Py-DiSMech: A Scalable and Efficient Framework for Discrete Differential Geometry-Based Modeling and Control of Soft Robots

Abstract: High-fidelity simulation has become essential to the design and control of soft robots, where large geometric deformations and complex contact interactions challenge conventional modeling tools. Recent advances in the field demand simulation frameworks that combine physical accuracy, computational scalability, and seamless integration with modern control and optimization pipelines. In this work, we present Py-DiSMech, a Python-based, open-source simulation framework for modeling and control of soft robotic structures grounded in the principles of Discrete Differential Geometry (DDG). By discretizing geometric quantities such as curvature and strain directly on meshes, Py-DiSMech captures the nonlinear deformation of rods, shells, and hybrid structures with high fidelity and reduced computational cost. The framework introduces (i) a fully vectorized NumPy implementation achieving order-of-magnitude speed-ups over existing geometry-based simulators; (ii) a penalty-energy-based fully implicit contact model that supports rod-rod, rod-shell, and shell-shell interactions; (iii) a natural-strain-based feedback-control module featuring a proportional-integral (PI) controller for shape regulation and trajectory tracking; and (iv) a modular, object-oriented software design enabling user-defined elastic energies, actuation schemes, and integration with machine-learning libraries. Benchmark comparisons demonstrate that Py-DiSMech substantially outperforms the state-of-the-art simulator Elastica in computational efficiency while maintaining physical accuracy. Together, these features establish Py-DiSMech as a scalable, extensible platform for simulation-driven design, control validation, and sim-to-real research in soft robotics.