Nonlinear level-set topology optimization of hyperelastic soft robots with design-dependent pneumatic actuation

This work presents a nonlinear level-set topology optimization framework for hyperelastic soft robotic structures with design-dependent pneumatic actuation. A compressible Neo-Hookean material model is adopted within a finite-strain setting, and an adjoint-based shape sensitivity analysis is derived that retains higher-order displacement-gradient terms, ensuring consistency between geometric and material nonlinearities without requiring initialization from a linear topology optimization. To enable co-optimization of structural topology and actuator geometry, a boundary-capturing and extraction algorithm is developed to identify pneumatic cavities from the implicit level-set representation and to discretize pressure traction along their evolving boundaries. Both a simplified dead-load formulation and a fully deformation-dependent traction model based on Nanson’s relation are presented, offering a systematic trade-off between computational efficiency and physical fidelity. The framework is demonstrated on benchmark problems, including an MBB beam and compliant gripper, followed by pneumatic soft grippers with fixed, parameterized, freeform, and multi-chamber actuator configurations. The framework also accommodates chamber volume redistribution and topological chamber merging through the implicit geometric representation of the level-set method Progressive increases in actuator design freedom are shown to yield substantially improved actuation efficiency and tip displacement. Optimized prototypes fabricated from silicone elastomer show deformation behavior consistent with the predicted mechanisms, with the pneumatic gripper demonstrating bidirectional tip motion under volume-controlled actuation.