Flying animals exhibit remarkable capabilities for both generating maneuvers and stabilizing their course and orientation after perturbation. Here we show that flapping fliers ranging in size from fruit flies to large birds benefit from substantial damping of angular velocity through a passive mechanism termed flapping counter-torque (FCT). Our FCT model predicts that isometrically scaled animals experience similar damping on a per-wingbeat time scale, resulting in similar turning dynamics in wingbeat time regardless of body size. The model also shows how animals may simultaneously specialize in both maneuverability and stability (at the cost of efficiency) and provides a framework for linking morphology, wing kinematics, maneuverability, and flight dynamics across a wide range of flying animals spanning insects, bats, and birds.

Body movements of flying insects change their effective wing kinematics and, therefore, influence aerodynamic force and torque production. It was found that substantial aerodynamic damping is produced by flapping wings through a passive mechanism termed “flapping countertorque” during fast yaw turns. We expand this study to include the aerodynamic damping that is produced by flapping wings during body translations and rotations with respect to all its six principal axes-roll, pitch, yaw, forward/backward, sideways, and heave. Analytical models were derived by the use of a quasi-steady aerodynamic model and blade-element analysis by the incorporation of the effective changes of wing kinematics that are caused by body motion. We found that aerodynamic damping, in all these cases, is linearly dependent on the body translational and angular velocities and increases with wing-stroke amplitude and frequency. Based on these analytical models, we calculated the stability derivatives that are associated with the linearized flight dynamics at hover and derived a complete 6-degree-of-freedom (6-DOF) dynamic model. The model was then used to estimate the flight dynamics and stability of four different species of flying insects as case studies. The analytical model that is developed in this paper is important to study the flight dynamics and passive stability of flying animals, as well as to develop flapping-wing micro air vehicles (MAVs) with stable and maneuverable flight, which is achieved through passive dynamic stability and active flight control.

SUMMARY Insects produce a variety of exquisitely controlled manoeuvres during natural flight behaviour. Here we show how hawkmoths produce and control one such manoeuvre, an avoidance response consisting of rapid pitching up, rearward flight, pitching down (often past the original pitch angle), and then pitching up slowly to equilibrium. We triggered these manoeuvres via a sudden visual stimulus in front of free-flying hawkmoths (Manduca sexta) while recording the animals9 body and wing movements via high-speed stereo videography. We then recreated the wing motions in a dynamically scaled model to: (1) associate wing kinematic changes with pitch torque production and (2) extract the open-loop dynamics of an uncontrolled moth. Next, we characterized the closed-loop manoeuvring dynamics from the observed flight behaviour assuming that hawkmoths use feedback control based on translational velocity, pitch angle and angular velocity, and then compared these with the open-loop dynamics to identify the control strategy used by the moth. Our analysis revealed that hawkmoths produce active pitch torque via changes in mean wing spanwise rotation angle. Additionally, body translations produce passive translational damping and pitch torque, both of which are linearly dependent on the translational velocity. Body rotations produce similar passive forces and torques, but of substantially smaller magnitudes. Our comparison of closed-loop and open-loop dynamics showed that hawkmoths rely largely on passive damping to reduce the body translation but use feedback control based on pitch angle and angular velocity to control their orientation. The resulting feedback control system remains stable with sensory delays of more than two wingbeats.

Micro aerial vehicles (MAV) with multiple rotors, or multicopters, have many promising applications ranging from environmental monitoring, agricultural inspection, to package delivery. These applications, however, usually face a critical problem: the flight time of MAVs is limited due to the low aerodynamic efficiency and high energy consumption. One promising solution is to make them rest on desired objects using perching, an important capability in biological flyers (e.g., birds). In this paper, we present the design and experimentation of a novel perching mechanism: a low cost, 3D printed gripper with bistability (i.e., two stable states). The gripper has two unique characteristics. First, using bistability, it can passively switch from open to closed state using the impact between the gripper and the perching object, alleviating the requirement for precise motion control. Second, the gripper has two perching methods for different objects. For objects with a small height, it can form a closed diamond shape to encircle the objects (encircling method). For objects with a large height, the gripper's two fingers can clip on each side of the objects to utilize the friction forces for perching (clipping method). We analyze the proposed gripper design to predict the required force for opening and closing the gripper. We also predict the size of objects that will allow for successful perching for the clipping method. All the theoretical analyses are experimentally verified. Finally, we integrate the gripper onto a palm-size quadcopter to enable a mechatronic system for perching, and demonstrate successful perching with both clipping and encircling methods as well as aerial grasping. Although our bistable gripper is used with a palm-size quadcopter, the design strategy can also be applied to large-size MAVs for both energy efficient perching and aerial grasping.

Hummingbirds are nature‘s masters of aerobatic manoeuvres. Previous research shows hummingbirds and insects converged evolutionarily upon similar aerodynamic mechanisms and kinematics in hovering. Herein, we use three-dimensional kinematic data to begin to test for similar convergence of kinematics used for escape flight and to explore the effects of body size upon manoeuvring. We studied four hummingbird species in North America including two large species (magnificent hummingbird, Eugenes fulgens, 7.8 g and blue-throated hummingbird, Lampornis clemenciae, 8.0 g) and two smaller species (broad-billed hummingbird, Cynanthus latirostris, 3.4 g and black-chinned hummingbirds Archilochus alexandri, 3.1 g). Starting from a steady hover, hummingbirds consistently manoeuvred away from perceived threats using a drastic escape response that featured body pitch and roll rotations coupled with a large linear acceleration. Hummingbirds changed their flapping frequency and wing trajectory in all three degrees-of-freedom on stroke-by-stroke basis, likely causing rapid and significant alteration of the magnitude and direction of aerodynamic forces. Thus it appears that the flight control of hummingbirds does not obey the “helicopter model” that is valid for similar escape manoeuvres in fruit flies. Except for broad-billed hummingbirds, the hummingbirds had faster reaction times than those reported for visual feedback control in insects. The two larger hummingbird species performed pitch rotations and global-yaw turns with considerably larger magnitude than the smaller species, but roll rates and cumulative roll angles were similar among the four species.

An electromagnetic actuator weighing 2.6 g and operated up to resonant frequencies in excess of 70 Hz is presented with the intended application to flapping-wing MAVs. Comprised of a single electromagnetic coil, a permanent magnet rotor, and a “virtual spring” magnet pair, system resonance is achieved using a periodic excitation voltage applied to the coil, resulting in harmonic wing motion. Analytical models describing the electrodynamic interactions of system components and flapping-wing aerodynamic mechanisms are used to develop the equations governing the system's dynamics. Preliminary analysis based on simulation is used to build a working prototype from which further validation is conducted. Wing kinematics and mean lift measurements from the prototype demonstrated a lift-to-weight ratio of over one at 24 V. Based on a simplified equation of motion, approximate solutions for primary resonance mode and peak-to-peak (pk-pk) stroke amplitude were determined using the method of multiple time scales. Validated from frequency response experiments conducted on bioinspired test wings, these approximate solutions are used as a basis for an optimization framework. Finally, the developed framework is used to investigate the performance of the proposed actuator at different scales, predicting lift-to-weight ratios well above one for a wide range of the parameter space.