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. The gist is that an augmented Kalman filter compresses contact, friction, and modeling error into one sensor-free disturbance state, giving nominal offsetfree regulation in free space while leaving force safety to the explicit constraint.

Interaction Dynamics Formulation

The paper formulates catheter–tissue interaction dynamics by considering a planar single-segment tendon-actuated catheter where the dominant bending dynamics follow a form: M(κ)¨κ + C(κ, κ˙) ˙κ + K(κ) = u + dcat, where dcat lumps tissue contact, friction, backlash, and hysteresis. The authors reformulate this into a configuration-invariant linear interaction-dynamics model by using a partial-physics feedforward to cancel the known nominal bending dynamics. This results in a double integrator model for the error state x = [e, e˙]⊤, where e is the error in the controllable normal coordinate.

Control Architecture and Disturbance Augmentation

The control architecture consists of two layers: Layer 1 handles interaction-dynamics normalization, and Layer 2 performs predictive correction. The key configuration-invariant model is defined by the state evolution: xe˙ = Ac (const) xe + Bc(κ) Fmpc + d(t), where Ac is constant, and only the scalar gain Bc(κ) varies through Λn(κ). To handle modeling error, contact, and cardiac loading, an augmented Kalman filter estimates a disturbance state ˆd ∈ R. This leads to the Disturbance Compression Principle, where the estimator tracks only the observer-accessible low-frequency projection PD(∆) of the residual.

Predictive Optimization and Hard Constraints

A predictive interaction-dynamics QP is constructed from this augmented dynamics (Equation 9). The objective is to choose u(t) so that "e(t) → 0 in the nominal free-space limit while respecting tendon limits ulo ≤ u ≤ uhi, predicted normal-force safety Fn ≤ Fsafe, and curvature limits κlo ≤ κ ≤ κmax under bounded unknown contact, friction, and hysteresis. The constraint is enforced by bounding the corrective input Fmpc: −Fsafe ≤ Fmpc,k ≤ Fsafe," which bounds the controller-induced/predicted quasi-static normal force to leading order.

Stability and Performance Results

The stability analysis establishes that the unconstrained, disturbance-free realization recovers classical catheter impedance law as a special realization of the same interaction dynamics. Theorem 2 proves nominal stability under certain conditions, and Theorem 3 shows that if the disturbance is bounded (∥d(t)∥ ≤ ¯d), the augmented system is input-to-state stable with an error bound that scales with the unmodeled time variation of d. Simulation results show that disturbance augmentation cuts free-space approach error by 90%, and only the force-constrained controller achieves both accurate tracking (0.03 mm) and safety (peak 0.47 N), whereas the unconstrained controller drives to 0.60 N, demonstrating that offset-free motion regulation and contact-force safety are coupled interaction-dynamics objectives.

Key Contributions

The paper's main contributions include:

1. Correct single-DOF formulation: Controlling the scalar tip-normal coordinate avoids overparameterization.

2. Configuration-invariant interaction dynamics: The partial cancellation reformulates uncertain mechanics into a linear model, and the Disturbance Compression Principle allows for an offset-free guarantee on PD(∆).

3. Predictive interaction-dynamics optimization: Establishing that the unconstrained realization recovers classical impedance while the constrained realization adds offset-free rejection and explicit interaction-constraint enforcement.

4. Hard interaction-dynamics constraints: The QP enforces the predicted tip-normal force bound over the horizon through tendon transmission, together with tendon and curvature limits.

Future Work

Future work includes hardware validation, FBG-based force estimation as a direct disturbance channel, cardiacphase-aware periodic disturbance models for force regulation use, extension to multi-segment catheters with m independent tendons (an mDOF version), energy-budget augmentation toward certified passivity during aggressive contact, and a hysteresis-aware disturbance model that augments the integrating state to capture the sign-dependent (Coulomb) component of tendon-sheath friction.

The gist

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

Here are the specific improvements to AI systems that can be derived from this scientific paper, categorized by capability:

) High-Fidelity, Safety-Constrained Robotic Manipulation Systems (e.g., Surgical Robotics, Industrial Continuum Robots)

1. A control system capable of simultaneously achieving precise trajectory tracking while guaranteeing that contact forces never exceed a clinically or physically defined safety threshold (e.g., 0.5 N).

2. The AI system will employ a two-layer predictive control architecture:

Ease of implementation and robustness against model uncertainty are improved by utilizing configuration-invariant linear interaction models derived from partial-physics cancellation, which makes the underlying dynamics predictable regardless of minor material variations (hysteresis, friction).

3. The system will incorporate an augmented Kalman filter to simultaneously estimate and compress unmodeled disturbances—including contact forces, friction biases, and modeling errors—into a single disturbance state. This allows for near-perfect offset-free regulation in free space.

4. The predictive optimizer will be formulated as a Quadratic Program (QP) that explicitly incorporates the hard contact-force bound as an interaction constraint over the prediction horizon. This ensures that even when aggressively tracking a target, the physical safety limit is respected, resolving the tension between accurate tracking and force safety.

5. The system will utilize configuration-adaptive control gains: instead of using a single fixed gain for impedance control, the controller will dynamically adjust its feedback gains based on the real-time measurement of catheter curvature (via an operational-space inertia normalization factor, e.g., 1.4x variation), ensuring consistent performance across different catheter configurations (i.e., different bending states).

) Enhanced Robustness and Disturbance Rejection Systems

1. The AI system will feature a disturbance rejection mechanism based on the Disturbance Compression Principle. This principle allows the controller to ignore high-frequency, fast-changing dynamics (like transient contact impacts or cardiac motion harmonics) by projecting them onto an observer-accessible subspace, ensuring that only slowly varying disturbances are actively regulated.

2. The system will be designed to exhibit Input-to-State Stability (ISS). This means that any unmodeled dynamics or disturbances will not lead to unbounded errors in the system state, providing a formal stability guarantee against external perturbations.

3. The AI architecture will include mechanisms for distinguishing between genuine model reduction error (slowly varying, rejected by the integrator) and synthetic bias (fast transients), leading to more accurate state estimation and reduced tracking error when operating in contact scenarios.

) Advanced Model-Based Control Systems

1. The system will move beyond simple classical impedance control by treating the problem as a formal interaction dynamics regulation task, allowing it to explicitly manage the coupled objectives of position tracking and force safety within a unified optimization framework.

2. The AI system will utilize an explicit feedforward term that cancels the known nominal dynamics (bending stiffness and damping) rather than relying on model-based feedback alone, leading to faster response times and reduced reliance on inverting uncertain physical models.

In summary, the improved AI system is a predictive, safety-critical controller for continuum robots that can perform high-precision motion while maintaining explicit hard constraints on contact forces through sophisticated disturbance estimation and configuration-aware gain scheduling.