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.

Soft robots can operate effectively inside confined spaces because their soft bodies can adapt to accommodate the geometry around them. When they interact with the environment, the presence of contact forces can dramatically change the dynamics of the robots. If a soft robot is in contact and the contact force is not known, the control action is still targeted for a free robot. Hence the robot may perform improper actions. Because a soft robot is deformable, it is quite challenging to determine the contact forces and the system states from sensor measurements. This paper proposes an observer design to estimate the states of a fabric-reinforced inflatable soft robot as well as the external contact forces. The soft robot is represented by the disc-thread model which results in a set of ordinary differential equations (ODEs). A linear parameter-varying (LPV) system including some subsystems is formed to represent the nonlinear robot. The observer is based on the sliding mode approach and includes a set of sub-observers corresponding to the subsystems in the LPV system. The observer is validated through simulations and an experiment. The simulation results show that the observer can estimate the angular positions and their rate of changes as well as assumed contact forces with no error in steady states. The experiment results display good tracking of the robot’s configurations compared to the ground truth data from the motion tracking system.