Bilinear Model Predictive Control Framework of the OncoReach, a Tendon-Driven Steerable Stylet for Brachytherapy

Steerable needles have the potential to improve interstitial brachytherapy by enabling curved trajectories that avoid sensitive anatomical structures. However, existing modeling and control approaches are primarily developed for custom needle designs and are not directly applicable to stylets compatible with commercially available clinical needles. This paper presents a bilinear model predictive control (MPC) framework for a tendon-driven steerable stylet integrated with a standard brachytherapy needle. \textcolor{black}{A geometric bilinear model is formulated with three virtual inputs (an insertion speed and two bending rates) which are mapped to physically realizable inputs consisting of the insertion speed and the associated tendon tensions.} The approach is validated through simulations and physical insertion experiments in tissue-mimicking phantom material using image-based tip tracking. While open-loop model validation yielded estimation errors below $2$~mm, corresponding to $3\%$ of the inserted needle length, and closed-loop fixed-target tracking achieved an error as low as $1.45$~mm, corresponding to $1.7\%$ of the inserted length, experiments showed larger position errors in certain bending directions, reaching $8.3$~mm, or $7.8\%$ of the inserted length. Overall, the results demonstrate the feasibility of fixed-target positioning and moving-target trajectory tracking for clinically compatible steerable brachytherapy systems, while highlighting necessary areas for future improvements in calibration and sensing.