Inverted landing is a routine behavior among a number of animal fliers. However, mastering this feat poses a considerable challenge for robotic fliers, especially to perform dynamic perching with rapid body rotations (or flips) and landing against gravity. Inverted landing in flies have suggested that optical flow senses are closely linked to the precise triggering and control of body flips that lead to a variety of successful landing behaviors. Building upon this knowledge, we aimed to replicate the flies' landing behaviors in small quadcopters by developing a control policy general to arbitrary ceiling-approach conditions. First, we employed reinforcement learning in simulation to optimize discrete sensory-motor pairs across a broad spectrum of ceiling-approach velocities and directions. Next, we converted the sensory-motor pairs to a two-stage control policy in a continuous optical flow space augmented by ceiling distance measurement. The control policy consists of a first-stage Flip-Trigger Policy, which employs a one-class support vector machine, and a second-stage Flip-Action Policy, implemented as a feed-forward neural network. To transfer the inverted-landing policy to physical systems, we utilized domain randomization and system identification techniques for a zero-shot sim-to-real transfer with emulated optical flow using external motion tracking. As a result, we successfully achieved a range of robust inverted-landing behaviors in small quadcopters, emulating those observed in flies.

The prominent maneuverability of flapping flight is enabled by rapid and significant changes in aerodynamic forces, which is a result of surprisingly subtle and precise changes of wing kinematics. The high sensitivity of aerodynamic forces to wing kinematic changes demands precise and instantaneous control of the flapping wing trajectories, especially in the presence of various types of uncertainties. In this work, we first present a dynamic model of a pair of direct-motor-driven flapping wings while taking into consideration the parameter uncertainties and external disturbances. We then present an Adaptive Robust Controller (ARC) to achieve robust performance of high-frequency (over 30Hz) instantaneous wing trajectory tracking with onboard feedback. The proposed control algorithm was experimentally validated on a 7.5 gram flapping-wing MAV which showed excellent tracking of various wing trajectories with different amplitude, bias, frequency, and split-cycles. Experimental results on various model wings demonstrated that the ARC can adapt to unknown parameters and show no performance degradation across wings of different geometries. The results of ARC were also compared with those of open-loop and classical PID controllers.

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.

Insects are able to create complex wing trajectories using power and steering muscles attached to the wing/thorax oscillation system. In this paper, we propose a dynamic model for such an oscillation system, and study its dynamic behavior. In particular, we model the wing as a rigid body with three degrees of freedom. The power muscle is modeled by a torque actuator and a torsional spring creating basic wing flapping (stroke) motion. Torsional springs at the wing longitudinal rotation and deviation axes are used to mimic the steering muscles. Aerodynamic forces and moments are calculated using blade-element analysis and quasi-steady aerodynamic model. Dimensional analysis shows that the dynamic behavior of the system is determined by the three spring coefficients and the input torque coefficient, and is characterized by four basic patterns of wing trajectories. By exploring the parameter space of these coefficients, we found that the wing trajectory that most similar to those of a real insect generates the best lift and power loading. Furthermore, a hybrid optimization algorithm is implemented to find the optimal stiffness coefficients that maximize the power loading. Notably, the results also indicate that the flapping trajectories with out-of-plane deviation achieve a better aerodynamic performance than those without it. The oscillatory property of this system does not only explain how insects use flight muscles to tune wing kinematics, but also allows for design simplifications of the wing driving mechanism of flapping micro air vehicles.

In this paper, we develop a theoretical framework for a flapping-wing actuation mechanism. Driven by oscillating magnetic torque acting on the rotor, the proposed actuator operates as a forced nonlinear oscillator. The resonance of the system is achieved by using a virtual magnetic spring without any mechanical components. Analytical models of the driving torque and the wing flapping (rotor) dynamics are derived and validated by experimental measurements from a parallel study. The flapping amplitude at primary resonance is obtained by solving the dynamic equation using the method of multiple time scale. The aerodynamic lift is then calculated based on quasi-steady aerodynamic model. Finally, the developed framework is used to investigate the feasibility and performance of the proposed actuator at different scales, while we show that a lift-to-weight ratio over one can be achieved in a large domain of design parameter space.

The design and construction of a 2.6 gram electromagnetic actuator operated at resonance is presented. This design is based on wedge-shaped electromagnetic coil generating a driving torque on a rotor embedded with permanent magnets. Additional permanent magnets are used to create a virtual spring effect, supply a restoring torque to the rotor and adding nonlinear system stiffness. Flapping wing parameters were varied systematically to generate 16 unique wing profiles, from which wings were fabricated. Independent bench tests for the coil and spring magnets were used to modify analytical models of the actuator, derived in detail in a parallel study. Based on the equations of motion, estimates for the primary mode of resonance and the peak-peak stroke amplitude were determined using an approximate solution. Frequency response tests were conducted on the flapper using the set of test wings at varying supply voltages and spring configurations to verify the predicted resonate frequencies and amplitudes. Wing kinematics and mean lift measurements were performed for the flapper operating at resonance, producing a lift-to-weight ratio for the actuator of over one at 24V.

In this study, we present a motor-driven flapping-wing actuator, designed to operate at its resonant frequency using a torsion spring. The wing is driven by a DC motor directly through gear transmission. Linear torsion springs mounted on the load shaft creates restoring torque when the wing is displaced from its mid-stroke position. The actuator dynamics is obtained using system identification. The flapping motion of the wing is achieved by closed-loop motor control, for example, tracking a sinusoidal wave with the frequency tuned to match the resonant frequency of the system. PID and LQR controllers are applied for instantaneous wing kinematics tracking: A PID controller is able to precisely track the trajectory with relatively large control input; on the other hand, a linear quadratic regulator (LQR) achieves large flapping amplitude with small input effort. We show that the mechanism is able to track sinusoidal motions with different amplitude, bias and frequencies with relatively large range by changing the springs, therefore generating roll and pitch torques that can be used for flight control. Then a Hopf oscillator based central pattern generator is also shown to be an alternative trajectory to track. The proposed wing actuation mechanism provides an at-scale wing testing platform for flapping wing micro aerial vehicles.

We measured the dynamic damping of a pair of flapping cicada wings mounted on a robotic insect thorax mechanism capable of high frequency flapping. The damping coefficients were derived based on the measurements of the wing-thorax mechanism translating along its body principal axes. The robotic mechanism has a 10cm wingtip-to-wingtip span, flaps up to 65Hz, and weigh 2.86 gram including the motor and wings. To measure the flapping induced damping during translation, we developed a pendulum system mounted with encoder, and attached the flapper at the end and in different orientations such that its motion is along its principle axes. The damping of the flapper is then calculated from the decaying rate of the magnitude of the oscillating pendulum. The damping coefficients calculated from the experiments are very close to those estimated based on our mathematic models using Blade-Element Theory (BET) and quasi-steady aerodynamic models. As expected, the damping linearly increases with the flapping frequency and is most prominent along forward/backward direction.

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.

We investigated whether flapping flight has an inherent stability by analyzing the inertial and aerodynamic effects of flapping wings on body dynamics. Based on wing and body kinematics of free flying fruit flies during rapid maneuvers, we found a passive counter torque due to body rotation. It is identified both in simulation through quasi-steady state aerodynamic model and through experiments on a dynamically scaled robotic wing. An analytical form is derived correspondingly. In the turning yaw axis, the estimated damping coefficient of flapping wings is significantly higher than body frictional damping; this indicates a passive deceleration during turning. By simulating insect to rotate about each principal axis of inertial and body frames, we calculated the corresponding damping coefficients, and further analyzed the attitude stability. The result reveals that, passive damping of flapping flight, while does not necessarily lead to a stable full body dynamics, provides a considerable passive restoring torque that could be critical for flight stabilization and control in the design of micro aerial vehicles. Preliminary analysis on the scaling parameters of passive damping was also performed.