Numerical analysis of pneumatically driven soft robots with contact using FEM-MPM

This study applies a hybrid finite element-material point method (FEM-MPM) framework to the simulation of pneumatically actuated soft robots undergoing large deformation and contact. Internal forces and pressure boundary conditions are evaluated using an explicit total Lagrangian FEM, while contact—including self-contact—is handled robustly via an MPM formulation with P2G/G2P mappings on a background Eulerian grid. Interactions with external bodies employ a frictional contact model, and self-contact is treated succinctly through MPM’s inherent non-penetration. The cavity volume enclosed by the FEM boundary mesh is updated incrementally via the divergence theorem, and internal pressure is prescribed through an isothermal equation of state, enabling an approximate coupling between deformation and internal pressure while avoiding the need for sophisticated full-scale fluid–structure interaction analysis. As verification, we analyze a self-contacting bending actuator and a four-finger soft gripper assembled from the actuator, reproducing grasping sequences with complex contact in a consistent manner. We further show that global deformation states can be identified from pressure time series alone, providing a basis for numerical analysis and data acquisition toward self-sensing soft robots using only injected volume and actuation profiles. Finally, a case study that systematically varies the initial arrangement and injected air quantity reveals―summarized as a phase diagram―that grasp success depends strongly on spatial configuration and actuation conditions. This application indicates that the hybrid FEM-MPM workflow can serve as a practical foundation for design exploration and future closed-loop control.