Kinetostatic Modeling and Position-Orientation Control of Bellow-Shaped Soft Continuum Robots

Bellow-shaped soft continuum robots with parallel mechanisms feature an excellent balance between structural stiffness and contact compliance, making them highly promising in various applications. However, their complex structures and nonlinear elastic characteristics pose significant challenges in modeling and control. In this work, we propose a kinetostatic model and a corresponding position-orientation controller for bellow-shaped soft continuum robots. First, bellow-shaped soft actuators are simplified into hyperelastic cylinder soft actuators with mechanical equivalence. In addition, the overall deformation is decoupled into elongation and bending components to enhance computational efficiency. Based on these two simplifying strategies, the kinetostatic model is developed with absolute nodal coordinate formulation theory. Then, forward and inverse kinetostatic mappings are defined, and the numerical solution algorithm is presented. Finally, the developed model is experimentally validated through configuration simulation and feedforward trajectory tracking. Experimental results demonstrate that the developed model achieves low prediction errors, with configuration simulation errors of 3.43%. Furthermore, with the model-based feedforward controller, a two-segment soft continuum robot can accurately follow desired trajectories with specified bending angles, achieving average position and angle errors of 4.14 mm and 1.58<inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$^{\circ }$</tex-math></inline-formula>, respectively.