Shape Reconstruction and Tip Force Estimation in Tendon-Driven Soft Robots Using Physics-Informed Neural Networks

This paper presents a theoretical model for the shape reconstruction of soft robots under a tip force, a tip moment, and a distributed load along the body, akin to blood flow forces acting on ablation catheters in the left atrium. The model is based on the Euler-Bernoulli beam theory and cubic Bézier curve approximation. Verification against a finite element model shows a maximum relative error below 5%. However, the average refresh rate (~1.1 Hz) falls short for clinical use, presenting a limitation. To address this, an artificial neural network (ANN) model is introduced and trained using data from the theoretical model over a range of tip forces, moments, and distributed loads. The ANN model exhibited an average refresh rate of 50 Hz, making it suitable for clinical applications. Given the importance of tip force estimation in minimally invasive surgery, an additional ANN model was developed to estimate the tip force, based on the deformed shape, tip moment, and distributed load. The model is trained and validated using rearranged data from the theoretical model and compared with in-vitro experimental results from a custom apparatus simulating blood flow interactions with ablation catheters. A strong agreement between the theoretical and experimental results was found, which confirms the model’s validity. This study underscores the potential of neural network models for accurate shape reconstruction and force estimation in soft robots, particularly in minimally invasive surgeries.