Preview-Based Relative-Motion Control of an Insertion Tool for Neural-Thread Placement in Pulsating Tissue

Abstract

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.\ 2.00~mN), since it drives to commanded depth rather than yielding to tissue. A 3-DOF extension reduces lateral shear velocity from 1.34 to 0.50~mm/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.