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

Flexible neural electrode threads must be placed at a prescribed depth while the cortical surface moves with cardiac and respiratory pulsation. A controller tracking a fixed point in the laboratory frame cannot distinguish commanded insertion from tissue motion; the error appears as both a depth offset and relative tip--tissue velocity during contact. This paper formulates thread insertion in tissue-relative coordinates: a harmonic observer predicts delayed cortical-surface motion over the control horizon, a constrained MPC regulates the tip relative to that prediction while limiting actuator effort and lateral relative velocity, and an augmented disturbance state removes the steady offset from persistent contact force and model mismatch. In a 1-DOF MuJoCo benchmark, the controller reaches RMS relative-placement errors of 12.0\um\ free-space and 1.9\um\ in contact, versus 18.3/176.8\um\ for delayed-feedback impedance and 286.1/275.5\um\ for laboratory-frame PD -- the lower contact offset costs more peak contact force (3.43 vs.\ 2.00mN), since it drives to commanded depth rather than yielding to tissue. A 3-DOF extension reduces lateral shear velocity from 1.34 to 0.50mm/s at 2.1\um\ lateral placement error, and a feasibility-restoring soft-slack formulation keeps the shear constraint solvable under degraded sensing where a matched hard-constraint controller fails. A two-vertex Lyapunov certificate for the finite-horizon gain holds over $-40\%/{+}50\%$ reflected-mass mismatch, and the 1-DOF QP solves in under 0.4~ms at the 95th percentile. These results are a simulation-based control benchmark, not a clinical safety claim: the modeled tip is a rigid contact point, and flexible-thread mechanics, a validated force constraint, biological damage thresholds, and hardware-realistic sensing and timing remain necessary before deployment.

Steerable catheters are the primary tool for cardiac electrophysiology (EP) procedures including radiofrequency ablation, where the tip must be positioned precisely at target tissue while maintaining controlled, stable contact. The central control problem is therefore not merely tip tracking and not merely force regulation; it is the regulation of catheter--tissue interaction dynamics. The interaction state must encode how the tip moves relative to tissue, how persistent friction and contact forces bias that motion, and how safety limits reshape what motion is physically allowable. Existing methods regulate these interaction dynamics through different mechanisms. Classical impedance control~\cite{hogan1985} shapes the tip port as a virtual mechanical impedance $Z(s) = M_d s^2 + D_d s + K_d$, providing passive compliance without an explicit contact model. Three complementary design requirements motivate the present formulation: (i)~an explicit force-related constraint, (ii)~compensation for steady error under persistent loading, and (iii)~a prediction model that can incorporate trajectory and actuator information.

Reliable estimation of surgical needle 3D position and orientation is essential for autonomous robotic suturing, yet existing methods operate almost exclusively under stereoscopic vision. In monocular endoscopic settings, common in transendoscopic and intraluminal procedures, depth ambiguity and rotational symmetry render needle pose estimation inherently ill-posed, producing a multimodal distribution over feasible configurations, rather than a single, well-grounded estimate. We present PinPoint, a probabilistic variational inference framework that treats this ambiguity directly, maintaining a distribution of pose hypotheses rather than suppressing it. PinPoint combines monocular image observations with robot-grasp constraints through analytical geometric likelihoods with closed-form Jacobians. This framework enables efficient Gauss-Newton preconditioning in a Stein Variational Newton inference, where second-order particle transport deterministically moves particles toward high-probability regions while kernel-based repulsion preserves diversity in the multimodal structure. On real needle-tracking sequences, PinPoint reduces mean translational error by 80% (down to 1.00 mm) and rotational error by 78% (down to 13.80°) relative to a particle-filter baseline, with substantially better-calibrated uncertainty. On induced-rotation sequences, where monocular ambiguity is most severe, PinPoint maintains a bimodal posterior 84% of the time, almost three times the rate of the particle filter baseline, correctly preserving the alternative hypothesis rather than committing prematurely to one mode. Suturing experiments in ex vivo tissue demonstrate stable tracking through intermittent occlusion, with average errors during occlusion of 1.34 mm in translation and 19.18° in rotation, even when the needle is fully embedded.