A simplified dynamic model for controlled insect hovering flight and control stability analysis

Abstract

In this paper, the controlled stability of insect hovering flight is analyzed in detail based on a simplified dynamic model of the flyer and flow. The simplified dynamic model incorporates PIDbased wing-kinematic controllers. The control stability of the hovering flight is evaluated based on the cycle-mean dynamic equations. The stability analyses and the simplified dynamic model allow us to derive and test the control coefficients for stable free hovering, firstly in the longitudinal mode of flight and then the lateral mode. In this manner, coefficients for wing-kinematic control for full CFD-FSI simulation could be obtained very efficiently. The coefficients thus determined are verified against full-fidelity CFD-FSI free flight simulations.

Forward flight and sideslip manoeuvre of a model hawkmoth

“…Potential delay/latency between feedback and control action was not considered in this study, due in part to a lack of definitive data concerning the stimuli-neural-motor response of the insect, and a desire to minimize the number of free variables in the problem. Analysis based on the simplified dynamics model of Yao & Yeo (2019b) shows that latency would cause a softening of the longitudinal PID control coefficients, by the order of 10 %-20 % and 20 %-40 % for half-and one-cycle control latency, respectively, depending on the individual coefficient, which were also verified by model simulations. Similar ranges of control coefficients are also applicable to cases where the interval of control intervention is extended to two and three wing cycles, respectively, instead of the one cycle used in this study.…”

“…The vector U(t) comprises updated kinematic control parameters to be used over the ensuing control cycle, where U 0 denotes the initial or baseline state. The control parameters involved in the current study are introduced in the sections that follow and the appendices; readers may refer to Wu et al (2014), Yao (2018) and Yao & Yeo (2019b) for further information. Initial estimates of the control coefficients were first obtained from the simplified dynamic model (Yao & Yeo 2019b) for hovering flight, which were then refined via full CFD-FSI (fluid-structure interaction) simulations before final adoption.…”

“…In free insect hovering flight, stable pitch control can generally be achieved by just varying the mean positional angle (γ ) of the unelevated wing strokes, which affects the mean aerodynamic pitching moment produced by the wings over a wing cycle (Wu et al 2014;Yao 2018;Yao & Yeo 2019b). However, this means of generating pitching moment to control and stabilize the posture of the insect may not be sufficient for an insect in forward flight at a significant speed due to the large buildup in pitch-up moment as indicated in figure 5.…”

“…The state-equation model consolidates the central two-dimensional longitudinal dynamics of controlled forward flight into an accessible form, in which the roles of the kinematic control actions are clearly identified. The reduced form (4.4) can be helpful for establishing control coefficients for stable flight, as in Yao & Yeo (2019b), when combined with a suitable wing force model. The actual 'real-time' simulations of controlled longitudinal free flight are, however, carried in full 3-D space in accordance with the methodologies of § § 4.1 and 3.…”

“…The reduced state equation (4.8) may permit further analysis to aid the selection of the control coefficients, when the key stability derivatives are determined from prescribed motion CFD simulations. In addition to the control for sideways and body rolling motion, the control for other degrees of motion remains the same as that for hovering flight (see Yao (2018) and Yao & Yeo (2019b) for details). As the insect approaches close to the target location, say 0.2 wing lengths, the sideslip manoeuvre controller is deactivated, and full hovering control is activated to stabilize the flyer at the new location.…”