Control of Pitch Attitude by Abdomen During Forward Flight of Two-Dimensional Butterfly

Abstract

The objective of this paper is to understand roles of abdominal motion in the pitch stability of flapping flights of butterflies numerically, and a two-dimensional butterfly model has thoracic pitch instability in the periodically flapping flight. Because the obtained uncontrolled flight is unstable, the hierarchical sliding-mode control is used to design the control input for thorax–abdomen joint torque. It is found in the controlled flight that the abdominal motion is sufficient to counteract the thoracic pitch instability and can maintain flapping flights with short recovery time to artificial thoracic torque perturbations. On the other hand, it is also found that the long-term pitch stabilization is not possible only by the abdominal control for all flapping trajectories. However, with the introduction of a wing lead–lag control, the long-term pitch stabilization is obtained. Hence, these observations indicate that the abdomen is used for a short-term control and the wing for a long-term control in stabilizing the pitch of the butterfly’s flight.