Analysis of Insect-Inspired Wingstroke Kinematic Perturbations for Longitudinal Control

I NSECTS display remarkable agility and flight-path control in the execution of their everyday tasks, all in the face of significant environmental uncertainties. Maneuvering forces are typically generated by small kinematic perturbations to high-frequency wing motions, such as changes in stroke amplitude, timing of wing rotation, or stroke plane tilting [1]. This clever approach of coupling high-frequency actuation with low-frequency rigid-body motion eliminates the need in most species for active sensing on and active deformation of the wing surface, otherwise evident in their avian [2] and mammalian [3] aerobatic counterparts. Previous analysis of insect-inspired flapping-wing locomotion has examined wing kinematic trajectories from the perspective of maximizing lift [4,5] or minimizing required power [6]. With the introduction of new tools to extract the finewingstroke towingstroke kinematics of insects from high-speed videography [7,8], a number of species-specific control strategies for maneuvering have been identified. In addition, with the development of microscale vehicles that can potentially generate lift forces greater than their weight [9], stability and control aspects of the problem are now a focal point of research. Despite the critical need, the inherent complexity of small-scale flapping flight aerodynamics has obscured a control-theoretic analysis of both biologically relevant and engineered wing kinematic perturbation strategies.While the detailed aerodynamic mechanisms involved in small-scale flight are still an area of active research [10], recent efforts have in fact yielded several approaches for extraction of reduced-order linear time-invariant (LTI) flight dynamics, either for single-degree-of-freedom experimental cases [11,12], direct analytic methods [13], or more general computationally [14] and spectrally derived models [15]. Such formulations are amenable to application of linear control analysis tools, and they should provide the next level of insight. Reachability (or more traditionally, controllability) characterizes the amount of control one has over the state of a system through the choice of the input. This is an important topic for small-scale flapping-wingmicro air vehicle (MAV)designers for several reasons. Size, weight, and power (SWAP) constraints are very stringent at this scale, and reductions in complexity that promote robustness and weight reduction are encouraged. In addition, these vehicles are intended to operate in gusty and possibly cluttered environments, and a high level of platformmaneuverability and actuation authority will be crucial to achieving robust flight-path control in the face of these uncertainties. This Note explores the reachable state space associated with biologically inspired kinematic control strategies seen in longitudinal motion about hover. In Sec. II, a frequency-based system identificationmethodology for identifying the stability derivatives of a small-scale flapping microsystem about hover is outlined, along with the control derivatives for biologically relevant wing kinematic perturbations for maneuvering. Section III applies controllability analysis tools to interpret these biologically relevant control strategies for MAV design, using the example of an MAV with Drosophila-like parameters.