Modeling and Control of a Pneumatic Soft Robotic Catheter Using Neural Koopman Operators
Authors: Yiyao Yue, Noah Barnes, Lingyun Di, Olivia Young, Ryan D. Sochol, Jeremy D. Brown, Axel Krieger
Organizations: Laboratory for Computational Sensing and Robotics, Johns Hopkins University, Baltimore, MD, USA. · Department of Mechanical Engineering, Johns Hopkins University, Baltimore, MD, USA. · Department of Mechanical Engineering, University of Maryland, College Park, MD, USA.
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 & tables
Fig. 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.
Fig. 2: The diagram of neural Koopman operator framework. The original state xk is lifted by encoder Φxe(xk,ωxe) . And the uk~ is encoded by Φue(xk,uk,ωue) to construct the evolution in lifted space. Original state and input can be recovered by decoders Φxd(γ(xk+1),ωxd) and Φud(xk,uk~,ωud) .
Koopman matrices A,B , encoders Φxe,Φue ,
decoders Φxd,Φud initial state x0 ,
desired target xides , control steps K ,
cost matrices Q,R , horizon R
Algorithm 1 Neural Koopman MPC (Open-loop)
Fig. 3: Geometry assignment of the PCC model. (a) Single segment. (b) Dual segment of the PSRC.
Fig. 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.
Fig. 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.
Method
AVG
STD
MAX
Acc(1.5)
Acc(3.5)
NNKM
0.7
0.4
1.2
100.00%
100.00%
LNKM
2.0
0.9
3.1
50.00%
83.33%
MBKM
4.1
1.3
6.6
0.00%
16.67%
SSM
8.0
2.8
11.9
0.00%
0.00%
TABLE I: Results of Experiment 1: Euclidean distance error statistics (unit: mm). Two accuracy values are reported with thresholds σ1=1.5 mm and σ2=3.5 mm.
Fig. 6: Real-world experimental results. (a) Exp. 1: successful interactive position control examples using the NINK model. (b) Exp. 1: failed trial examples using other models. (c) Exp. 2: definition of position and orientation errors. (d) Exp. 2: intermediate result at Target 2 before moving the linear stage. (e) Exp. 2: Successful pose control examples. (f) Exp. 2: Distribution of position errors for each target. (g) Exp. 2: Distribution of angular errors for each target. Abbreviations: Nonlinear Input Neural Koopman + MPC(NNKM); Linear Input Neural Koopman + MPC(LNKM); Monomial Basis Koopman + MPC(MBKM); State-Space + MPC(SSM).
Method
AVG pos
STD pos
AVG ori
STD ori
Time(s)
NNKM
2.1
0.4
4.9
0.6
54.2
LNKM
4.0
0.7
8.0
1.4
58.9
MBKM
4.9
1.2
15.1
2.9
71.3
SSM
6.8
2.1
17.9
3.6
76.3
PCC
5.0
0.7
11.8
1.0
57.1
TABLE II: Results of Experiment 2: Overall position (unit: mm) and orientation (unit: deg) errors, and average time cost.
Robotic endovascular intervention uses robotic systems to navigate vascular instruments and perform procedures with greater precision, control, or autonomy.
Knee rehabilitation plays a critical role in restoring patients' mobility and functional independence. Traditional rigid rehabilitation exoskeletons are often bulky and cumbersome to wear, whereas soft pneumatic exoskeletons offer lightweight, wearable, and intrinsically compliant solutions that are better suited for human--robot interaction. However, achieving precise motion control for soft exoskeletons remains challenging due to the difficulty of accurately modeling pneumatic actuators and the patient-specific human--robot coupled dynamics during rehabilitation training. To address these challenges, this paper proposes a Koopman-based Model Predictive Control (KMPC) framework for soft knee rehabilitation exoskeletons. The nonlinear human--robot coupled system is represented through a lifted linear Koopman model, enabling predictive control with explicit handling of constraints. In addition to actuation commands used to control valves and pumps, electromyography (EMG) signals are incorporated as system inputs, allowing the Koopman model to capture voluntary neuromuscular contribution and individual neuromuscular characteristics. Experimental results on both healthy participants and patients demonstrate that the proposed framework improves model prediction accuracy and effectively captures subject-specific behaviors, thereby supporting EMG-informed subject-specific assistance within the tested seated knee-rehabilitation setting. Compared with conventional Proportional--Integral--Derivative (PID) control, the proposed KMPC approach achieves lower tracking errors and reduced actuation effort in both passive and active rehabilitation modes. Additional comparisons with Iterative Learning Control (ILC) further validate the tracking performance of the proposed controller.
Junxiang Wang, Han Zhang, Zehao Wang +3
School of Automation and Intelligent Sensing, Institute of Medical Robotics, Shanghai Jiao Tong University, and Key Laboratory of System Control and Information Processing, Ministry of Education of China, Shanghai 200240, China · Seventh Affiliated Hospital, SunYat-sen University, Shenzhen 510275, China
Multi-segment soft robotic arms can continuously reconfigure their body shapes for safe interaction, but tip control alone is insufficient for constrained-space tasks. Therefore, shape control is a more important task for multi-segment soft arms than tip control, but remains challenging due to the high dimensionality and nonlinear dynamics of continuum deformation. In existing work, shape control accuracy is defined by the error in the global frame (global shape error). For multi-segment soft arms, using only global shape error as the control objective is insufficient, as segment coupling, gravity-induced loading, and inertial effects become more significant. This difficulty increases with the number of segments. In this paper, we present a Koopman-based model predictive control framework that combines global and local observables, enabling real-time shape control on multi-segment soft robotic arms. The framework is evaluated through numerical and physical experiments. Numerical experiments demonstrate the scalability of the proposed controller by achieving shape control on robots with up to 10 independently actuated segments. The physical experiments demonstrate that the controller is capable of (1) real-time shape control of 3- and 5-segment robotic arms with tip speeds up to 0.6 m/s, (2) robust tracking without retraining, including distal payloads up to 400g and recovery from a 7N lateral disturbance, and (3) the potential for future inspection applications through a confined-space demonstration. These results demonstrate that the proposed framework enables dynamic, scalable, and accurate real-time shape control on multi-segment soft robotic arms.
Controlling robots with strongly nonlinear, high-dimensional dynamics remains challenging, as direct nonlinear optimization with safety constraints is often intractable in real time. The Koopman operator offers a way to represent nonlinear systems linearly in a lifted space, enabling the use of efficient linear control. We propose a data-driven framework that learns a Koopman embedding and operator from data, and integrates the resulting linear model with the Safe Set Algorithm (SSA). This allows the tracking and safety constraints to be solved in a single quadratic program (QP), ensuring feasibility and optimality without a separate safety filter. We validate the method on a Kinova Gen3 manipulator and a Go2 quadruped, showing accurate tracking and obstacle avoidance.
Sebin Jung, Abulikemu Abuduweili, Jiaxing Li +1
Robotics Institute, Carnegie Mellon University, Pittsburgh, PA.