Direct and inverse modeling of soft robots by learning a condensed FEM model (2307.11408v1)

Abstract: 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.

• The paper introduces a compact FEM representation that efficiently captures nonlinear compliance in actuator and effector spaces.
• It employs a white-box learning approach using an MLP to create a differentiable compliance matrix for direct and inverse kinematics.
• Simulations on a diamond-like structure and a soft gripper validate the method's real-time performance and practical control applications.

Analyzing Soft Robot Modeling through Condensed FEM Framework

The paper entitled "Direct and inverse modeling of soft robots by learning a condensed FEM model" presents an approach to enhance the modeling and control of soft robots by leveraging a condensed Finite Element Method (FEM) representation. This paper aligns with ongoing efforts to simplify the computational demands associated with soft robotic control, which have traditionally required extensive expertise in numerical computation and optimization.

Core Contributions

The key contribution of this work is the introduction of a compact mechanical representation based on the FEM model, capable of robustly capturing the nonlinear compliance data in the actuator/effector space. Such data is distilled into a condensed compliance matrix, which is instrumental in enabling fast and accurate direct and inverse kinematics modeling through machine learning techniques, particularly with the use of a MultiLayer Perceptron (MLP). The proposed method contrasts existing solutions by integrating both mechanical and learning-based approaches, thus facilitating real-time modeling and control without exhaustive computational overhead.

Theoretical Foundations and Methodology

The methodology adopted in this paper is rooted in the quasi-static behavior of soft robots captured through the FEM, particularly focusing on the compliance matrices that link actuator efforts to effector displacements. The authors define the compliance matrix $W$ as a pivotal construct that succinctly represents the mechanical relationship between constraints in the robot's actuator and effector spaces. The matrix $W$ is learned using MLPs, providing a differentiable model that can predict the required compliance configurations based on initial conditions and actuation states.

A notable aspect of this paper is its employment of a "white box" learning approach, wherein the structure of the mechanical model is used to guide the learning process, improving the interpretability and applicability of the learned representation. This approach contrasts with the traditional "black box" methods, which often lack transparency regarding the underlying physical behavior of the model.

Empirical Validation

The efficacy of the proposed compact representation is validated through simulation on two soft robotic systems: a diamond-like structure actuated by cables and a soft gripper composed of two fingers. The results illustrate the model's capability to handle direct and inverse kinematics effectively, with the learned models showing significant accuracy in simulating the physical behavior of the robots in comparison to their full FEM counterparts. Control tasks executed with the learned models closely match those using the complete FEM model, validating the proposed approach's robustness.

Implications and Future Directions

The paper opens avenues for practical applications in the embedded control systems of soft robots, offering a highly computationally efficient alternative to traditional FEM models. The implications stretch beyond control to potentially influence the design process of soft robotics, wherein the compact model could enable rapid prototyping and adaptation. Moreover, the differentiable nature of the learned model presents opportunities for integration into model-based reinforcement learning frameworks, paving the way for advanced control strategies without the high computational cost of full FEM simulations.

Future research, as suggested by the authors, could focus on expanding the framework to handle dynamic behaviors and contacts with the environment, potentially incorporating more sophisticated neural networks such as Graph Neural Networks (GNNs) to accommodate variable constraint interactions. Furthermore, addressing the dimensionality challenges associated with scaling to more complex actuators or entire robotic assemblies represents another promising direction.

In conclusion, this paper makes a significant technical contribution by proposing a learning-based condensed FEM model that significantly eases the computational challenges of soft robot control and design. The approach maintains high fidelity in modeling while allowing for real-time applications, marking a notable step forward in the domain of soft robotics.