The effects of wing inertial forces and mean stroke angle on the pitch dynamics of hovering insects.

This paper discusses the wing inertial effects and the important role of the mean stroke angle on the pitch dynamics of hovering insects. The paper also presents a dynamic model appropriate for averaging and discusses the pitch stability results derived from the model. The model is used to predict the body angle of five insect species during hover, which are in good agreement with the available experimental results from different literature. The results suggest that the wing inertial forces have a considerable effect on pitch dynamics of insect flight and should not be ignored in dynamic analysis of hovering insects. The results also suggest that the body of hovering insects can not be vibrationally stabilized in a non-vertical orientation. Instead, the pitch angle of a hovering insect's body is mainly due to a balance of the moment of the insect's weight and the aerodynamic moment due to flapping kinematics with a nonzero mean stroke angle. Experiments with a flapping wing device confirm this results. To clearly explain the used model and clarify the difference between vibrational and non-vibrational stabilization, first this paper discusses the vibrational control of a three-degree-of-freedom force-input pendulum with its pivot moving in a vertical plane.

Control of gliding in a flying snake-inspired n-chain model.

Flying snakes of genus Chrysopelea possess a highly dynamic gliding behavior, which is dominated by an undulation in the form of lateral waves sent posteriorly down the body. The resulting high-amplitude periodic variations in the distribution of mass and aerodynamic forces have been hypothesized to contribute to the stability of the snake's gliding trajectory. However, a previous 2D analysis in the longitudinal plane failed to reveal a significant effect of undulation on the stability in the pitch direction. In this study, a theoretical model was used to examine the dynamics and stability characteristics of flying snakes in three dimensions. The snake was modeled as an articulated chain of airfoils connected with revolute joints. Along the lines of vibrational control methods, which employ high-amplitude periodic inputs to produce desirable stable motions in nonlinear systems, undulation was considered as a periodic input to the system. This was implemented either by directly prescribing the joint angles as periodic functions of time (kinematic undulation), or by assuming periodic torques acting at the joints (torque undulation). The aerodynamic forces were modeled using blade element theory and previously determined force coefficients. The results show that torque undulation, along with linearization-based closed-loop control, could increase the size of the basin of stability. The effectiveness of the stabilization provided by torque undulation is a function of the amplitude and frequency of the input. In addition, kinematic undulation provides open-loop stability for sufficiently large frequencies. The results suggest that the snakes need some amount of closed-loop control despite the clear contribution of undulation to glide stability. However, as the closed-loop control system needs to work around a passively stable trajectory, undulation lowers the demand for a complex closed-loop control system. Overall, this study demonstrates the possibility of maintaining stability during gliding using a morphing body instead of symmetrically paired wings.

The need for higher-order averaging in the stability analysis of hovering, flapping-wing flight.

Because of the relatively high flapping frequency associated with hovering insects and flapping wing micro-air vehicles (FWMAVs), dynamic stability analysis typically involves direct averaging of the time-periodic dynamics over a flapping cycle. However, direct application of the averaging theorem may lead to false conclusions about the dynamics and stability of hovering insects and FWMAVs. Higher-order averaging techniques may be needed to understand the dynamics of flapping wing flight and to analyze its stability. We use second-order averaging to analyze the hovering dynamics of five insects in response to high-amplitude, high-frequency, periodic wing motion. We discuss the applicability of direct averaging versus second-order averaging for these insects.