Physics-Informed LSTM for Shape and Contact Force Prediction of a Flexible Surgical Robot*

Abstract

Real-time morphological perception and precise end force feedback prediction of surgical robots constitute critical technical elements for ensuring safety and efficacy in complex interventional procedures such as Endoscopic Retrograde Cholangiopancreatography (ERCP). In this paper, we design a miniature flexible surgical robot (FSR) with a nested spring structure and proposed a physics-informed deep learning approach to simultaneously predict both the FSR's shape and 2D contact forces at its end-effector. The physical constraints were derived from a quasi-static model of the FSR, which is capable of characterizing persistent environmental interactions. Our method eliminates the need for end-effector sensors, not only ensuring high accuracy in both shape and contact force predictions but also maintaining consistent predictive performance under continuous environmental interactions. Experimental validation of the method revealed a high consistency between predicted values and reference data, achieving a 34.97% improvement in computational speed and a maximum prediction accuracy enhancement of 71.64% compared to conventional LSTM approaches.