Beam on Foundation Modelling and Closed Loop Control of Tool to Tissue Interaction for Percutaneous Needle Steering

This paper presents a MATLAB simulated pipeline for robot assisted bevel tipped needle steering, aimed at applications such as biopsy, brachytherapy, and targeted drug delivery. It combines four established parts into one closed feedback loop: an assumed modes Euler Bernoulli beam on a Winkler elastic foundation, a nonholonomic bicycle kinematic model, duty cycle bevel steering, and a pole placement PID controller with a saturation aware integral rule. None of these four parts is new on its own. The contribution is how they are wired together: a single explicit coupling rule lets the mechanics sub model drive the real time curvature command, via one calibration constant that converts a beam computed tip slope into a curvature. This exposes something a disconnected simulation would not, that the effective plant gain changes with insertion depth, which a fixed gain PID controller cannot correct for, producing a threefold drop in weak regulation accuracy.