Mathematical modeling of modular soft robotic arm

Abstract As an important supplement to rigid robotic arms, the soft robotic arm demonstrates broader application potential in non-structural environments. This article proposes a modular soft robotic arm with a pneumatic network structure. Each module features three symmetrical and independent pneumatic cavities that can control air pressure to achieve axial elongation and spatial bending movements. Coordinated control of multiple modules enables enhanced motion capabilities. To analyze the motion and deformation of each module, we established a mathematical model describing the relationships between air pressure and bending/elongation deformation, using the constant curvature assumption and large deformation beam theory. Furthermore, we investigated the influence of the soft arm’s gravity on deformation performance, providing modified analytical models for single-module and double-module configurations. The kinematic analysis was conducted to determine the soft arm’s workspace through integration of the proposed model and kinematic model. Experimental validation showed bending and elongation angles agreeing well with theoretical predictions and finite element simulations under 0–80 kPa pressure, with maximum deviations below 5.7%. This work provides a theoretical foundation for optimizing the design and analysis of soft robotic arms.