Coordinating tiny limbs and long bodies: geometric mechanics of diverse undulatory lizard locomotion

Although typically possessing four limbs and short bodies, lizards have evolved diverse body plans including elongate trunks with tiny limbs. These elongate morphologies are hypothesized to aid locomotion in cluttered and fossorial environments. However, mechanisms of propulsion in such forms – e.g. the use of body and/or limbs to interact with the substrate – and potential body/limb coordination remain unstudied. Here, we use biological experiments, a geometric theory of locomotion, and robophysical models to comparatively investigate body-limb coordination in a diverse sample of lizard morphologies. Locomotor field studies in short limbed, elongate lizards (Brachymeles and Lerista) and laboratory studies of fully limbed lizards (U. scoparia and S. olivaceus) and a snake (C. occipitalis) reveal that body wave dynamics can be described by a combination of standing and traveling waves; the ratio of the amplitudes of these components is inversely related to the degree of limb reduction and body elongation. The geometric theory helps explain our observations, predicting that the advantage of traveling wave body undulations (compared with a standing wave) emerges when the dominant thrust generation mechanism arises from the body rather than the limbs. We test our hypothesis in biological experiments by inducing use of traveling waves in stereotyped lizards via modulating the ground penetration resistance. Study of a limbed/undulatory robophysical model demonstrates that a traveling wave is beneficial when thrust is generated by body-environment interaction. Our models could be valuable in understanding functional constraints on the evolutionary process of elongation and limb reduction in lizards, as well as advancing robot designs.