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

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.

Figures (9)

• Figure 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.
• Figure 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).
• Figure 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.
• Figure 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 $A$ and the phase shift between adjacent yaw (and pitch) joints is denoted by $2\pi n/N$.
• Figure 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 $t=0$ to $t=T$: (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).