Analytical Tip Force Estimation on Tendon-driven Catheters Through Inverse Solution of Cosserat Rod Model

Tip force estimation on continuum arms is of crucial clinical importance for catheter-based procedures, i.e., catheter-based ablation therapies. In this study, an analytical solution for force estimation based on inverse Cosserat rod modeling was proposed and validated. Initially, a previously validated Bezier-based shape interpolation was used to parameterize the deformation and the kinematics and balance equations of the catheter were derived thereof. The tip force estimation problem was formulated as an inverse problem with a functional minimization technique and was solved analytically. In the end, the proposed method was experimentally tested for accuracy and computation efficiency through a series of simulations and experiments. The results showed that the estimated forces were in agreement with reference measurement with a mean-absolute error of 0.024 ± 0.020 N and a computation time of 7 ± 5 ms per frame. The exhibited performance was comparable to other studies and was in compliance with the requirements of catheter-based procedures.