Mechanics of Legless Animal Locomotion (The investigation of passive endogenous and exogenous dynamics of undulatory locomotion in different environments)

Building an efficient and robust robot that does not use appendages for locomotion requires inspiration and a thorough understanding of the working principles of limbless animals’ locomotion. In these animals, the passive properties of their morphology and material allow them to dwell in complex terrains at different animals’ scales by using only a simple mode of locomotion, i.e., undulatory locomotion. A better understanding of these animals can inspire efficient locomotion strategies and lead to multi-gait terrain adaptation that exploits their physical intelligence. This study endeavors to model undulatory locomotion in various environments and study the effect of endogenous and exogenous dynamics in limbless bodies. First, undulatory locomotion is modeled analytically using the Lagrangian mechanics approach in a dry frictional environment. A discrete multi-bar system is set to get the propulsive force through frictional anisotropy. The system is then non-dimensionalized to determine the factors representing material and environmental properties. The principal components of the model are body stiffness, internal damping, moment of inertia, and frictional anisotropy. Simulations showed the interdependence of these quantities to achieve the desired speed. The results also highlighted the interdependence of endogenous and exogenous dynamics to achieve different locomotion gaits. Swimming, crawling, and polychaete-like locomotion are characterized based on stiffness factor, frictional factor, and frictional coefficient ratio. The model is validated by inputting the required parameters of the corn snake from the literature. Then undulatory locomotion is modeled in a viscous environment, and the results are compared with the dry environment. It is found that the optimum weight of dry and viscous frictional factors can be found in a hybrid environment to achieve better speed performance. Finally, the experimental validation is carried out in a dry friction environment. The results from experimental and physical models are compared. The physical robot is a wheel-based modular system with flexible joints moving on different substrates. The influence of the spatial distribution of the body stiffness on the speed performance is also explored. Findings suggest that the environment affects the performance of undulatory locomotion based on the body stiffness distribution. Although quantitatively the stiffness varies with the environment, we obtained a qualitative constitutive law for all environments. Specifically, we expect the stiffness distribution to exhibit either an ascending-descending or an ascending-plateau pattern along the length of the object, from head to tail. Furthermore, undulatory locomotion showed sensitivity to contact mechanics: solid-solid or solid-viscoelastic contact produced different locomotion dynamics. Our findings elucidate how terrestrial limbless animals achieve undulatory locomotion performance by exploiting the passive properties of the environment and the body. Application of the obtained results can lead to better-performing long-segmented robots exploiting the aptness of passive body dynamics and the characteristics of the environment where they need to move.