A Discrete Geometric Approach to Simulation of Soft Multi-limbed Robots

Because they are primarily composed of mechanically compliant and deformable materials, soft limbed robots can navigate through unstructured terrain and confined spaces without dependency on highly articulated motion and sensing. However, design and control requires a painstaking trial and error process owing to the absence of an accurate and efficient simulation and modeling tools. Here, we present a numerical simulation tool for limbed soft robots inspired by a discrete differential geometry-based computational framework that can run faster than real-time on a single thread of a contemporary desktop processor. The simulation incorporates an implicit method to account for the elasticity of the structure, contact with an uneven surface, and Coulombic friction between the soft robot limbs and ground. To validate the simulation, we build a novel, shape memory alloy driven star-shaped soft robot comprised of seven compliant limbs that can cyclically change shape through electrical Joule heating and passive cooling. Our experiments and simulations show reasonable quantitative agreement and indicate the potential role of this discrete geometric approach as a computational framework in predictive simulations for soft robot design and control.