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<p>The operation of magnetic soft continuum robots depends on external magnetic fields to realize deformation and motion in their flexible magnetic tips, thereby achieving desired functionalities. These magnetic tips essentially behave as flexible cantilever beams. Precise prediction of the deformation behavior in such magnetic soft cantilevers is of critical importance for the design, control, and real-world applications of these robotic systems. The current approach to designing magnetic soft cantilevers predominantly depends on experienced designers refining the design through iterative processes involving extensive simulation and experimentation. Furthermore, studying their mechanical properties and responses typically requires labor-intensive testing or costly computational simulations. Compared to traditional methods, machine learning has revolutionized magnetic soft cantilever design, enabling deformation prediction and geometric generation without prior knowledge. It also shifts the design process from a forward to an inverse approach, eliminating repetitive simulations and offering a faster, more efficient solution. In this study, we introduced a machine learning-based method for forward prediction and inverse design, specifically tailored to magnetic soft cantilever under defined boundary conditions. The forward deformation prediction was carried out using a weighted ensemble method-based multi-layer perceptron (WEM-MLP) machine learning model, followed by simulation and experimental validations. For the inverse design problem, a cascade ensemble method-based MLP (CEM-MLP) model was proposed and validated through simulation. The results confirmed the effectiveness of the proposed methods. The coefficient of determination R<sup>2</sup> for forward prediction model reached 0.9962, while R<sup>2</sup> for inverse design model was 0.9490. The well-trained machine learning model offers an alternative approach, enabling faster high-precision calculations under resource-limited conditions. This facilitates the prediction of deformation results and inverse design of magnetic soft continuum robots, offering valuable guidance for the practical application of these systems.</p>

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Machine learning-based deformation prediction and inverse design of magnetic soft cantilever using deformation simulation data

  • 期刊论文

  • 发表日期：

    2025年5月30日

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  • Zili Wang,
  • Zhaoxin Li,
  • Ding Weng,
  • Lei Chen,
  • Yuan Ma,
  • Jiadao Wang

摘要

The operation of magnetic soft continuum robots depends on external magnetic fields to realize deformation and motion in their flexible magnetic tips, thereby achieving desired functionalities. These magnetic tips essentially behave as flexible cantilever beams. Precise prediction of the deformation behavior in such magnetic soft cantilevers is of critical importance for the design, control, and real-world applications of these robotic systems. The current approach to designing magnetic soft cantilevers predominantly depends on experienced designers refining the design through iterative processes involving extensive simulation and experimentation. Furthermore, studying their mechanical properties and responses typically requires labor-intensive testing or costly computational simulations. Compared to traditional methods, machine learning has revolutionized magnetic soft cantilever design, enabling deformation prediction and geometric generation without prior knowledge. It also shifts the design process from a forward to an inverse approach, eliminating repetitive simulations and offering a faster, more efficient solution. In this study, we introduced a machine learning-based method for forward prediction and inverse design, specifically tailored to magnetic soft cantilever under defined boundary conditions. The forward deformation prediction was carried out using a weighted ensemble method-based multi-layer perceptron (WEM-MLP) machine learning model, followed by simulation and experimental validations. For the inverse design problem, a cascade ensemble method-based MLP (CEM-MLP) model was proposed and validated through simulation. The results confirmed the effectiveness of the proposed methods. The coefficient of determination R2 for forward prediction model reached 0.9962, while R2 for inverse design model was 0.9490. The well-trained machine learning model offers an alternative approach, enabling faster high-precision calculations under resource-limited conditions. This facilitates the prediction of deformation results and inverse design of magnetic soft continuum robots, offering valuable guidance for the practical application of these systems.