Optimizing energetics of lateral undulatory locomotion: unveiling morphological adaptations in different environments

Ongoing efforts seek to unravel theories that can make simple, quantitative and reasonably accurate predictions of the morphological adaptive changes that arise with the size variation. Yet, relatively scant attention has been directed towards lateral undulatory locomotion. In the current study, we explore: (i) the constraints imposed by the variation of length and mass in viscous and dry friction environments on the cost of transport (COT) of lateral undulatory locomotion and (ii) the role of the body, environment and input oscillations in such an intricate interplay. In a dry friction environment, minimum COT correlates with stiffer and longer bodies, higher frictional anisotropy and angular amplitudes greater than approximately 10^o. Conversely, a viscous environment favours flexible long bodies, higher frictional anisotropy and angular amplitudes lower than approximately 30^o. In both environments, optimizing mass and maintaining low angular frequencies minimizes COT. Our conclusions are applicable only in the low-Reynolds-number regime, and it is essential to consider the interdependence of parameters when applying the generalized results. Our findings highlight musculoskeletal and biomechanical adaptations that animals may use to mitigate the consequences of size variation and to meet the energetic demands of lateral undulatory locomotion. These insights enhance foundational biomechanics knowledge while offering practical applications in robotics and ecology.