Insect flight dynamics: Stability and control

Insects can hover, fly forward, climb, and descend with ease while demonstrating amazing stability, and they can also maneuver in impressive ways as no other organisms can. Is their flight inherently stable? If so, how can they maneuver so well? In recent years, significant progress has been made in revealing the dynamic flight stability and flight control mechanisms of insects and has partially answered these questions. Here the most recent advances in this active area are reviewed. The aim is to provide the background necessary to do research in the area and raise questions that need to be addressed in the future. This review begins with an overview of the flapping kinematics and aerodynamics of insect flight. It is followed by a summary of the governing equations of insect motion and the simplified theoretical models used for analysis of dynamic stability and control. Next, the stability properties of hovering flight and forward flight are scrutinized. Then the flight control properties are explored, dealing in turn with flight stabilization control, steady-state control for changing from hovering to forward flight and from one forward-flight speed to another, and control for maneuvers near hovering. Finally, remarks are given on the state of the art of this research field and speculation is made on its outlook in the near future.

Figure 1

(a) Sketch of insect body and stroke plane. Here $\beta$ is the stroke-plane angle; $\chi$ is the body angle. (b) Angles of a flapping wing that determine the wing orientation relative to the stroke plane. The $(x_1,y_1,z_1)$ coordinates are in a system with its origin at the wing root; the $y_1$ axis points to the side of the insect and the $x_1\text{−}{y}_1$ plane coincides with the stroke plane. $l$ is a line that is perpendicular to the wing span and parallel to the stroke plane. ${\varphi }_w$, ${\psi }_w$, and ${\theta }_w$ are the positional angle, pitch angle, and deviation angle of the wing, respectively. ${\psi }_w$ is related to the angle of attack of the wing, $\alpha$, in the downstroke, $\alpha ={\psi }_w$, and in the upstroke, $\alpha =180°-\psi$. (c) Sketch showing the stroke amplitude $\mathrm{\Phi }=\max$ ${\varphi }_w-\min$ ${\varphi }_w$, and the mean stroke angle $\overline{\varphi }=(\max {\varphi }_w-\min {\varphi }_w)/2$.

Figure 2

Diagram of wing motion in the upstroke of a drone fly in hovering flight, showing the instantaneous wing profiles at 25% and 75% wing lengths ($R$). The arrow represents the direction of the wing motion. From [142].

Figure 3

Definition of aerodynamic lift and drag.

Figure 4

Polar diagram of a fruit-fly (Drosophila virilis) wing. The angle of attack is given in degrees along the curve. Adapted from [138].

Figure 5

Flow visualization of the LEV over a model hawk-moth wing (smoke was released from the leading edge). From [46].

Figure 6

Reference frames and sketch of insect body and wings. $(X_E,Y_E,Z_E)$ is a frame fixed on the Earth. $(x_b,y_b,z_b)$ is a frame fixed on the insect body with its origin at the center of mass of the insect body. $(x_w,y_w,z_w)$ is a frame fixed on the wing, with its origin at the wing root, the $x_w$ axis along the wing span and the $z_w$ axis along the chordwise direction. ${\mathbf{R}}_{\mathrm{cg}}$ is the vector of the center of mass of the body relative to the Earth’s frame; ${\mathbf{R}}_h$ is the vector of the wing root relative to the body frame. Adapted from [119].

Figure 7

Definition of the state variables and sketches of the reference frame. (a) Lateral view and (b) back view. $(x_b,y_b,z_b)$ is a frame fixed on the insect body with its origin at the center of mass of the insect body; the $x_b$, $y_b$, and $z_{\mathit{b}}$ axes are chosen so that at equilibrium, the $x_b$ and $y_b$ axes are horizontal, the $x_b$ axis points forward, and the $y_b$ axis points to the right of the insect. The model insect is shown during a perturbation ( $v$, $w$, $p$, $q$, $r$, $\theta$, and $\varphi$ are zero at reference flight). Adapted from [175].

Figure 8

Vorticity plots at the $0.7R$ wing section at various times for the left and right wings (solid and dashed lines indicate positive and negative vorticities, respectively; the magnitude of the nondimensional vorticity at the outer contour is 2 and the contour interval is 3). Left column: results of the left wing; right column: results of the right wing. The insect moves to its right at $\mathrm{\Delta }v/U=0.1$. The “lateral wind” due to the side motion of the insect increases the axial velocity of the LEV on the left wing and decreases that on the right wing, causing the LEV of the left wing to be more concentrated than that of the right wing. Adapted from [177].

Figure 9

Diagram (side view) of the body attitude ($\mathrm{\Delta }\theta$), forward-backward translation speed ($\mathrm{\Delta }u$), pitch rate ($\mathrm{\Delta }q$), and the forces and moments, during the first cycle of the disturbed motion when the unstable slow oscillatory mode is excited. $F_0$ is the total aerodynamic force at equilibrium, $F_0=mg$. The forward translation produces a pitch-up moment ($M_u\mathrm{\Delta }u$ positive) that enhances the pitch-up rotation and the backward translation produces a pitch-down moment ($M_u\mathrm{\Delta }u$ negative) that enhances the pitch-down rotation, causing the instability. Adapted from [121], and [119].

Figure 10

Diagram of the body attitude (roll angle $\mathrm{\Delta }\gamma$), side translation speed ($\mathrm{\Delta }v$), and roll rate ($\mathrm{\Delta }p$), and the forces and moments during the disturbed motion when the lateral unstable slow divergence mode is excited (insect moving to the right, back view). $F_0$ is the total aerodynamic force at equilibrium, $F_0=mg$. The side motion ($\mathrm{\Delta }v>0$) produces a moment $L_v\mathrm{\Delta }v(>0)$ that will enhance the roll and at the same time, the roll tilts the vertical force ($F_0$) to the right, which will enhance the side motion, producing the destabilizing effects. Adapted from [173].

Figure 11

Curves showing the comparison between simulation and the averaged-model theory for the longitudinal-disturbance motion of (a) the model dronefly and (b) the model hawk moth. The initial disturbances are $\mathrm{\Delta }u=0.1$ and $\mathrm{\Delta }w=\mathrm{\Delta }q=\mathrm{\Delta }\theta =0$, which simulate a horizontal longitudinal gust ($U$ is the mean flapping velocity). Adapted from [173].

Figure 12

Block diagram illustrating the overall architecture of the simulation framework which simulates the flight dynamics and control strategies of flies. The framework consists of five main components: a model of body dynamics, a model of aerodynamic forces and moments, a sensory systems model, a control model, and an environment model. Adapted from [32].