Flapping flight shows promise for micro air vehicle design because flapping wings provide superior aerodynamic performance than that of fixed wings and rotors at low Reynolds numbers. In these flight regimes, unsteady effects become increasingly important. This thesis explores some of the unsteady effects that provide additional lift to flapping wings through an experiment-based optimization of the kinematics of a flapping wing mechanism in a water tunnel. The mechanism wings and flow environment were scaled to simulate the flight of the hawkmoth (Manduca sexta) at hovering or near-hovering speeds. The optimization was repeated using rigid and flexible wings to evaluate the impact that wing flexibility has on aerodynamic performance of flapping wings. The trajectories that produced the highest lift were compared using particle image velocimetry to characterize the flow features produced during the periods of peak lift. A leading edge vortex was observed with all of the flapping trajectories and both wing types, the strength of which corresponded to the measured amount of lift of the wing. This research furthers our understanding of the lift-generating mechanisms used in nature and can be applied to improve the design of micro air vehicles.

The unsteady aerodynamic and aeroelastic analysis of flapping flight under various kinematics and flow parameters is presented in this dissertation. The main motivation for this study arises from the challenges facing the development of micro air vehicles. Micro air vehicles by requirement are compact with dimensions less than 15-20 cm and flight speeds of around 10-15 m/s. These vehicles operate in low Reynolds number range of 10,000 to 100,000. At these low Reynolds numbers, the aerodynamic efficiency of conventional fixed airfoils significantly deteriorates. On the other hand, flapping flight employed by birds and insects whose flight regime coincides with that of micro air vehicles offers a viable alternate solution. For the analysis of flapping flight, a boundary fitted moving grid algorithm is implemented in a flow solver, GenIDLEST. The dynamic movement of the grid is achieved using a combination of spring analogy and trans-finite interpolation on displacements. The additional conservation equation of space required for moving grid is satisfied. The solver is validated with well known flow problems such as forced oscillation of a cylinder, a heaving airfoil, a moving indentation channel, and a hovering fruitfly. The performance of flapping flight is analyzed using Large Eddy Simulation (LES) for a wide range of Reynolds numbers and under various kinematic parameters. A spiral Leading Edge Vortex (LEV) forms during the downstroke due to the high angle of attack, which results in high force production. A strong spanwise flow of the order of the flapping velocity is observed along the core of the LEV. In addition, the formation of a negative spanwise flow is observed due to the tip vortex, which slows down the removal of vorticity from the LEV. This leads to the instability of the LEV at around mid-downstroke. Analysis with different rotation kinematics shows that a continuous rotation results in better propulsive efficiency as it generates thrust during the entire flapping cycle. Analysis with different angles of attack shows that a moderate angle of attack which results in complete shedding of the LEV offers high propulsive efficiency. The analysis of flapping flight at Reynolds numbers ranging from 100 to 100,000 shows that higher lift and thrust values are obtained for Re?100. The critical reasons are that at higher Reynolds numbers, the LEV is closer to the surface and as it sheds and convects it covers most of the upper surface. However, the Reynolds number has no or little effect on the lift and thrust as identical values are obtained for Re=10,000 and 100,000. The analysis with different tip shapes shows that tip shapes do not have a significant effect on the performance. Introduction of stroke deviation to kinematics leads to drop in average lift as wing interacts with the LEV shed during the downstroke. A linear elastic membrane model with applied aerodynamic load is developed for aeroelastic analysis. Analysis with different wing stiffnesses shows that the membrane wing outperforms the rigid wing in terms of lift, thrust and propulsive efficiency. The main reason for the increase in force production is attributed to the gliding of the LEV along the camber, which results in a high pressure difference across the surface. In addition, a high stiffness along the spanwise direction and low stiffness along the chordwise direction results in a uniform camber and high lift and thrust production. / Ph. D.

This thesis focuses on the design and development of a fixed wing micro air vehicle (MAV) and on the development of randomized sampling based motion planning and control algorithms for path planning and stabilization of the MAV. In addition, the thesis also contains probabilis-tic analyses of the algorithmic properties of randomized sampling based algorithms, such as completeness and asymptotic optimality. The thesis begins with a detailed discussion on aerodynamic design, computational fluid dy-namic simulations of propeller wake, wind tunnel tests of a 150mm fixed wing micro air ve-hicle. The vehicle is designed in such a way that in spite of the various adverse effects of low Reynolds number aerodynamics and the complex propeller wake interactions with the airframe, the vehicle shows a balance of external forces and moments at most of the operating conditions. This is supported by various CFD analysis and wind tunnel tests and is shown in this thesis. The thesis also contains a reasonably accurate longitudinal and lateral dynamical model of the MAV, which are verified by numerous flight trials. However, there still exists a considerable amount of model uncertainties in the system descrip-tion of the MAV. A robust feedback stabilized close loop flight control law, is designed to attenuate the effects of modelling uncertainties, discrete vertical and head-on wind gusts, and to maintain flight stability and performance requirements at all allowable operating conditions. The controller is implemented in the MAV autopilot hardware with successful close loop flight trials. The flight controller is designed based on the probabilistic robust control approach. The approach is based on statistical average case analysis and synthesis techniques. It removes the conservatism present in the classical robust feedback design (which is based the worst case de-sign techniques) and associated sluggish system response characteristics. Instead of minimizing the effect of the worst case disturbance, a randomized techniques synthesizes a controller for which some performance index is minimized in an empirical average sense. In this thesis it is shown that the degree of conservatism in the design and the number of samples used to by the randomized sampling based techniques has a direct relationship. In particular, it is shown that, as the lower bound on the number of samples reduces, the degree of conservatism increases in the design. Classical motion planning and obstacle avoidance methodologies are computationally expen-sive with the number of degrees of freedom of the vehicle, and therefore, these methodologies are largely inapplicable for MAVs with 6 degrees of freedom. The problem of computational complexity can be avoided using randomized sampling based motion planning algorithms such as probabilistic roadmap method or PRM. However, as a pay-off these algorithms lack algorith-mic completeness properties. In this thesis, it is established that the algorithmic completeness properties are dependent on the choice of the sampling sequences. The thesis contains analy-sis of algorithmic features such as probabilistic completeness and asymptotic optimality of the PRM algorithm and its many variants, under the incremental and independent problem model framework. It is shown in this thesis that the structure of the random sample sequence affects the solution of the sampling based algorithms. The problem of capturing the connectivity of the configuration space in the presence of ob-stacles, which is a central problem in randomized motion planning, is also discussed in this thesis. In particular, the success probability of one such randomized algorithm, named Obsta-cle based Probabilistic Roadmap Method or OBPRM is estimated using geometric probability theory. A direct relationship between the weak upper bound of the success probability and the obstacle geometric features is established. The thesis also contains a new sampling based algorithm which is based on geometric random walk theory, which addresses the problem of capturing the connectivity of the configuration space. The algorithm shows better performance when compared with other similar algorithm such as the Randomized Bridge Builder method for identical benchmark problems. Numerical simulation shows that the algorithm shows en-hanced performance as the dimension of the motion planning problem increases. As one of the central objectives, the thesis proposes a pre-processing technique of the state space of the system to enhance the performance of sampling based kino-dynamic motion plan-ner such as rapidly exploring random tree or RRT. This pre-processing technique can not only be applied for the motion planning of the MAV, but can also be applied for a wide class of vehicle and complex systems with large number of degrees of freedom. The pre-processing techniques identifies the sequence of regions, to be searched for a solution, in order to do mo-tion planning and obstacle avoidance for an MAV, by an RRT planner. Numerical simulation shows significant improvement over the basic RRT planner with a small additional computa-tional overhead. The probabilistic analysis of RRT algorithm and an approximate asymptotic optimality analysis of the solution returned by the algorithm, is also presented in this thesis. In particular, it is shown that the RRT algorithm is not asymptotically optimal. An integral part of the motion planning algorithm is the capability of fast collision detection between various geometric objects. Image space based methods, which uses Graphics Pro-cessing Unit or GPU hardware, and do not use object geometry explicitly, are found to be fast and accurate for this purpose. In this thesis, a new collision detection method between two convex/non-convex objects using GPU, is provided. The performance of the algorithm, which is an extension of an existing algorithm, is verified with numerous collision detection scenarios.

The objective of this research is to verify the three degree of freedom capabilities of a bio-inspired quad flapping-wing micro aerial vehicle in simulation and in hardware. The simulation employs a nonlinear plant model and input-output feedback linearization controller to verify the three degree of freedom capabilities of the vehicle. The hardware is a carbon fiber test bench with four flapping wings and an embedded avionics system which is controlled via a PD linear controller. Verification of the three degree of freedom capabilities of the quad flapping-wing concept is achieved by analyzing the response of both the simulation and test bench to pitch, roll, and yaw attitude commands.

The conventional Mini and Large scale Unmanned Aerial Vehicle systems span anywhere from approximately 12 inches to 12 feet; endowing them with larger propulsion systems, batteries/fuel-tanks, which in turn provide ample power reserves for long-endurance flights, powerful actuators, on-board avionics, wireless telemetry etc. The limitations thus imposed become apparent when shifting to Micro Aerial Vehicles (MAVs) and trying to equip them with equal or near-equal flight endurance, processing, sensing and communication capabilities, as their larger scale cousins. The conventional MAV as outlined by The Defense Advanced Research Projects Agency (DARPA) is a vehicle that can have a maximum dimension of 6 inches and weighs no more than 100 grams. Under these tight constraints, the footprint, weight and power reserves available to on-board avionics and actuators is drastically reduced; the flight time and payload capability of MAVs take a massive plummet in keeping with these stringent size constraints. However, the demand for micro flying robots is increasing rapidly. The applications that have emerged over the years for MAVs include search&rescue operations for trapped victims in natural disaster succumbed urban areas; search&reconnaissance in biological, radiation, natural disaster/hazard succumbed/prone areas; patrolling&securing home/office/building premises/urban areas. VTOL capable rotary and fixed wing flying vehicles do not scale down to micro sized levels, owing to the severe loss in aerodynamic efficiency associated with low Reynolds number physics on conventional airfoils; whereas, present state of the art in flapping wing designs lack in one or more of the minimum qualities required from an MAV: Appreciable flight time, appreciable payload capacity for on-board sensors/telemetry and 6DoF hovering/VTOL performance. This PhD. work is directed towards overcoming these limitations. Firstly, this PhD thesis presents the advent of a novel Quad-Wing MAV configuration (called the QV). The Four-Wing configuration is capable of performing all 6DoF flight maneuvers including VTOL. The thesis presents the design, conception, simulation study and finally hardware design/development of the MAV. Secondly, this PhD thesis proves and demonstrates significant improvement in on-board Energy-Harvesting resulting in increased flight times and payload capacities of the order of even 200%-400% and more. Thirdly, this PhD thesis defines a new actuation principle called, Fixed Frequency, Variable Amplitude (FiFVA). It is demonstrated that by the use of passive elastic members on wing joints, a further significant increase in energy efficiency and consequently reduction in input power requirements is observed. An actuation efficiency increase of over 100% in many cases is possible. The natural evolution of actuation development led to invention of two novel actuation systems to illustrate the FiFVA actuation principle and consequently show energy savings and flapping efficiency improvement. Lastly, but not in the least, the PhD thesis presents supplementary work in the design, development of two novel Micro Architecture and Control (MARC) avionics platforms (autopilots) for the application of demonstrating flight control and communication capability on-board the Four-Wing Flapping prototype. The design of a novel passive feathering mechanism aimed to improve lift/thrust performance of flapping motion is also presented.

Flapping-wing micro air vehicle (MAV) is an emerging micro-robotic technology, which has several challenges toward its practical implementation. Inspired by insect flight, researchers have adopted bio-mimicking approach to accomplish its engineering model. There are several methods to synthesize such an electromechanical system. A piezoelectric actuator driven flapping mechanism, being voltage controlled, monolithic, and of solid state type exhibits greater potential than any conventional motor driven flapping wing mechanism at small scale. However, the demand for large tip deflection with constrained mass introduces several challenges in the design of such piezoelectric actuators for this application. The mass constraint restricts the geometry, but applying high electric field we can increase the tip deflection in a piezoelectric actuator. Here we have investigated performance of rectangular piezo-actuator at high electric field. The performance measuring attributes such as, the tip deflection, block force, block moment, block load, output strain energy, output energy density, input electrical energy, and energy efficiency are analytically calculated for the actuator at high electric field. The analytical results suggest that the performance of such an actuator can be improved by tailoring the geometry while keeping the mass and capacitance constant. Thereby, a tapered piezoelectric bimorph cantilever actuator can provide better electromechanical performance for out-of-plane deflection, compared to a rectangular piezoelectric bimorph of equal mass and capacitance. The constant capacitance provides facility to keep the electronic signal bandwidth unchanged. We have analytically presented improvement in block force and its corresponding output strain energy, energy density and energy effi- ciency with tapered geometry. We have quantitatively and comparatively shown the per- formance improvement. Then, we have considered a rigid extension of non-piezoelectric material at the tip of the piezo-actuator to increase the tip deflection. We have an- alytically investigated the effect of thick and thin rigid extension of non-piezoelectric material on the performance of this piezo-actuator. The formulation provides scope for multi-objective optimization for the actuator subjected to mechanical and electrical con- straints, and leads to the findings of some useful pareto optimal solutions. Piezoelectric materials are polarized in a certain direction. Driving a piezoelectric actuator by high electric field in a direction opposite to the polarized direction can destroy the piezo- electric property. Therefore, unipolar high electric field is recommended to drive such actuators. We have discussed the drawbacks of existing switching amplifier based piezo- electric drivers for flapping wing MAV application, and have suggested an active filter based voltage driver to operate a piezoelectric actuator in such cases. The active filter is designed to have a low pass bandwidth, and use Chebyshev polynomial to produce unipolar high voltage of low flapping frequency. Adjustment of flapping frequency by this voltage driver is compatible with radio control communication. To accomplish the flapping-wing mechanism, we have addressed a compatible dis- tributed compliant mechanism, which acts like a transmission between the flapping wing of a micro air vehicle and the laminated piezoelectric actuator, discussed above. The mechanism takes translational deflection at its input from the piezoelectric actuator and provides angular deflection at its output, which causes flapping. The feasibility of the mechanism is investigated by using spring-lever (SL) model. A basic design of the com- pliant mechanism is obtained by topology optimization, and the final mechanism is pro- totyped using VeroWhitePlus RGD835 material with an Objet Connex 3D printer. We made a bench-top experimental setup and demonstrated the flapping motion by actuating the distributed compliant mechanism with a piezoelectric bimorph actuator.

The flow field and forces on an isolated oscillating NACA 0012 airfoil in a uniform flow is studied using viscous vortex particle method. The simulations are carried out at very low chord (c) based Reynolds number (Re=1000), motivated by the current interest in development of Micro Air Vehicles (MAV). The airfoil is forced to oscillate in both heave and pitch at different normalized oscillation frequencies (f), which is represented by the non-dimensional reduced frequency fc/U).( From the unsteady loading on the airfoil, the net energy transfer to the airfoil is calculated to determine the propensity for the airfoil to undergo self-induced oscillations or flutter at these very low Reynolds numbers. The simulations are carried out using a viscous vortex particle method that utilizes discrete vortex elements to represent the vorticity in the flow field. After validation of the code against test cases in the literature, simulations are first carried out for the stationary airfoil at different angles of attack, which shows the stall characteristics of the airfoil at this very low Reynolds numbers. For the airfoil oscillating in heave, the airfoil is forced to oscillate at different reduced frequencies at a large angle of attack in the stall regime. The unsteady loading on the blade is obtained at different reduced frequencies. This is used to calculate the net energy transfer to the airfoil from the flow, which is found to be negative in all cases studied. This implies that stall flutter or self-induced oscillations are not possible under the given heave conditions. The wake vorticity dynamics is presented for the different reduced frequencies, which show that the leading edge vortex dynamics is progressively more complex as the reduced frequency is increased from small values. For the airfoil oscillating in pitch, the airfoil is forced to oscillate about a large mean angle of attack corresponding to the stall regime. The unsteady moment on the blade is obtained at different reduced frequencies, and this is used to calculate the net energy transfer to the airfoil from the flow, which is found to be positive in all cases studied. This implies that stall flutter or self-induced oscillations are possible in the pitch mode, unlike in the heave case. The wake vorticity dynamics for this case is found to be relatively simple compared to that in heave. The results of the present simulations are broadly in agreement with earlier stall flutter studies at higher Reynolds numbers that show that stall flutter does not occur in the heave mode, but can occur in the pitch mode. The main difference in the present very low Reynolds number case appears to be the broader extent of the excitation region in the pitch mode compared to large Re cases studied earlier. region in the pitch mode compared to large Re cases studied earlier.

This thesis contributes to the state of the art in integrated design of insect-scale piezoelectric actuated flapping wing vehicles through the development of novel theoretical models for flapping wing aerodynamics and piezoelectric actuator dynamics, and integration of these models into a closed form design process. A comprehensive literature review of available engineered designs of miniature rotary and flapping wing vehicles is provided. A novel taxonomy based on wing and actuator kinematics is proposed as an effective means of classifying the large variation of vehicle configurations currently under development. The most successful insect-scale vehicles developed to date have used piezoelectric actuation, system resonance for motion amplification, and passive wing pitching. A novel analytical treatment is proposed to quantify induced power losses in normal hover that accounts for the effects of non uniform downwash, wake periodicity and effective flapping disc area. Two different quasi-steady aerodynamic modelling approaches are undertaken, one based on blade element analysis and one based on lifting line theory. Both approaches are explicitly linked to the underlying flow physics and, unlike a number of competing approaches, do not require empirical data. Models have been successfully validated against experimental and numerical data from the literature. These models have allowed improved insight into the role of the wing leading-edge vortex in lift augmentation and quantification of the comparative contributions of induced and profile drag for insect-like wings in hover. Theoretical aerodynamic analysis has been used to identify a theoretical solution for the optimum planform for a flapping wing in terms of chord and twist as a function of span. It is shown that an untwisted elliptical planform minimises profile power, whereas a more highly tapered design such as that found on a hummingbird minimises induced power. Aero-optimum wing kinematics for hovering are also assessed. It is shown that for efficient flight the flapping velocity should be constant whereas for maximum effectiveness the flapping velocity should be sinusoidal. For both cases, the wing pitching at stroke reversal should be as rapid as possible. A dynamic electromechanical model of piezoelectric bending actuators has been developed and validated against data obtained from experiments undertaken as part of this thesis. An expression for the electromechanical coupling factor (EMCF) is extracted from the analytical model and is used to understand the influence of actuator design variables on actuator performance. It is found that the variation in EMCF with design variables is similar for both static and dynamic operation, however for light damping the dynamic EMCF will typically be an order of magnitude greater than for static operation. Theoretical contributions to aerodynamic and electromechanical modelling are integrated into a low order design method for propulsion system sizing. The method is unique in that aside from mass fraction estimation, the underlying models are fully physics based. The transparency of the design method provides the designer with clear insight into effects of changing core design variables such as the maximum flapping amplitude, wing mass, transmission ratio, piezoelectric characteristics on the overall design solution. Whilst the wing mass is only around 10% of the actuator mass, the effective wing mass is 16 times the effective actuator mass for a typical transmission ratio of 10 and hence the wing mass dominates the inertial contribution to the system dynamics. For optimum aerodynamic effectiveness and efficiency it is important to achieve high flapping amplitudes, however this is typically limited by the maximum allowable field strength of the piezoelectric material used in the actuator.

Bats are some of the most agile flyers in nature. Their wings are highly articulated which affords them very fine control over shape and form. This thesis investigates the flight of Hipposideros Pratti. The flight pattern studied is nominally level and straight. Measured wing kinematics are used to describe the wing motion. It is shown that Proper Orthogonal Decomposition (POD) can be used to effectively to filter the measured kinematics to eliminate outliers which usually manifest as low energy higher POD modes, but which can impact the stability of aerodynamic simulations. Through aerodynamic simulations it is established that the first two modes from the POD analysis recover 62% of the lift, and reflect a drag force instead of thrust, whereas the first three modes recover 77% of the thrust and even more lift than the native kinematics. This demonstrates that mode 2, which features a combination of spanwise twisting (pitching) and chordwise cambering, is critical for the generation of lift, and more so for thrust. Based on these inferences, it is concluded that the first 7 modes are sufficient to represent the full native kinematics. The aerodynamic simulations are conducted using the immersed boundary method on 128 processors. They utilize a grid of 31 million cells and the bat wing is represented by about 50000 surface elements. The movement of the immersed wing surface is defined by piecewise cubic splines that describe the time evolution of each control point on the wing. The major contribution of this work is the decomposition of the native kinematics into canonical flapping wing physical descriptors comprising of the flapping motion, stroke-plane deviation, pitching motion, chordwise, and spanwise cambering. It is shown that the pitching mode harvests a Leading Edge Vortex (LEV) during the upstroke to produce thrust. It also stabilizes the LEV during downstroke, as a result, larger lift and thrust production is observed. Chordwise cambering mode allows the LEV to glide over and cover a large portion of the wing thus contributing to more lift while the spanwise cambering mode mitigates the intensification of LEV during the upstroke by relative rotation of outer part of the wing ( hand wing ) with respect to the inner part of the wing ( arm wing). While this thesis concerns itself with near straight-level flight, the proposed decomposition can be applied to any complex flight maneuver and provide a basis for unified comparison not only over different bat flight regimes but also across other flying insects and birds. / MS