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 nonlinear 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.

翻译：有限元法（FEM）是预测软体机器人行为的有力建模工具。然而，对于非数值计算专业领域的研究者来说，将其用于控制可能较为困难：这需要优化计算以实现实时性。本文提出一种基于学习的方法，以获得紧凑但足够丰富的力学表征。我们的选择基于执行器/效应器空间中的非线性柔顺数据，这些数据来自有限元模型的压缩过程。我们证明，该紧凑模型可通过合理数量的数据学习得到，同时具有极高的建模效率，因为可由此推导出机器人的正向与逆向运动学。我们还展示了如何将单独学习得到的若干模型进行耦合，特别是在一个由两个软体手指组成的夹爪实例上。其他结果则通过对比全阶有限元模型推导出的逆模型与紧凑学习版本所构建的逆模型来呈现。这项工作为软体机器人的嵌入式控制及其设计开辟了新前景，本文亦对这些前景进行了探讨。