In this paper, we derive longitudinal nonlinear equations of motion of a hovering insect with deformable abdomen to investigate the effect of the abdominal motion to the longitudinal dynamics. The blade-element theory, which is based on experimentally obtained aerodynamic coefficients, is used for the periodic force and moment excitation to the system. Here, we focus on the role of the deformable abdomen to investigate whether or not the flexible body is a decisive factor to the longitudinal flight dynamic stability. Three cases: 1) rigid connection between the thorax and abdomen, 2) flexible connection, and 3) active connection with a feedback control, are compared to check the role of the abdomen deformation on the longitudinal flight dynamic stability, by examining eigenvalues of the linearized system model of each case. The results show that an active control of the abdominal angle can stabilize the longitudinal flight dynamics of the insect modeled in this study.
In this study, we develop a flexible multibody model of the Hawkmoth Manduca Sexta and its six degrees of freedom (6- DOF) flight dynamic simulation environment. The wings of the Hawkmoth model are constructed as a flexible structure which has similar structural dynamic characteristics to the real Hawkmoth wings. The other body components: head, thorax, and abdomen are also modeled independently to consider each component’s mass and inertia properties. Based on this flexible multibody dynamics environment, a wing kinematics that enables a hovering flight of the Hawkmoth model is searched. This kinematics is compared with experimentally measured wing kinematics from literature, and the result shows that a slight modification to the measured wing kinematics is sufficient to reproduce the hovering flight of the Hawkmoth model. The 6-DOF flight dynamic states at the hovering condition are also computed and these state variables are compared with those of a rigid-winged Hawkmoth model to see the effect of the flexibility on the flight dynamics. Here, the rigid- and flexible-winged Hawkmoth models are the same except for the wing flexibility. A qualitative and comparative analysis is performed on the 6-DOF flight states during the hovering flight between the two Hawkmoth models, and the effect of wing flexibility on the flight dynamics is addressed.