Root Buckling of Tip-Growing Robots Under Self-Weight, Tip Load, and Obstacle Contact: Unified Modeling and Experimental Validation

• unified buckling framework for tip-growing robots is established. • Critical buckling length under self-weight is derived analytically. • Obstacle-contact buckling regimes are mapped by angle and pressure. • Quantitative criteria distinguish sliding, jamming, and turning modes. Tip-growing robots, which rely on flexible eversion-based growth mechanism, have exhibited unique advantages in post-disaster rescue, pipeline inspection, and navigation in confined environments. However, their buckling behavior under self-weight, external radial loads, and environmental contact remains insufficiently understood, leading to structural and task planning that still relies on empirical tuning. To address this gap, this paper proposes a tip-growing robot buckling model (TGRBM) for analyzing three typical working conditions: self-weight–dominated suspended growth, deformation under external loading, and environment-induced buckling during obstacle contact. Critical buckling conditions for all three scenarios are derived, and the model is validated. The study determines the maximum self-supporting length under gravity, the critical buckling load under external forces, and the dominant buckling regions during oblique obstacle contact, and further establishes quantitative criteria for distinguishing sliding, jamming, and buckling-assisted turning behaviors. TGRBM provides practical guidelines for structural dimensioning, pressure regulation, payload integration, and path planning, forming a mechanics-based foundation for reliable deployment of tip-growing robots in inspection, confined-space navigation, and load-bearing tasks.