A Modular Approach to Discrete Differential Geometry-based Simulation of Soft Robots*

Owing to their resemblance to natural organisms in terms of structural compliance and reversibility, soft robots can navigate through unstructured environments via interaction with the environment. A bottleneck for real-world application of such robots is the lack of accurate and efficient predictive modeling tools. Geometric and material nonlinearity of the structure, and the complex interaction with the surrounding medium, pose challenges to comprehensively understanding and predicting the movement of the robot. As a result,  soft robots are almost invariably designed and controlled through a cumbersome trial and error process. The most typical soft robots is comprised of a number of slender structures. Here, we present a numerical simulator for articulated soft robots inspired by a discrete differential geometry-based computational framework. Simulating several robotic testbeds, it runs faster than real-time on a single thread of a modern desktop processor. The simulator features an implicit approach for accounting for material elasticity, geometric nonlinearity and the motor actuation, and can easily incorporate external forces such as gravity, hydrodynamics, and magnetic forces. We explore the physics of locomotion in granular media and viscous fluids using our simulation tool and an articulated robot testbed with multiple elastic tails. Our experiments and simulations show reasonable quantitative agreement, implying that this discrete geometric approach could be used as a computational framework for predictive simulations of soft robot design and control.