DiSMech: A Simulator for Soft Robots and Flexible Structures based on Discrete Differential Geometry

The study of soft slender structures has garnered substantial interest in diverse scientific realms, including mechanics, robotics, computer graphics, and biomechanics. Owing to their pronounced non-linear deformations under minimal loads, accurately capturing the dynamics of such structures and predicting their motion in real-time presents a formidable challenge. In this research, we present DiSMech, an open-source simulator for intricate soft robots and structures that can be modeled as flexible rods, shells, or interconnected elements thereof. DiSMech leverages Discrete Differential Geometry (DDG) methods, employing discrete elastic rod algorithms for rods and mid-edge normal based shape operators for shells to model the continuum mechanics. A distinctive feature of DiSMech lies in its fully implicit handling of equations of motion, unlike previous simulation frameworks focusing on soft structure physics. This implicit treatment enables significantly larger time step sizes, resulting in simulations that are an order of magnitude faster than existing state-of-the-art counterparts, while preserving the physical accuracy. The framework allows users to design customized geometric configurations using individual elastic rods and shells through an intuitive input interface. For applications in robotics, control is achieved by manipulating the natural curvatures of individual elements. The innovative combination of computational efficiency and physical fidelity positions DiSMech as a powerful tool for studying and advancing soft slender structures in various scientific disciplines and practical domains.