Water Surface Swimming in a Centipede and its Robophysical Model

Elongate multi-legged robots use coordinated body waves and distributed legs to move through cluttered terrestrial environments. However, as housing actuators for independent leg control can require bulky body segments, their non-streamlined body and limb structure makes it difficult to achieve swimming capability comparable to their terrestrial locomotor performance. At the water surface, we found that the multi-legged robots we tested unexpectedly moved backward: their body waves traveled in the same direction as their displacement, i.e., swimming with a direct wave. We found similar behavior in the centipede Lithobius forficatus, which swims with a direct body wave and periodic leg movement. To study how distributed legs contribute to direct-wave swimming, we analyze animal kinematics and develop a multi-legged robophysical model that allows independent variation of leg morphology and stiffness, body-wave direction, and leg coordination. Robophysical experiments show that direct body waves produce consistent forward motion under the tested conditions and that swimming performance depends on body--leg coordination. Additionally, directionally compliant legs increase displacement from approximately 0.08 to 0.21 body lengths per cycle relative to rigid legs under matched anti-phase actuation. These findings clarify how distributed appendages contribute to surface swimming and establish gait and morphology design principles for extending multi-legged field robots from terrestrial locomotion into aquatic environments.