Expanding the Workspace of Electromagnetic Navigation Systems Using Dynamic Feedback for Single- and Multi-agent Control

TL;DR

The paper investigates electromagnetic navigation systems (eMNS) and demonstrates that system-level control can substantially expand the available magnetic workspace by reducing actuation currents. It introduces five architectural ingredients—motion-centric torque/force objectives, energy-optimal current allocation, real-time pose estimation, dynamic feedback, and high-bandwidth hardware—and validates them across single- and multi-agent scenarios on OctoMag and Navion platforms. A core finding is that torque/force-based control with minimum-energy allocation achieves up to two orders of magnitude lower currents than field-alignment while maintaining performance, thereby expanding usable distances from the coils (e.g., up to 50 cm with Navion). The study provides a rigorous comparison between the two paradigms, introduces a formal workspace analysis with Feasibility Margin metrics, and presents the first independent stabilization of two identical 3D inverted pendulums in a shared magnetic workspace, highlighting the practical impact for scalable clinical magnetic manipulation.

Abstract

Electromagnetic navigation systems (eMNS) enable a number of magnetically guided surgical procedures. A challenge in magnetically manipulating surgical tools is that the effective workspace of an eMNS is often severely constrained by power and thermal limits. We show that system-level control design significantly expands this workspace by reducing the currents needed to achieve a desired motion. We identified five key system approaches that enable this expansion: (i) motion-centric torque/force objectives, (ii) energy-optimal current allocation, (iii) real-time pose estimation, (iv) dynamic feedback, and (v) high-bandwidth eMNS components. As a result, we stabilize a 3D inverted pendulum on an eight-coil OctoMag eMNS with significantly lower currents (0.1-0.2 A vs. 8-14 A), by replacing a field-centric field-alignment strategy with a motion-centric torque/force-based approach. We generalize to multi-agent control by simultaneously stabilizing two inverted pendulums within a shared workspace, exploiting magnetic-field nonlinearity and coil redundancy for independent actuation. A structured analysis compares the electromagnetic workspaces of both paradigms and examines current-allocation strategies that map motion objectives to coil currents. Cross-platform evaluation of the clinically oriented Navion eMNS further demonstrates substantial workspace expansion by maintaining stable balancing at distances up to 50 cm from the coils. The results demonstrate that feedback is a practical path to scalable, efficient, and clinically relevant magnetic manipulation.

Figures (14)

• Figure 1: We balance two 3D inverted pendulums simultaneously within the same magnetic workspace, leveraging the magnetic field created by the OctoMag eMNS. Because both pendulums are identical, independent actuation under a global field requires exploiting the nonlinearity of the magnetic field. This setup is used as an experimental platform to compare different strategies for multi-agent control. Each inverted pendulum system includes an arm driven by the external magnetic field and a non-magnetic pendulum. Balancing two inverted pendulums within the same magnetic workspace is challenging due to coupling effects not only between each coil and the permanent magnets, but also between the magnets themselves.
• Figure 2: The figure highlights an inverted-pendulum balancing on a magnetically driven arm controlled by the clinically-ready Navion eMNS. While the arm is moved manually through space (see accompanying video ), a closed-loop optimal-energy controller continuously transfers magnetic energy into the actuator’s motion with very high efficiency, so the pendulum remains stable even several coil diameters away from the coils. The feedback strategy therefore expands the eMNS’s effective electromagnetic workspace well beyond what open-loop control can achieve. In this setup, instead of connecting the actuator and inverted pendulum through a spherical joint, the pole tip is balanced directly on a (non-magnetic) 3D-printed support plate.
• Figure 3: Schematic of orientation conventions for the multi-agent platform. Each pendulum–actuator unit has four DOFs: actuator tilts $(\alpha_i,\beta_i)$ and pendulum tilts $(\varphi_i,\theta_i)$, with $i\in\{1,2\}$ for left/right. The pendulums are separated by $\approx\unit[6.5]{cm}$. Masses: actuator rod $m$, pendulum rod $M$, spherical joint $m_\mathrm{j}$, magnets $m_\mathrm{m}$. Lengths: actuator $\ell$, pendulum $L$, and $\ell_\mathrm{m}$ (distance from magnet centers to the pivot). Figure adapted from zughaibi2024balancing.
• Figure 4: Block diagram illustrating how open-loop field-alignment can be interpreted as a magnetic field acting as a proportional controller. The diagram is mathematically equivalent to the linearized dynamics in \ref{['eq:line_eom_actuator_P_ctrl']} and \ref{['eq:line_eom_actuator_field_based']}. In this formulation, the input $u_\alpha$ parameterizes the orientation of the magnetic field vector. Due to the proportional-like nature of the magnetic torque, the dipole naturally tends to align with the applied field direction. Open-loop field-alignment is commonly used in electromagnetic navigation due to its intuitive nature. However, viewing it from a control systems perspective clarifies both its capabilities and inherent limitations.
• Figure 5: Closed-loop control architecture for field-alignment control a) and torque-based control with minimum-energy allocation b), used for stabilizing the single 3D inverted pendulum. The key difference lies in the allocation strategy: while the field-alignment approach does not account for the current orientation of the magnetic dipole, the torque-based method explicitly requires the dipole's orientation in order to compute the corresponding currents. The setpoints $\alpha_\mathrm{SP}$ and $\beta_\mathrm{SP}$ are mapped to the corresponding state vectors using $\mathrm{\Psi}_{x, \alpha}: \alpha_\mathrm{SP} \mapsto \alpha_\mathrm{SP}0\dot{\alpha}_\mathrm{SP}0 ^\top$, and analogously for $\beta_\mathrm{SP}$. Integral control is applied only to the angles $\alpha$ and $\beta$, i.e. using the gain matrix $\bm{\mathrm{K}}_{\mathrm{I}} = k_\mathrm{I} \bm{\mathrm{I}}^{2 \times 2} \otimes \operatorname{diag}\{ 1000 \}$. For the field-alignment approach, the gradients are set to ${\bm{g}} = 0$. In multi-task applications, the overall architecture remains decoupled, though the allocation strategy is adjusted accordingly.