Modeling and Experimental Validation of Inflatable Tube Robot with External Shaping Actuator Under Combined Bending, Indentation and Wrinkling

Soft robots have attracted extensive attention owing to their high flexibility. Inflatable membrane tubes offer lightweight and safe environmental interaction, and external shaping actuators have further expanded their applicability. However, modeling such rigid-flexible gas coupled systems remains challenging due to the internal pressure, external loads, and complex deformations including bending, indentation, and wrinkling. To address curvature variation caused by tube deformation hysteresis, this study presents a static model based on virtual work and a segmented approach for inflatable robots. In the actuator unit, the irregular curvature variation and centerline deviation are quantified. In the cantilever unit, the effective bending moment, as well as the wrinkling and failure criteria are derived. The post-buckling deflection equation characterizes the abrupt curvature variation at the tube root caused by the local wrinkling and collapse. A multi-sensor experimental platform is conducted. The experimental results show that the proposed models achieve superior performance in static parameter identification and kinematic prediction. The bending torque error is below 7%, and the tip position error is less than 5% within the bending angle range of 0° to 100°, which confirm that the proposed models accurately predict the coupled deformation and provide a theoretical basis for the precise control of rigid–flexible gas coupled systems.