Undulatory and pedundulatory robotic locomotion via direct and retrograde body waves

The present paper explores the effect of the mechanism-substrate frictional interface on the locomotion characteristics of robotic mechanisms employing traveling waves for propulsion. For these investigations, an extended class of undulatory robotic locomotors is considered, termed pedundulatory, which augment lateral body undulations by coordinated dorso-ventral oscillations of multiple pairs of lateral paddle-shaped appendages (parapodia). We examine how, the same robotic prototype, allows the implementation of four distinct bio-inspired undulatory and pedundulatory modes of locomotion, by modifying the motion control strategy depending on the mechanism-substrate frictional interface. These modes employ retrograde or direct body waves, either standalone (giving rise to eel-like and ochromonas-like undulatory locomotion modes, respectively), or combined with appropriately coordinated substrate contact by the parapodial appendages (giving rise to centipede-like and polychaete-like pedundulatory modes, respectively). These four modes are investigated and comparatively assessed, both in simulation and via extensive experiments on granular substrates with the Nereisbot prototype. Our results validate the identified locomotion principles and also highlight the enhanced performance and gait repertoire of pedundulatory systems, compared to purely undulatory ones.