Regression-Based 3D Shape Monitoring in a Flexible Structure with Helically-Coiled Optical Fiber

This work presents an innovative optical fiber macrobend sensor for monitoring the shape of a flexible structure. The system integrates a helically embedded fiber along the axis of a cylindrical elastomeric body. Deformations of this structure modify the bending geometry of the fiber, resulting in spectral changes in the transmitted light. The transmission spectrum from 475 nm to 750 nm serves as input data for shape reconstruction aided by artificial intelligence. Five specific points along the structure were tracked using a video-based system, allowing the creation of reference datasets for supervised learning. Two machine learning algorithms, Support Vector Regression and XGBoost Regression, were compared in terms of their ability to predict the $(x,y,z)$ spatial coordinates of the five monitored points. Support Vector Regression provided the best trade-off between prediction accuracy and computational efficiency, achieving mean absolute errors of up to 10% of the maximum displacement of each monitored point in the x and y coordinates, while also requiring the shortest training time. Hence, the Support Vector Regression model was selected to generate three-dimensional reconstructions of the structure. The sensor features standard telecommunication fiber, cost-effective and simple fabrication, and broadband operation in the visible spectral range, with potential applications in shape sensing for flexible robotic systems.