Meeting Abstract
Swinging tails, flailing limbs and bending spines all produce inertial forces through which animals can control orientation, enabling aerial righting among other feats of agility. To compare inertial reorientation (IR) ability across diverse taxa and appendages, we developed the simplest possible model (a template) that captures the salient behavior underpinning IR in both animals and robots. The model features a body and an appendage pinned at their shared center of mass and equipped with a velocity-dependent actuator to capture the effect of limited power on performance. Owing to its linear dynamics, the template is analytically integrable for an optimal reorientation, revealing the link between performance (rotation in finite time) and morphology (parameterized by range of motion, specific power, maximum rotation speed and IR effectiveness, defined as the body rotation produced by a differential shape change). More detailed planar rigid-body models for each appendage type reduce to the template, allowing direct comparison of the effect of size and morphology. Effectiveness depends only on inertial properties, which may be measured directly or estimated through morphometrics, enabling characterization of both extant and extinct animals. Power needed for reorientation is inversely proportional to effectiveness, favoring long tails over smaller appendages for fast maneuvers. Effectiveness scales isometrically, but the specific power to reorient in one body length of vertical fall scales as the square root of size. A small increase in mass dedicated to a tail was needed to retain righting performance across a 50-fold increase in mass for two biologically inspired robots. Animals capable of effective IR likely span a larger range, from 3 gram geckos to 20 kilogram theropod dinosaurs and beyond.
