Stiffness Imaging with a Continuum Appendage: Real-time Shape and Tip Force Estimation from Base Load Readings

In this letter, we propose benefiting from load readings at the base of a continuum appendage for real-time forward integration of Cosserat rod model with application in configuration and tip load estimation. The application of this method is successfully tested for stiffness imaging of a soft tissue, using a 3-DOF hydraulically actuated braided continuum appendage. Multiple probing runs with different actuation pressures are used for mapping the tissue surface shape and directional linear stiffness, as well as detecting non-homogeneous regions, e.g. a hard nodule embedded in a soft silicon tissue phantom. Readings from a 6-axis force sensor at the tip is used for comparison and verification. As a result, the tip force is estimated with 0.016–0.037 N (7–20%) mean error in the probing and 0.02–0.1 N (6–12%) in the indentation direction, 0.17 mm (14%) mean error is achieved in estimating the surface profile, and 3.4–15 [N/m] (10–16%) mean error is observed in evaluating tissue directional stiffness, depending on the appendage actuation. We observed that if the appendage bends against the slider motion (toward the probing direction), it provides better horizontal stiffness estimation and better estimation in the perpendicular direction is achieved when it bends toward the slider motion (against the probing direction). In comparison with a rigid probe, $\approx \!\!10$ times smaller stiffness and $\approx \!\!7$ times larger mean standard deviation values were observed, suggesting the importance of a probe stiffness in estimation the tissue stiffness.