Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Fluoroscopy-Constrained Magnetic Robot Control via Zernike-Based Field Modeling and Nonlinear MPC

Xinhao Chen, Hongkun Yao, Anuruddha Bhattacharjee, Suraj Raval, Lamar O. Mair, Yancy Diaz-Mercado, Axel Krieger

TL;DR

This work tackles the challenge of precise magnetic actuation under fluoroscopy-like feedback conditions by introducing a Zernike-polynomial-based magnetic-field model and integrating it into a nonlinear model predictive control framework augmented with a Kalman filter. The method directly computes coil currents from pose targets, accounts for hardware constraints, and provides analytic field gradients for efficient optimization. Experimental validation in 3D-printed and spine phantom environments demonstrates submillimeter tracking accuracy (e.g., RMS position ~1.18 mm) and safe margin maintenance near anatomical boundaries despite low-rate, noisy feedback. The results indicate strong potential for clinically relevant, fluoroscopy-constrained magnetic navigation and targeted drug delivery, with clear avenues for extending to 3D motion, lighter hardware, and true fluoroscopic tracking in future work.

Abstract

Magnetic actuation enables surgical robots to navigate complex anatomical pathways while reducing tissue trauma and improving surgical precision. However, clinical deployment is limited by the challenges of controlling such systems under fluoroscopic imaging, which provides low frame rate and noisy pose feedback. This paper presents a control framework that remains accurate and stable under such conditions by combining a nonlinear model predictive control (NMPC) framework that directly outputs coil currents, an analytically differentiable magnetic field model based on Zernike polynomials, and a Kalman filter to estimate the robot state. Experimental validation is conducted with two magnetic robots in a 3D-printed fluid workspace and a spine phantom replicating drug delivery in the epidural space. Results show the proposed control method remains highly accurate when feedback is downsampled to 3 Hz with added Gaussian noise (sigma = 2 mm), mimicking clinical fluoroscopy. In the spine phantom experiments, the proposed method successfully executed a drug delivery trajectory with a root mean square (RMS) position error of 1.18 mm while maintaining safe clearance from critical anatomical boundaries.

Fluoroscopy-Constrained Magnetic Robot Control via Zernike-Based Field Modeling and Nonlinear MPC

TL;DR

This work tackles the challenge of precise magnetic actuation under fluoroscopy-like feedback conditions by introducing a Zernike-polynomial-based magnetic-field model and integrating it into a nonlinear model predictive control framework augmented with a Kalman filter. The method directly computes coil currents from pose targets, accounts for hardware constraints, and provides analytic field gradients for efficient optimization. Experimental validation in 3D-printed and spine phantom environments demonstrates submillimeter tracking accuracy (e.g., RMS position ~1.18 mm) and safe margin maintenance near anatomical boundaries despite low-rate, noisy feedback. The results indicate strong potential for clinically relevant, fluoroscopy-constrained magnetic navigation and targeted drug delivery, with clear avenues for extending to 3D motion, lighter hardware, and true fluoroscopic tracking in future work.

Abstract

Magnetic actuation enables surgical robots to navigate complex anatomical pathways while reducing tissue trauma and improving surgical precision. However, clinical deployment is limited by the challenges of controlling such systems under fluoroscopic imaging, which provides low frame rate and noisy pose feedback. This paper presents a control framework that remains accurate and stable under such conditions by combining a nonlinear model predictive control (NMPC) framework that directly outputs coil currents, an analytically differentiable magnetic field model based on Zernike polynomials, and a Kalman filter to estimate the robot state. Experimental validation is conducted with two magnetic robots in a 3D-printed fluid workspace and a spine phantom replicating drug delivery in the epidural space. Results show the proposed control method remains highly accurate when feedback is downsampled to 3 Hz with added Gaussian noise (sigma = 2 mm), mimicking clinical fluoroscopy. In the spine phantom experiments, the proposed method successfully executed a drug delivery trajectory with a root mean square (RMS) position error of 1.18 mm while maintaining safe clearance from critical anatomical boundaries.
Paper Structure (14 sections, 11 equations, 10 figures, 2 tables)

This paper contains 14 sections, 11 equations, 10 figures, 2 tables.

Table of Contents

  1. Introduction
  2. Methods
  3. Electromagnetic System and Magnetic Agents
  4. Zernike-Based Magnetic Field & Gradient Modeling
  5. NMPC and Kalman Filter Based Control
  6. Comparative Control Methods
  7. Tracking Algorithm and Mimic Fluroscopy Feedback
  8. Experiments and Results
  9. NMPC Pose Prediction Accuracy Test
  10. Errors vs Tracking Rate
  11. Errors vs Tracking Noise
  12. Errors vs Tracking Rate Under Fixed Noise Level
  13. Spine Phantom Experiment
  14. Discussion and Conclusion

Figures (10)

  • Figure 1: (a) Electromagnetic coil system used in this study. The experimental workspace (yellow square) is centered between the coil stacks. (b) Spine phantom workspace imaged with an optical camera (left) and fluoroscopy X-rays (right). The robot agent is visible in both. (c) Robotic agents evaluated, including a drug-delivery capsule that can be filled with liquid medication.
  • Figure 2: (a) The spine structure in sagittal (longitudinal) plane. (b) The spine structure in transverse (horizontal) plane. nagel2018spinal
  • Figure 3: (a) CAD model of a human vertebral segment sectioned in the sagittal plane. (b) Spine phantom fabricated from ABS, agarose gel, and a glycerin–water solution. The epidural space is indicated by purple lines.
  • Figure 4: (a) Mean absolute error (MAE) and $R^2$ score of Zernike model with different polynomial order. (b) FEA-computed magnetic-field magnitude for a small coil at unit current (coil located at the bottom of the figure). (c) Absolute fitting-error distribution for the Zernike model under the same condition.
  • Figure 5: Flow chart of the proposed control method
  • ...and 5 more figures