Dynamics and design of passive tails for enhanced stability of motion

In this work, we study the nonlinear dynamics of tail motion using numerical simulations and experiments. Our simulations are based on a discrete model comprising rigid cylinders (representing vertebrae) coupled by longitudinal, shear, and bending springs (representing tissues). We consider how various parameter combinations, such as geometric and stiffness gradients in the tail, affect the dynamic response of tails subjected to impulse loading. Using numerical and experimental approaches, we quantify pulse propagation in tails, demonstrating that flexible tails can support a stable wavefront. By incorporating a gradient that gradually decreases the length of each vertebra (geometric gradient) and the stiffness of its connecting tissues (stiffness gradient), we significantly enhance the lateral displacement and velocity of the propagating pulse towards the tip. We show that this effect can be used to improve stability of robotic vehicles subjected to impulses.