Methods for stabilizing the longitudinal dynamics of a biomimetic robotic hummingbird in hovering flight

Marques P. (2013). Flight stability and control of tailless lambda unmanned aircraft. International Journal of Unmanned Systems Engineering. 1(S2): 1-4. This paper illustrates the unique challenges with which Aerospace Engineers are presented in achieving dynamic stability and autonomous flight control in tailless lambda unmanned aircraft. The static margin in lambda configurations is short, making the aircraft unstable. To compensate for the short static margin, a priority in lambda UAV design is to obtain a small linear pitching moment. Negligible pitching moment is implemented using reflex camber airfoils that complement the longitudinal dihedral provided by combined wing sweep back and washout. The reflex airfoil permits a wider choice of wing planform and enhances control authority with minimum elevon deflection. Stability analysis shows that a lambda UCAV is longitudinally unstable in ground effect, in both the flaps extended and flaps retracted configurations. Vortical flow and asymmetrical vortex bursting unsteadiness in a rapidly maneuvering next generation near-lambda 1303 UCAV are responsible for unexpected changes in pitch, roll and yaw coefficients and illustrate the difficulty in maneuvering the UCAV beyond certain critical angles of attack. The primary mechanism of lateral-directional control in a W–shaped flying wing UAV is provided by drag rudders, however lateral-directional control in such aircraft requires a sophisticated on-board flight control system. © Marques Aviation Ltd – Press.

Micro Air Vehicles (MAVs) with flapping wings try to mimic their biological counterparts, insects and hummingbirds, as they can combine high agility manoeuvres with precision hovering flight. Near-hovering flapping flight is naturally unstable and needs to be stabilized actively. We present a novel mechanism for pitch moment generation in a robotic hummingbird that uses wing twist modulation via flexible wing root bars. A custom build force balance, sensitive enough to measure the cycle averaged pitch moment as well as lift force, is also presented. The introduced prototype mechanism generates pitch moment of up to ± 0.5 mNm. Finally we integrate a Shape Memory Alloy (SMA) wire to actuate the wing root bar ends. We present achievable displacement versus bandwidth as well as generated pitch moment.

A modern approach to graduate flight dynamics, stability, and control courses

Sensory Systems and Flight Stability: What do Insects Measure and Why?

Results from a wind-tunnel test of two delta-wing aircraft in close proximity are presented and compared with predictions from a vortex lattice method. Large changes in lift, pitching moment, and rolling moment are found on the trail aircraft as it moves laterally relative to the lead aircraft. The magnitude of these changes is reduced as the trail aircraft moves vertically with respect to the lead aircraft. Lift-to-drag ratio of the trail aircraft is increased when the wing tips are slightly overlapped. Wake-induced lift is overpredicted slightly when the aircraft overlap in the spanwise direction. Wake-induced pitching and rolling moments are well predicted. A maximum induced drag reduction of 25% is measured on the trail aircraft, compared with a 40% predicted reduction. Three positional stability derivatives, change in lift and pitching moment with vertical position and change in rolling moment with lateral position, are studied. Predicted boundaries between stable and unstable regions were generally in good agreement with experimentally derived boundaries.

The velocity-vector roll is defined as an angular rotation of an airplane about its instantaneous velocity vector, constrained to be performed at constant angle of attack (AOA), no sideslip, and constant velocity. Consideration of the aerodynamic force equations leads to requirements for body-axis yawing and pitching rotations that must be present to satisfy these constraints. Here, the body-axis rotations and the constraints are used in the moment equations to determine the aerodynamic moments required to perform the velocity-vector roll. The total aerodynamic moments, represented in the reference body-axis coordinate system, are then analyzed to determine the conditions under which their maxima occur. It is shown, for representative tactical airplanes, that the conditions for maximum pitching moment are strongly a function of the orientation of the airplane, occurring at about 90 deg of bank in a level trajectory. Maximum required pitching moment occurs at peak roll rate and is achieved at an AOA in excess of 45 deg. The conditions for maximum rolling moment depend on the value of the roll mode time constant. For a small time constant (fast response) the maximum rolling moment occurs at maximum roll acceleration and zero AOA, largely independent of airplane orientation; for a large time constant, maximum required rolling moment occurs at maximum roll rate, at maximum AOA, and at 180 deg of bank in level flight. The maximum yawing moment occurs at maximum roll acceleration and maximum AOA and is largely independent of airplane orientation. Results are compared with those obtained using conventional assumptions of zero pitch and yaw rates and show significant improvement, especially in the prediction of maximum-pitching-moment requirements.

A nonlinear reference model architecture motivated by dynamic inversion based flight control is introduced. As a novel feature, only one integrated reference model is used to provide reference commands, for longitudinal axis: the flight path angle, vertical load factor (or angle of attack), and pitch rate, while admitting flight path rate command as input; for lateral axis, bank angle and roll rate; for directional axis, lateral load factor and yaw rate. Flight dynamics, actuator dynamics with rate and position limits, and envelope protections can also be incorporated in a straight forward way in the reference model. One advantage of this non-cascaded reference model is that at least the attitude of the reference response can be restored and flown at an early stage of the flight control system design cycle. The second feature is that the reference model is parameterized, allowing the opportunity of updating the knowledge of aircraft dynamics (e.g. damaged) and flying qualities design. With these two aspects, the physical consistency in terms of the reference commands among different channels and reference commands reasonable with respect to true aircraft dynamics can be assured. Although designed for General Aviation aircraft, the framework can be generalized for other aircraft considering only rigid body dynamics.

The paper discusses an experimental effort aimed at quantifying and comparing the relative flight dynamics and gust response of a two-winged, biomimetic, hover-capable robotic hummingbird (RH) with wing kinematic modulation methods for flight control, against those of a quadrotor (QR) with the same mass, inertias, and motor and battery mass fractions as the robotic hummingbird. Comparing the linear flight dynamics models, the RH model had 2–3 ×greater translational aerodynamic coefficients along the longitudinal and lateral axes, and rotational aerodynamic coefficients of similar magnitude but opposite sign about these axes. The pitching moment response to longitudinal velocity was similar in the two, while the rolling moment response to lateral velocity was 3.5 × greater in the RH model. Control authority in the longitudinal dynamics was found to be greater in the QR, though this was attributed to mechanism limitations in the RH. The lateral and direction control authority was 1.3 and 4.3 × larger respectively in the RH model. Both vehicles were subjected to a gust in the laboratory. Although the average total movement of the RH was greater than the QR, when the gust speed was non-dimentionalized by the tip speed, the RH had a lesser response. Further, the pitching response was similar between the two, but the rolling response was ≈ 2 × greater in the RH. Finally, the error between the measured and modeled vehicle responses as a function of wind gust velocity was quantified, which generally increased, especially so for speeds > 5 ft/s. The rotational acceleration equations contained the greatest errors. These results suggest that the linear flight dynamics models are not valid for relatively moderate excursions from hovering flight.

Insects must fly in highly variable natural environments filled with gusts, vortices, and other transient aerodynamic phenomena that challenge flight stability. Furthermore, the aerodynamic forces that support insect flight are produced from rapidly oscillating wings of time-varying orientation and configuration. The instantaneous flight forces produced by these wings are large relative to the average forces supporting body weight. The magnitude of these forces and their time-varying direction add another challenge to flight stability, because even proportionally small asymmetries in timing or magnitude between the left and right wings may be sufficient to produce large changes in body orientation. However, these same large-magnitude oscillating forces also offer an opportunity for unexpected flight stability through nonlinear interactions between body orientation, body oscillation in response to time-varying inertial and aerodynamic forces, and the oscillating wings themselves. Understanding the emergent stability properties of flying insects is a crucial step toward understanding the requirements for evolution of flapping flight and decoding the role of sensory feedback in flight control. Here, we provide a brief review of insect flight stability, with some emphasis on stability effects brought about by oscillating wings, and present some preliminary experimental data probing some aspects of flight stability in free-flying insects.

This paper reports the principle of an micro-machined gyroscope (angular rate sensor), whose output signal is fuse both roll rate and yaw rate two information. The output sine wave frequency is the rotating carrier roll rate, which is easily detected, but the amplitude depends on the roll rate and yaw rate. Otherwise, fabrication defects are always inevitably present, which gives rise to the scale factor of different gyroscope can not be identical. In order to solve these problems, a simple method is presented. The results show that the relationship between output signals and yaw rate is linearity and thus reduce the effect of the roll rate variety on the output signal. Further, different gyroscopes have the same scale factor.

Intelligent adaptive nonlinear flight control for a high performance aircraft with neural networks

Considering that if a pitching hydrofoil moves in a circle, the mechanical structure of the turbine can be further simplified, which is much simpler than a traditional oscillating hydrofoil tidal current turbine, therefore the performance of a pitching hydrofoil with such simple trajectory has attracted our interest. In this paper, numerical method was adopted to simulate a pitching circular motion hydrofoil with variety of motion parameters. Before that, the method was verified and validated. Then, instantaneous hydrodynamic forces, vortex flow field and power coefficients of the hydrofoil were studied. More importantly, the effect of pitch amplitude and circular motion frequency was investigated. Results show that, the vertical force (lift) is the main power for the hydrofoil to harvest energy. For most of the time in one motion period, the horizontal force and pitch moment do negative work. The favorable interaction between vortex and hydrofoil can increase the positive work done by the lift and reduce the negative work done by horizontal force and pitch moment, thus improving the energy harvest efficiency. There are optimal values for the two main motion parameters, which can maximize the energy harvest efficiency. When the pitch amplitude is 75 degrees and the reduced frequency is 0.14, the efficiency can reach more than 40%.

1. In the Small Tortoiseshell (Aglais urticae L.), flying tethered on a flight balance in front of a wind tunnel (Fig. 1), different kinematic and aerodynamic flight variables were recorded under ‘closed loop’ conditions, i.e., when the butterfly's drag was compensated by its thrust. The wings are moved synchronously and nearly in a vertical plane (Fig. 2). Both ‘flight speed’ (in relation to the air) and lift depend on body angle (Fig. 3). Wing-beat frequency, wing-stroke angle, lift and flight speed do not vary significantly with flight duration in normal insects. Amputation of one flagellum does not influence this normal flight behavior. If both flagella are cut off, these variables remain independent of flight duration, but wing-beat frequency, wing-stroke angle and flight speed are increased, and lift is decreased relative to normal (Fig. 4). 2. Flight variables were also measured under ‘open loop’ conditions, i.e., air speed of the wind tunnel was changed stepwise between 0 and 2.5 m/s. In normal animals, wing-beat frequency and lift increase with increasing air speed, whereas wing-stroke angle and horizontal force (= thrust — drag) decrease simultaneously (Fig. 5). After cutting off the flagella, wing-beat frequency, wing-stroke angle and horizontal force increase with respect to normal, and lift decreases. In normalAglais, the lift is positively correlated with wing-beat frequency, but negatively correlated with wing-stroke angle and horizontal force (Fig. 6). 3. The antennal angle during flight is about 43 ° and independent of air speed up to 2.0 m/s (Fig. 7). Under normal flight conditions, the passive antennal deflection is below 0.2 ° (Fig. 8).

An insect-like tailless flapping wing micro air vehicle (FW-MAV) without feedback control eventually becomes unstable after takeoff. Flying an insect-like tailless FW-MAV is more challenging than flying a bird-like tailed FW-MAV, due to the difference in control principles. This work introduces the design and controlled flight of an insect-like tailless FW-MAV, named KUBeetle. A combination of four-bar linkage and pulley-string mechanisms was used to develop a lightweight flapping mechanism that could achieve a high flapping amplitude of approximately 190°. Clap-and-flings at dorsal and ventral stroke reversals were implemented to enhance vertical force. In the absence of a control surface at the tail, adjustment of the location of the trailing edges at the wing roots to modulate the rotational angle of the wings was used to generate control moments for the attitude control. Measurements by a 6-axis load cell showed that the control mechanism produced reasonable pitch, roll and yaw moments according to the corresponding control inputs. The control mechanism was integrated with three sub-micro servos to realize the pitch, roll and yaw controls. A simple PD feedback controller was implemented for flight stability with an onboard microcontroller and a gyroscope that sensed the pitch, roll and yaw rates. Several flight tests demonstrated that the tailless KUBeetle could successfully perform a vertical climb, then hover and loiter within a 0.3 m ground radius with small variations in pitch and roll body angles.

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