Force Estimation With Concentric-Tube Robots for Surgical Palpation

Abstract

This paper presents the design, modeling, and experimental verification of a deflection-based force-sensing probe in a concentric-tube robot for palpation during robotic surgery. The proposed method leverages the inherent elastic compliance of the robot and a quasi-static Cosserat rod model to estimate contact forces from real-time tip deflections measured by a 5-DOF magnetic tracker, eliminating the need for distal force sensors. The system was experimentally validated on the Virtuoso Endoscopy System (Virtuoso Surgical, Nashville, TN) across multiple palpation locations and directions, including experiments on compliant tissue phantoms. The proposed method achieved a mean absolute force error of approximately 0.05 N, evaluated using a leave-one-group-out cross-validation scheme across palpation locations. Simulation studies using a real-time deformable-tissue model further demonstrate the tool’s potential for automated tissue stiffness mapping, which is further demonstrated by stiffness mapping a tissue phantom to localize an embedded simulated tumor. These results establish a compact, sensor-efficient, and accurate framework for model-based force sensing in continuum robotic palpation, providing a foundation for future clinical applications in minimally invasive surgery.