Modeling and Control of a Pneumatic Soft Robotic Catheter Using Neural Koopman Operators

TL;DR

This work proposes a neural network-enhanced Koopman operator framework that jointly learns the lifted space representation and Koopman operator in an end-to-end manner and investigates open-loop control strategies using neural Koopman operators to reliably reach target poses without continuous imaging feedback.

Abstract

Catheter-based interventions are widely used for the diagnosis and treatment of cardiac diseases. Recently, robotic catheters have attracted attention for their ability to improve precision and stability over conventional manual approaches. However, accurate modeling and control of soft robotic catheters remain challenging due to their complex, nonlinear behavior. The Koopman operator enables lifting the original system data into a linear "lifted space", offering a data-driven framework for predictive control; however, manually chosen basis functions in the lifted space often oversimplify system behaviors and degrade control performance. To address this, we propose a neural network-enhanced Koopman operator framework that jointly learns the lifted space representation and Koopman operator in an end-to-end manner. Moreover, motivated by the need to minimize radiation exposure during X-ray fluoroscopy in cardiac ablation, we investigate open-loop control strategies using neural Koopman operators to reliably reach target poses without continuous imaging feedback. The proposed method is validated in two experimental scenarios: interactive position control and a simulated cardiac ablation task using an atrium-like cavity. Our approach achieves average errors of 2.1 +- 0.4 mm in position and 4.9 +- 0.6 degrees in orientation, outperforming not only model-based baselines but also other Koopman variants in targeting accuracy and efficiency. These results highlight the potential of the proposed framework for advancing soft robotic catheter systems and improving catheter-based interventions.

Figures (6)

• Figure 1: Overview of soft robotic catheter applications for atrium ablation and control framework. (a) Illustrative robotic catheter ablation for atrial fibrillation. (b) Neural Koopman operator framework with model predictive control method.
• Figure 2: The diagram of neural Koopman operator framework. The original state $x_k$ is lifted by encoder $\Phi_x^e(x_k, \omega_x^e)$. And the $\tilde{u_k}$ is encoded by $\Phi_u^e(x_k, u_k,\omega_u^e)$ to construct the evolution in lifted space. Original state and input can be recovered by decoders $\Phi_x^d(\gamma(x_{k+1}), \omega_x^d)$ and $\Phi_u^d(x_k,\tilde{u_k}, \omega_u^d)$.
• Figure 3: Geometry assignment of the PCC model. (a) Single segment. (b) Dual segment of the PSRC.
• Figure 4: Experimental setup. (a) CAD design of the PSRC. (b) Fabricated PSRC indicating tip vector and base vector. (c) PSRC positioned inside an atrium model, with an overhead camera view. Colored arrows represent two bending directions and one translation direction. (d) Translation stage for precise positioning. (e) Dual syringe pumps for pressure control of bending.
• Figure 5: Modeling performance evaluated by prediction accuracy and RMSE across different models. The first row of the legend represents four models. The second row represents RMSE across x and y positions and orientations.