Modeling the dynamics of soft robots by discs and threads

In this paper, we propose a new tractable ordinary differential equation formulation for dynamic simulation of fabric- reinforced inflatable soft robots. The method performs a lumped-parameter discretization of the continuum robot into discrete discs (inertia), spring elements, and threads (representing the inextensible fabric reinforcement). Using the repetition in the structure of the Lagrangian formulation of the dynamic equations of motion, a method is developed that outputs machine- readable analytical expressions for the equations of motion. The method does not require symbolic computation of derivatives. The recursive nature allows us to scale the model to an arbitrary number N discs, and can represent buckling, twisting, and pleating that is commonly seen in very soft robots. The expressions generated were validated against manually-derived equations of motion for the two-disc case using both Lagrangian and Newton-Euler means. A simulation environment which parses and evaluates the analytical expressions generated at run-time was used to numerically integrate and predict the response of a four-disc example robot. Trajectories observed varied smoothly and plausibly predicted the behavior envisioned in robots like these.