cs.ROMar 8, 2026

Unifying Sidewinding and Rolling: A Wave-Based Framework for Self-Righting in Elongated Limbless and Multi-Legged Robots

Authors: Hangjun Liu, Jiarui Geng, Jinxuan Ding, Gengzhi He, Xiyuan Wang, Melisa Arukgoda, Joe DiGennaro, George Ubertalli, 

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Abstract

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.

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Fig. 1: Centipedes and centipede-inspired robot. (A) Example of a centipede robot necessitating self-righting. (a.1) A centipede robot fell over from a elevated platform. (a.2) The centipede robot flipped upside down after falling from the platform. (B) Biological centipedes with distinct limb morphologies: (b.1) Scolopendra subspinipes , characterized by relatively short limbs, and (b.2) a house centipede, characterized by elongated limbs. (C) Centipede-inspired robotic platform with adjustable limb length: (c.1) no limbs, (c.2) short limbs, and (c.3) long limbs.
Fig. 2: Centipede drop-test setup, representative self-righting modes, and height-dependent mode probabilities. (a) Controlled drop arena and imaging configuration using two synchronized 240 fps high-speed cameras (front and side views). (b) Representative image sequences for modes observed in each species. House centipedes exhibit aerial righting , post-bounce righting , and ground wave righting . S. subspinipes exhibits post-bounce righting , ground wave righting , and ground one-shot righting (often accompanied by a pronounced C-shaped body posture). (c) Mode probability as a function of drop height for house centipedes (left) and S. subspinipes (right), shown as stacked distributions (each height: ≥\geq 10 trials; three individuals per species).
Fig. 3: Righting time versus drop height for each self-righting mode. Top row: house centipedes, from left to right: aerial, post-bounce, and ground wave righting. Bottom row: S. subspinipes , from left to right: post-bounce, ground wave, and ground one-shot righting (aerial righting was not observed for S. subspinipes in our tests). Points show mean righting time; error bars indicate mean ±\pm standard error of the mean . Modes not observed at a given height are omitted events.
Fig. 4: Robot self-righting gait (a) The limbless robophysical model consists of a series of alternating yaw and pitch joints, with a yaw and a pitch joint labeled. (b) The sinusoidal signals sent to the ( left ) yaw joints and ( right ) pitch joints. The joint amplitude is denoted by AA and the phase shift between adjacent yaw ( and pitch ) joints is denoted by 2πn/N2\pi n/N .
Fig. 5: Experimental setup and representative locomotion modes. (A) Two mounted 240 fps cameras capturing robot motion from top and side perspectives for kinematic analysis. (B) Time-lapse snapshots of the limbless robot from t=0t=0 to t=Tt=T : (B.1) no-spin sidewinding (pure lateral translation without axial rotation), (B.2) in-place spinning (axial rotation with minimal net translation), and (B.3) sidewinding spin (coupled axial rotation and lateral translation).
Fig. 6: Behavior diagrams of displacement and axial rotation. (a) Parameter space of limbless robot self-righting, with axes corresponding to pitch-joint amplitude ( ApA_{p} ) and number of body waves ( nn ). (b) Behavior diagram of net displacement over the parameter space (color bar unit: body lengths per cycle, BL/cycle). (c) Behavior diagram of average axial rotation over the parameter space (color bar unit: rad/s). (d) Locomotion mode distribution across the parameter space. I: self-righting in place; II: sidewinding; III: sidewinding spinning; IV: kinematic saturation.
Fig. 7: Robot Displacements under different yaw and pitch wave phase offsets (a) Forward displacement of the limbless robot in body lengths (BL) per cycle as a function of Δd\Delta d , the difference between the phase offset between the yaw joints and pitch joints. (b) Robot spinning (axial rotation) per cycle as a function of Δd\Delta d .
Fig. 8: Effect of limb size on behavior diagrams. (a) From top to bottom: the robot equipped with nine pairs of short, medium, and long legs. (b) Behavior diagrams of net displacement over the parameter space (color bar unit: BL/cycle). (c) Behavior diagrams of average axial rotation over the parameter space (color bar unit: rad/s). We observe that the successful self-righting rate decreases as limb length increases: only a single parameter combination yields successful self-righting for medium-length legs, and none for long legs. (d) Locomotion mode distribution across the parameter space. I: self-righting in place; II: sidewinding; III: sidewinding spinning; IV: kinematic saturation.
Fig. 9: Effect of limb number on behavior diagrams. (a) The robot equipped with different numbers of legs (leg length: 6.06 cm). (b) Net displacement over the parameter space (BL/cycle). (c) Average axial rotation over the parameter space (rad/s). As the number of legs increases, the feasible region for successful self-righting decreases. (d) Locomotion mode distribution across the parameter space. I: self-righting in place; II: sidewinding; III: sidewinding spinning; IV: kinematic saturation.
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