Learning-Based Modeling of Soft Actuators Using Euler Spiral-Inspired Curvature (2504.18692v1)

Abstract: Soft robots, distinguished by their inherent compliance and continuum structures, present unique modeling challenges, especially when subjected to significant external loads such as gravity and payloads. In this study, we introduce an innovative data-driven modeling framework leveraging an Euler spiral-inspired shape representations to accurately describe the complex shapes of soft continuum actuators. Based on this representation, we develop neural network-based forward and inverse models to effectively capture the nonlinear behavior of a fiber-reinforced pneumatic bending actuator. Our forward model accurately predicts the actuator's deformation given inputs of pressure and payload, while the inverse model reliably estimates payloads from observed actuator shapes and known pressure inputs. Comprehensive experimental validation demonstrates the effectiveness and accuracy of our proposed approach. Notably, the augmented Euler spiral-based forward model achieves low average positional prediction errors of 3.38%, 2.19%, and 1.93% of the actuator length at the one-third, two-thirds, and tip positions, respectively. Furthermore, the inverse model demonstrates precision of estimating payloads with an average error as low as 0.72% across the tested range. These results underscore the potential of our method to significantly enhance the accuracy and predictive capabilities of modeling frameworks for soft robotic systems.

• The paper presents a learning-based framework using Euler spiral-inspired curvature representations to model soft actuators under external forces, employing neural networks for efficient shape and payload prediction.
• Extensive experimental validation shows the framework achieves low average positional prediction errors (e.g., 1.93% at the tip) and accurately estimates payloads with an average error of only 0.72%.
• This computationally efficient modeling approach significantly advances soft robotics by enabling more accurate real-time control and potentially extending to multi-segment or 3D applications.

Learning-Based Modeling of Soft Actuators Using Euler Spiral-Inspired Curvature

In this paper, the authors present an advanced modeling framework for soft actuators based on Euler spiral-inspired curvature representations. The inherent compliance and complex shapes of soft robots pose significant challenges, particularly in modeling their behavior under substantial external forces like payloads and gravity. To address these challenges, the authors have leveraged machine learning techniques to develop forward and inverse models that accurately predict deformations and estimate payloads of fiber-reinforced pneumatic bending actuators.

Methodological Overview

The paper introduces a data-driven approach employing Euler spiral-inspired shape representations that express the curvature as a polynomial function of arc length. This formulation enables compact and efficient parameterization, contrasting more traditional approaches requiring complex partial differential equations or intensive computations typically associated with variable curvature (VC) modeling. By applying neural networks in the form of multilayer perceptrons (MLPs), the authors have developed models capable of capturing the nonlinear characteristics of soft actuators subjected to external forces.

The forward model predicts the actuator’s shape based on given actuation pressures and payloads, while the inverse model deduces the payload from known actuator shapes and pressure inputs. A unique application of $G^1$ Hermite interpolation facilitates the extraction of the curvilinear parameters essential for the shape representation, effectively solving the problem of obtaining accurate curvature measurements.

Experimental Validation and Results

Extensive experimental validation underscores the utility and precision of the proposed framework. The paper reports low average positional prediction errors of 3.38%, 2.19%, and 1.93% of the actuator length at the one-third, two-thirds, and tip positions, respectively, marking a significant enhancement in predictive accuracy compared to conventional modeling techniques. Furthermore, the inverse model achieves remarkable precision, estimating payloads with an average error as low as 0.72%. These results indicate the efficacy of the augmented Euler spiral-based model in providing an improved approximation of the actuator shape under varying pressures and payloads.

Implications and Future Directions

The proposed modeling approach substantially advances the field of soft robotic systems, enabling more accurate and computationally efficient descriptions of complex robotic shapes and behaviors. Implementing models that require lower computational resources may facilitate real-time applications in soft robotics control and interactive operations where quick and reliable predictions are critical.

Although this paper focuses on a single-segment pneumatic bending actuator, its implications potentially extend to multi-segment continuum arms and more general deformations in three-dimensional settings. Future research could explore integrating dynamic considerations into the models and developing learning-based controllers that harness these predictive capabilities to enhance the performance of soft robotic systems and their interactions with environments.

In summary, the authors provide an instrumental framework that bridges modeling accuracy with computational efficiency, leveraging machine learning to foster advancements in the soft robotics domain. The research sets a foundation for continued exploration into more sophisticated control strategies and adaptive robotic systems.