering and Applied Science

Flapping Wing Micro Air Vehicles: An Analysis of the Importance of the Mass of the Wings to Flight Dynamics, Stability, and Control.

The flight dynamics, stability, and control of a model flapping wing micro air vehicle are analyzed with a focus on the inertial and mass effects of the wings on the position and orientation of the body. A multi-body, flight dynamics model is derived from first principles. The multi-body model predicts significant differences in the position and orientation of the flapping wing micro air vehicle, when compared to a flight dynamics model based on the standard aircraft, or six degree of freedom, equations of motion. The strongly coupled, multi-body equations of motion are transformed into first order form using an approximate inverse and appropriate assumptions. Local (na ̈ıve) averaging of the first order system does not produce an accurate result and a new approximation technique named ‘quarter-cycle’ averaging is proposed. The technique is effective in reducing the error by at least an order of magnitude for three reference flight conditions. A stability analysis of the local averaged equations of motions, in the vicinity of a hover condition, produces a modal structure consist with the most common vertical takeoff or landing structure and independent stability analyses of the linearized flight dynamics of insect models. The inclusion of the wing xv effects produces a non-negligible change in the linear stability of a hawkmoth-sized model. The hovering solution is shown, under proper control, to produce a limit cycle. The control input to achieve a limit cycle is different if the flight dynamics model includes the wing effects or does not include the wing effects. Improper control input application will not produce the desired limit cycle effects. A scaling analysis is used to analyze the relative importance of the mass of the wings, based on the quarter-cycle approximation. The conclusion of the scaling analysis is that the linear momentum effects of the wings are always important in terms of the inertial position of the flapping wing micro air vehicle. Above a flapping frequency of approximately 30-40 Hz, the mass and inertial effects of the wings on the orientation of the body can be neglected.Ph.D.Aerospace EngineeringUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/86350/1/cptorlo_1.pd

An Analytical Investigation of Flapping Wing Structures for Micro Air Vehicles

An analytical model of flapping wing structures for bio-inspired micro air vehicles is presented in this dissertation. Bio-inspired micro air vehicles (MAVs) are based on insects and hummingbirds. These animals have lightweight, flexible wings that undergo large deformations while flapping. Engineering studies have confirmed that deformations can increase the lift of flapping wings. Wing flexibility has been studied through experimental construction-and-evaluation methods and through computational numerical models. Between experimental and numerical methods there is a need for a simple method to model and evaluate the structural dynamics of flexible flapping wings. This dissertation's analytical model addresses this need. A time-periodic assumed-modes beam analysis of a flapping, flexible wing undergoing linear deformations is developed from a beam analysis of a helicopter blade. The resultant structural model includes bending and torsion degrees of freedom. The model is non-dimensionalized. The ratio of the system's structural natural frequency to wingbeat frequency characterizes its constant stiffness, and the amplitude of flapping motion characterizes its time-periodic stiffness. Current flapping mechanisms and MAVs are compared to biological fliers on the basis of the characteristic parameters. The beam analysis is extended to develop an plate model of a flapping wing. The time-periodic stability of the flapping wing model is assessed with Floquet analysis. A flapping-wing stability diagram is developed as a function of the characteristic parameters. The analysis indicates that time-periodic instabilities are more likely for large-amplitude, high-frequency flapping motion. Instabilities associated with the first bending mode dominate the stability diagram. Due to current limitations of flapping mechanisms, instabilities are not likely in current experiments but become more likely at the operating conditions of biological fliers. The effect of structural design parameters, including wing planform and material stiffness, are assessed with an assumed-modes aeroelastic model. Wing planforms are developed from an empirical model of biological planforms. Non-linearities are described in the effect of membrane thickness on lift generation. Structural couplings due to time-periodic stiffness are identified that can decrease lift generation at certain wingbeat frequencies

Low Speed Flap-bounding in Ornithopters and its Inspiration on the Energy Efficient Flight of Quadrotors

Flap-bounding, a form of intermittent flight, is often exhibited by small birds over their entire range of flight speeds. The purpose of flap-bounding is unclear during low to medium speed (2 - 8 m/s) flight from a mechanical-power perspective: aerodynamic models suggest continuous flapping would require less power output and lower cost of transport. This thesis works towards the understanding of the advantages of flap-bounding and tries to employ the underlining principle to design quadrotor maneuver to improve power efficiency. To explore the functional significance of flap-bounding at low speeds, I measured body trajectory and kinematics of wings and tail of zebra finch (Taeniopygia guttata, N=2) during flights in a laboratory between two perches. The flights consist of three phases: initial, descending and ascending. Zebra finch first accelerated using continuous flapping, then descended, featuring intermittent bounds. The flight was completed by ascending using nearly-continuous flapping. When exiting bounds in descending phase, they achieved higher than pre-bound forward velocity by swinging body forward similar to pendulum motion with conserved mechanical energy. Takeoffs of black-capped chickadees (Poecile atricapillus, N=3) in the wild was recorded and I found similar kinematics. Our modeling of power output indicates finch achieves higher velocity (13%) with lower cost of transport (9%) when descending, compared with continuous flapping in previously-studied pigeons. To apply the findings to the design of quadrotor motion, a mimicking maneuver was developed that consisted of five phases: projectile drop, drop transition, pendulum swing, rise transition and projectile rise. The quadrotor outputs small amount (4 N) of thrust during projectile drop phase and ramps up the thrust while increasing body pitch angle during the drop transition phase until the thrust enables the quadrotor to advance in pendulum-like motion in the pendulum swing phase. As the quadrotor reaches the symmetric point with respect to the vertical axis of the pendulum motion, it engages in reducing the thrust and pitch angle during the rise transition phase until the thrust is lowered to the same level as the beginning of the maneuver and the body angle of attack minimized (0.2 deg) in the projectile rise phase. The trajectory of the maneuver was optimized to yield minimum cost of transport. The quadrotor moves forward by tracking the cycle of the optimized trajectory repeatedly. Due to the aggressive nature of the maneuver, we developed new algorithms using onboard sensors to determine the estimated position and attitude. By employing nonlinear controller, we showed that cost of transport of the flap-bounding inspired maneuver is lower (28%) than conventional constant forward flight, which makes it the preferable strategy in high speed flight (≥15 m/s)

Neuroinspired control strategies with applications to flapping flight

This dissertation is centered on a theoretical, simulation, and experimental study of control strategies which are inspired by biological systems. Biological systems, along with sufficiently complicated engineered systems, often have many interacting degrees of freedom and need to excite large-displacement oscillations in order to locomote. Combining these factors can make high-level control design difficult. This thesis revolves around three different levels of abstraction, providing tools for analysis and design. First, we consider central pattern generators (CPGs) to control flapping-flight dynamics. The key idea here is dimensional reduction - we want to convert complicated interactions of many degrees of freedom into a handful of parameters which have intuitive connections to the overall system behavior, leaving the control designer unconcerned with the details of particular motions. A rigorous mathematical and control theoretic framework to design complex three-dimensional wing motions is presented based on phase synchronization of nonlinear oscillators. In particular, we show that flapping-flying dynamics without a tail or traditional aerodynamic control surfaces can be effectively controlled by a reduced set of central pattern generator parameters that generate phase-synchronized or symmetry-breaking oscillatory motions of two main wings. Furthermore, by using a Hopf bifurcation, we show that tailless aircraft (inspired by bats) alternating between flapping and gliding can be effectively stabilized by smooth wing motions driven by the central pattern generator network. Results of numerical simulation with a full six-degree-of-freedom flight dynamic model validate the effectiveness of the proposed neurobiologically inspired control approach. Further, we present experimental micro aerial vehicle (MAV) research with low-frequency flapping and articulated wing gliding. The importance of phase difference control via an abstract mathematical model of central pattern generators is confirmed with a robotic bat on a 3-DOF pendulum platform. An aerodynamic model for the robotic bat based on the complex wing kinematics is presented. Closed loop experiments show that control dimension reduction is achievable - unstable longitudinal modes are stabilized and controlled using only two control parameters. A transition of flight modes, from flapping to gliding and vice-versa, is demonstrated within the CPG control scheme. The second major thrust is inspired by this idea that mode switching is useful. Many bats and birds adopt a mixed strategy of flapping and gliding to provide agility when necessary and to increase overall efficiency. This work explores dwell time constraints on switched systems with multiple, possibly disparate invariant limit sets. We show that, under suitable conditions, trajectories globally converge to a superset of the limit sets and then remain in a second, larger superset. We show the effectiveness of the dwell-time conditions by using examples of nonlinear switching limit cycles from our work on flapping flight. This level of abstraction has been found to be useful in many ways, but it also produces its own challenges. For example, we discuss death of oscillation which can occur for many limit-cycle controllers and the difficulty in incorporating fast, high-displacement reflex feedback. This leads us to our third major thrust - considering biologically realistic neuron circuits instead of a limit cycle abstraction. Biological neuron circuits are incredibly diverse in practice, giving us a convincing rationale that they can aid us in our quest for flexibility. Nevertheless, that flexibility provides its own challenges. It is not currently known how most biological neuron circuits work, and little work exists that connects the principles of a neuron circuit to the principles of control theory. We begin the process of trying to bridge this gap by considering the simplest of classical controllers, PD control. We propose a simple two-neuron, two-synapse circuit based on the concept that synapses provide attenuation and a delay. We present a simulation-based method of analysis, including a smoothing algorithm, a steady-state response curve, and a system identification procedure for capturing differentiation. There will never be One True Control Method that will solve all problems. Nature's solution to a diversity of systems and situations is equally diverse. This will inspire many strategies and require a multitude of analysis tools. This thesis is my contribution of a few

ANALYTICAL MODELING AND EXPERIMENTAL EVALUATION OF A PASSIVELY MORPHING ORNITHOPTER WING

Ornithopters or flapping wing Unmanned Aerial Vehicles (UAVs) have potential applications in both civil and military sectors. Amongst all categories of UAVs, ornithopters have a unique ability to fly in low Reynolds number flight regimes and have the agility and maneuverability of rotary wing aircraft. In nature, birds achieve such performance by exploiting various wing kinematics known as gaits. The objective of this work was to improve the steady level flight wing performance of an ornithopter by implementing the Continuous Vortex Gait (CVG) using a novel passive compliant spine. The CVG is a set of bio-inspired kinematics that natural flyers use to produce lift and thrust during steady level flight. A significant contribution of this work was the recognition that the CVG is an avian gait that could be achieved using a passive morphing mechanism. In contrast to rigid-link mechanisms and active approaches, reported by other researchers in the open literature, passive morphing mechanisms require no additional energy expenditure, while introducing minimal weight addition and complexity. During the execution of the CVG, the avian wing wrist is the primary joint responsible for the wing shape changes. Thus a compliant mechanism, called a compliant spine, was fabricated, and integrated in the ornithopter's wing leading edge spar where an avian wrist would normally exist, namely at 37% of the wing half span. Each compliant spine was designed to be flexible in bending during the wing upstroke and stiff in bending during the wing downstroke. Inserting a variable stiffness compliant mechanism in the leading edge (LE) spar of the ornithopter could affect its structural stability. An analytical model was developed to determine the structural stability of the ornithopter LE spar. The model was validated using experimental measurements. The LE spar equations of motion were then reformulated into Mathieu's equation and the LE spar was proven to be structurally stable with a compliant spine design insert. A research ornithopter platform was tested in air and in vacuum as well as in free and constrained flight with various compliant spine designs inserted in its wings. Results from the constrained flight tests indicated that the ornithopter with a compliant spine inserted in its wings consumed 45% less electrical power and produced 16% of its weight in additional lift, without incurring any thrust penalties. Results from, the vacuum constrained tests attributed these benefits to aerodynamic effects rather than inertial effects. Free flight tests were performed at Wright Patterson Air Force Base, which houses the largest indoor flight laboratory in the country. The wing kinematics along with the vehicle dynamics were captured during this testing using Vicon® motion tracking cameras. These flight tests proved to be successful in producing consistent and repeatable flight data over more than eight free flight flapping cycles of free flight and validated a new and novel testing technique. The ornithopter body dynamics were shown to be significant, i.e. ±4gs. Inserting the compliant spine into the leading edge spar of the ornithopter during free flight reduced the baseline configuration body vertical center of mass positive acceleration by 69%, which translates into overall lift gains. It also increased the horizontal propulsive force by 300%, which translates into thrust gains. &#8195