Control of gliding in a flying snake-inspired n-chain model

Flying snakes of genus Chrysopelea possess a highly dynamic gliding behavior, which is dominated by an undulation in the form of lateral waves sent posteriorly down the body. The resulting high-amplitude periodic variations in the distribution of mass and aerodynamic forces have been hypothesized to contribute to the stability of the snake's gliding trajectory. However, a previous 2D analysis in the longitudinal plane failed to reveal a significant effect of undulation on the stability in the pitch direction. In this study, a theoretical model was used to examine the dynamics and stability characteristics of flying snakes in three dimensions. The snake was modeled as an articulated chain of airfoils connected with revolute joints. Along the lines of vibrational control methods, which employ high-amplitude periodic inputs to produce desirable stable motions in nonlinear systems, undulation was considered as a periodic input to the system. This was implemented either by directly prescribing the joint angles as periodic functions of time (kinematic undulation), or by assuming periodic torques acting at the joints (torque undulation). The aerodynamic forces were modeled using blade element theory and previously determined force coefficients. The results show that torque undulation, along with linearization-based closed-loop control, could increase the size of the basin of stability. The effectiveness of the stabilization provided by torque undulation is a function of the amplitude and frequency of the input. In addition, kinematic undulation provides open-loop stability for sufficiently large frequencies. The results suggest that the snakes need some amount of closed-loop control despite the clear contribution of undulation to glide stability. However, as the closed-loop control system needs to work around a passively stable trajectory, undulation lowers the demand for a complex closed-loop control system. Overall, this study demonstrates the possibility of maintaining stability during gliding using a morphing body instead of symmetrically paired wings.