Mechanics of Torque-Free Rolling in Soft Actuated Tubes: Experiments, Simulations, and Models

Rolling locomotion in soft, deformable bodies can arise from internal shape change without relying on rigid wheels or externally applied torques. However, the mechanics underlying such motion remain unclear due to the combined effects of large deformation, distributed friction, and time-dependent actuation. In this work, we study torque-free rolling in a soft, pneumatically actuated tubular structure through experiments, finite-element simulations, and theoretical modeling. A reduced-order dynamic model is formulated within an extended Lagrangian framework, treating the system as a continuously bending body subject to time-varying actuation moments and spatially inhomogeneous friction with stick-slip transitions. Experimental measurements of rolling kinematics, curvature evolution, and ground reaction forces, together with finite-element simulations that resolve large deformations and contact migration, show quantitative agreement with model predictions. The analysis shows that rolling dynamics are governed by phase locking between the internal actuation cycle and mechanical responses. At low actuation frequencies, a stable phase-locked state exists with nearly constant curvature and uniform rolling. Increasing the frequency leads to phase unlocking due to the inertial effect and dissipation, resulting in oscillatory velocity and reduced net translation. A lock-unlock phase diagram is constructed in the space of actuation frequency, peak pressure, and actuator number, identifying a bounded operating window for stable rolling. These results provide a mechanics-based framework for understanding and designing shape-driven locomotion in next-generation soft robotic systems.