Water Surface Swimming in a Centipede and its Robophysical Model

Zhaochen J. Xu; Delfin Aydin; Abdullah Mustafa; Margarita B. Levin; Jianfeng Lin; Tianyu Wang; Daniel I. Goldman

cs.ROSep 22, 2026

Water Surface Swimming in a Centipede and its Robophysical Model

Authors: Zhaochen J. Xu, Delfin Aydin, Abdullah Mustafa, Margarita B. Levin, Jianfeng Lin, Tianyu Wang, Daniel I. Goldman

Organizations: Georgia Institute of Technology, Atlanta, GA 30332, USA

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 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.

Figures & tables

Fig. 1: Centipede surface swimming and a multi-legged robophysical model. (A) Lithobius forficatus swimming at the air-water interface with lateral body undulation. (B) Six-link robophysical model with independently actuated body joints and directionally compliant legs.

Fig. 2: L. forficatus direct body-wave propagation during swimming. (A) Tracked configurations between 0 and 2 body-wave periods, showing tail-to-head wave. (B) PCA profile of first two modes from Eq. ( 2 ); clockwise rotation denotes tail-to-head phase progression. (C) Centerline-curvature heatmap over four periods. Diagonal bands and the red arrow show the wave traveling from tail to head.

Fig. 3: L. forficatus leg wave and contralateral coordination. (A) Stacked leg-angle traces from the left and right sides. Successive peaks propagate from posterior legs toward anterior legs, demonstrating a direct leg wave traveling from tail to head ( $\xi_{\mathrm{leg}}\approx 1.14$ ). Scale bars indicate $30^{\circ}$ . (B) Contralateral phase between homologous left–right leg pairs along the body. The mean phase difference was $170.2^{\circ}$ , close to $180^{\circ}$ anti-phase and distinct from $90^{\circ}$ quadrature and $0^{\circ}$ in-phase coordination. Gray lines show individual trial data and the black line shows the mean.

Fig. 4: Robophysical model and compliant-leg construction. (A) Six-link robot with five actuated yaw joints and one servo-driven leg on each side of every cabin. (B) Four-link leg with stiffness decreasing toward the distal end, a servo-driven root, and three passive torsional-spring joints.

Mass	Single Link: 0.237 kg
	Full 6-Link Robot: 1.422 kg
Dimensions	12.0 cm Width
	102 cm Length (full body)
Power	5.6 V, 1 A (normal operation)
Communication	UART serial (Controller $\rightarrow$ Servo Driver)
Actuation	Body Servos: 4.41 N $\cdot$ m (stall)

Table 5

Fig. 5: Body-wave propagation and swimming direction. Left: body heading, wave directions, and shared body-mode diagram. (A,D) Commanded joint-angle heatmaps. (B,E) Representative configurations over 10 s. (C,F) Signed displacement over 5 s, normalized by body length. Head-to-tail waves produce backward motion, while tail-to-head waves produce forward motion; both displacements follow same gait. Curves and error bars show means and standard deviations across three trials.

Fig. 6: Leg coordination changes direct-wave swimming. (A) An illustrative traveling-wave command at $\xi_{\mathrm{leg}}=1.0$ produces a tail-to-head leg wave. (B) Displacement per cycle versus body-wave spatial frequency for physical anti-phase ( $180^{\circ}$ ), quadrature ( $90^{\circ}$ ), in-phase ( $0^{\circ}$ ), and passive-leg conditions. The active-leg experiments in (B) use $\xi_{\mathrm{leg}}=0$ , with no longitudinal leg phase gradient. Points and error bars are trial means and sample standard deviations. The inset defines the measured leg angle.

Fig. 7: Directional compliance improves displacement. (A) One-sided stops resist bending in the power-stroke direction, while opposite loading bends the spring joints. (B) Representative leg shapes during power and recovery. (C) Displacement per cycle versus body-wave spatial frequency for directionally compliant and rigid legs at physical anti-phase. Gray shows five trials from one L. forficatus specimen.

Fig. 8: Direct-wave locomotion through hydro-clutter. Representative configurations in (A) a compliant post lattice at $t=0$ , 10, and 30 s and (B) a rigid post lattice at $t=0$ , 14, and 60 s. Insets show the two laboratory obstacle arrays.

Robot Locomotion

Robot locomotion studies how robots move efficiently and reliably across varied terrains, environments, and movement modes.

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Legged Robotics Robot Locomotion Robot Morphology-Control Co-Design

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Centipede-like robots offer unique locomotion advantages due to their small cross-sectional area for accessing confined spaces, and their redundant legs enhance robustness in cluttered environments such as search-and-rescue and pipe inspection. However, elongated robots are particularly vulnerable to tipping over when climbing large obstacles, making reliable self-righting essential for field deployment. Self-righting strategies for elongate, multi-legged systems remain poorly understood. In this study, we conduct a comparative biomechanics and robophysical investigation to address three key questions: (1) What self-righting strategies are effective for elongate, many-legged systems? (2) How should these strategies depend on morphological parameters such as leg length and leg number? (3) Is there a morphological limit beyond which reliable self-righting becomes infeasible? We compare two biological exemplars: Scolopendra subspinipes (short legs) and Scutigera coleoptrata (house centipedes with long legs). Scolopendra subspinipes reliably self-rights both during aerial phases and through ground-assisted self-righting, whereas house centipedes rely predominantly on aerial reorientation and struggle to generate effective self-righting torques during ground contact. Motivated by these observations, we construct a parameterized space of bio-inspired self-righting strategies and develop an elongate robot with adjustable leg lengths. Systematic experiments reveal that increasing leg length necessitates a shift in control strategy to prevent torque over-concentration in mid-body actuators, and we identify a critical limb-length threshold above which robust self-righting becomes challenging. These results establish morphology-strategy coupling principles for self-righting in elongate robots and provide design guidelines for centipede-like systems operating in uncertain terrain.

Abstract

Robot Locomotion

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