Robotic Needle-Tissue Interaction: Real-Time Friction and Preoperative Stiffness Estimation

Measuring needle-tissue interaction forces has traditionally been essential for estimating the needle state and ensuring patient safety, particularly in procedures involving heterogeneous and multilayered tissues. These conditions more accurately reflect real-time clinical environments, where modeling becomes more complex. While various mechanics-based models have been proposed to describe needle-tissue interactions, capturing the dynamic nature of friction remains a significant challenge. Friction is inherently nonlinear, time-dependent, and has a profound impact on procedural accuracy. This study introduces a method for identifying the dynamic friction component during needle insertion using the Generalized Maxwell Slip (GMS) model, which captures the nonlinear and rate-dependent characteristics of friction. An Online Least Squares (OLS) algorithm is employed for real-time parameter estimation. The system’s total potential energy includes bending and tensile strain energies, along with a non-conservative virtual work term from the GMS model, resulting in a reduced-order system of coupled second-order differential equations. Supporting lemmas are developed to establish the existence and harmony of the solution under frictional loading. Additionally, the approach integrates Winkler foundation and Westergard theory to model localized tissue stiffness variations.