Interaction Dynamics Modeling and Predictive Control for Safe Steerable Catheter--Tissue Interaction

Safe steerable catheter control is fundamentally a problem of interaction dynamics: the tip must follow a planned motion, remain compliant against moving tissue, reject friction and hysteresis, and respect a clinically meaningful never-exceed contact-force bound.

We formulate catheter--tissue interaction dynamics in the scalar tip-normal coordinate of a single-segment single-tendon catheter.

A partial-physics feedforward cancels only the reliable nominal bending dynamics, exposing a configuration-invariant linear interaction-dynamics model whose input gain varies through the scalar catheter inertia.

A predictive optimizer then regulates this interaction state subject to hard contact-force, tendon-force, and curvature constraints.

An augmented Kalman filter compresses contact, friction, and modeling error into one sensor-free disturbance state, giving nominal offset-free regulation in free space while leaving force safety to the explicit constraint.

The unconstrained and disturbance-free limit recovers classical catheter impedance as a special realization of the same interaction dynamics, rather than as the main design object.

In a MuJoCo distributed-compliance simulation of an eight-link tendon-driven catheter, disturbance augmentation cuts free-space approach error by 90\%, and only the force-constrained predictive interaction-dynamics controller reconciles tracking with the 0.5\,N bound: the unconstrained controller drives contact force to 0.60\,N against a penetrating target, while the constrained one holds 0.47\,N at identical tracking.

These results show that offset-free motion regulation and contact-force safety are coupled interaction-dynamics objectives, and that the explicit predictive constraint resolves their tension under stiff tissue contact.

The bound also holds under $0.5$\,mm, $1.2$\,Hz cardiac motion.

Hardware validation is future work.