The finite element method (FEM) is a powerful modeling tool for predicting soft robots' behavior, but its computation time can limit practical applications. In this article, a learning-based approach based on condensation of the FEM model is detailed. The proposed method handles several kinds of actuators and contacts with the environment. We demonstrate that this compact model can be learned as a unified model across several designs and remains very efficient in terms of modeling since we can deduce the direct and inverse kinematics of the robot. Building upon the intuition introduced in (Ménager et al., 2023), the learned model is presented as a general framework for modeling, controlling, and designing soft manipulators. First, the method's adaptability and versatility are illustrated through optimization-based control problems involving positioning and manipulation tasks with mechanical contact-based coupling. Second, the low-memory consumption and the high prediction speed of the learned condensed model are leveraged for real-time embedding control without relying on costly online FEM simulation. Finally, the ability of the learned condensed FEM model to capture soft robot design variations and its differentiability are leveraged in calibration and design optimization applications.

The Finite Element Method (FEM) is a powerful modeling tool for predicting the behavior of soft robots. However, its use for control can be difficult for non-specialists of numerical computation: it requires an optimization of the computation to make it real-time. In this paper, we propose a learning-based approach to obtain a compact but sufficiently rich mechanical representation. Our choice is based on non-linear compliance data in the actuator/effector space provided by a condensation of the FEM model. We demonstrate that this compact model can be learned with a reasonable amount of data and, at the same time, be very efficient in terms of modeling, since we can deduce the direct and inverse kinematics of the robot. We also show how to couple some models learned individually in particular on an example of a gripper composed of two soft fingers. Other results are shown by comparing the inverse model derived from the full FEM model and the one from the compact learned version. This work opens new perspectives, namely for the embedded control of soft robots, but also for their design. These perspectives are also discussed in the paper.

Soft robot is an emergent research field which has variant promising applications. However, the design of soft robots nowadays still follows the trial-and-error process, which is not at all efficient. This paper proposes to design soft robots by pre-checking controllability during the numerical design phase. Finite-element method is used to model the dynamics of silicone soft robots, based on which the differential geometric method is applied to analyze the controllability of the points of interest. Such a verification is also investigated via model order reduction technique and Galerkin projection. The proposed methodology is finally validated by numerically designing a controllable parallel soft robot.

Obtaining an accurate mechanical model of a soft deformable robot compatible with the computation time imposed by robotic applications is often considered an unattainable goal. This paper should invert this idea. The proposed methodology offers the possibility to dramatically reduce the size and the online computation time of a finite element model (FEM) of a soft robot. After a set of expensive offline simulations based on the whole model, we apply snapshot-proper orthogonal decomposition to sharply reduce the number of state variables of the soft-robot model. To keep the computational efficiency, hyperreduction is used to perform the integration on a reduced domain. The method allows to tune the error during the two main steps of complexity reduction. The method handles external loads (contact, friction, gravity, etc.) with precision as long as they are tested during the offline simulations. The method is validated on two very different examples of FEMs of soft robots and on one real soft robot. It enables acceleration factors of more than 100, while saving accuracy, in particular compared to coarsely meshed FEMs and provides a generic way to control soft robots.