Water Surface Swimming in a Centipede and its Robophysical Model
Abstract
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 \textit{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.
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BibTeX
@misc{xu2026water,
title = {{Water Surface Swimming in a Centipede and its Robophysical Model}},
author = {Zhaochen J. Xu and Delfin Aydin and Abdullah Mustafa and Margarita B. Levin and Jianfeng Lin and Tianyu Wang and Daniel I. Goldman},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.27088},
eprint = {2609.27088},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.27088},
note = {CC BY-NC-ND 4.0},
}
RIS
TY - UNPB
TI - Water Surface Swimming in a Centipede and its Robophysical Model
AU - Zhaochen J. Xu
AU - Delfin Aydin
AU - Abdullah Mustafa
AU - Margarita B. Levin
AU - Jianfeng Lin
AU - Tianyu Wang
AU - Daniel I. Goldman
PY - 2026
DA - 2026/09/22
PB - arXiv
DO - 10.48550/arxiv.2609.27088
UR - https://arxiv.org/abs/2609.27088
AB - 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 \textit{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.
ER -