Electromagnetic Navigation Systems enable remote actuation of untethered micro and nanorobots, as well as the precise control of magnetic surgical tools for minimally invasive medical procedures. Accurate modeling of the magnetic fields generated by the electromagnets composing these systems is essential for achieving reliable and precise navigation. Existing modeling approaches either neglect nonlinear effects such as electromagnet saturation or fail to ensure that the field predictions are physically consistent. These limitations can lead to significant prediction errors, particularly in the estimation of field gradients, which directly impacts force calculations. As a result, inaccurate gradient predictions degrade force control performance, limiting the precision of magnetic actuation. In this work, we investigate physics-informed and data-driven modeling techniques to improve the accuracy of magnetic field and gradient predictions. Additionally, we introduce an approach for solving the inverse problem, developing models capable of predicting the required electromagnet currents to generate a desired magnetic field and gradient based on this approach. By incorporating physical constraints into the models, we enhance the predictive accuracy and physical consistency of the field estimates. In the experimental section, we demonstrate the benefits of these methods to enable improved force control in open-loop for untethered robots using a small-scale Electromagnetic Navigation System.

Remote magnetic navigation provides a promising approach for improving the maneuverability and safety of surgical tools, such as catheters and endoscopes, in complex anatomies. The lack of existing localization systems compatible with this modality, beyond fluoroscopy and its harmful ionizing radiation, impedes its translation to clinical practice. To address this challenge, we propose a localization method that achieves full pose estimation by superimposing oscillating magnetic fields for localization onto actuation fields generated by an electromagnetic navigation system. The resulting magnetic field is measured using a three-axis magnetic field sensor embedded in the magnetic device to be localized. The method is evaluated on a three-coil system, and simultaneous actuation and localization is demonstrated with a magnetic catheter prototype with a Hall effect sensor embedded at its tip. We demonstrate position estimation with mean accuracy and precision below 1 mm, and orientation estimation with mean errors below 2$^\circ$at 10 Hz in a workspace of 80 × 80 × 60 mm. This contribution aims to advance the clinical adoption of remote magnetic navigation in minimally invasive surgery.

In remote magnetic navigation, a magnetic navigation system is used to generate magnetic fields to apply mechanical wrenches to steer a magnetic object. This technique can be applied to navigate untethered micro- and nanorobots, as well as tethered magnetic surgical tools for minimally invasive medicine. The design and characterization of these systems have been extensively investigated over the past decade. The determination of the region in space in which these systems can operate has yet to be formalized within the research community. This region is commonly referred to as the “workspace” and constitutes a central concept for any class of robotic system. We focus on magnetic navigation systems comprised of electromagnets and propose a first set of definitions for a magnetic workspace, a methodology to determine it, and evaluation metrics to analyze its characteristics. Our methodology and tools are illustrated with several examples of planar and spatial electromagnetic magnetic navigation systems for both didactic and realistic navigation scenarios.

Variable stiffness catheters typically rely on thermally induced stiffness transitions with a transition temperature above body temperature. This imposes considerable safety limitations for medical applications. In this work, we present a variable stiffness catheter using a hybrid control strategy capable of actively heating and actively cooling the catheter material. The proposed catheter is made of a single biocompatible shape memory polymer, which significantly increases its manufacturability and scalability compared to existing designs. Potentially increased safety is obtained by ensuring a lower-risk compliant state at body temperature while maintaining higher stiffness ranges in actively controlled states. Additionally, the combined use of variable stiffness and magnetic actuation increases the dexterity and steerability of the device compared to existing robotic tools.

Remote magnetic navigation is used for the manipulation of untethered micro and nanorobots, as well as tethered magnetic surgical tools for minimally invasive medicine. Mathematical modeling of the magnetic fields generated by magnetic navigation systems is a fundamental task in the control of such tools for biomedical applications. In this article, we describe and compare several existing and newly developed methods for representations of continuous magnetic fields using interpolation in the context of remote magnetic navigation. Clinical-scale electromagnetic navigation systems feature nonlinear magnetization and magnetization interactions between electromagnets, which renders accurate magnetic field modeling challenging. We first introduce a method that can adapt existing linear models to correct for nonlinear magnetization, with similar performance to the current state-of-the-art nonlinear model. Furthermore, we present a method based on convolutional neural networks.

Electromagnetic Navigation Systems (eMNS) can be used to control a variety of multiscale devices within the human body for remote surgery. Accurate modeling of the magnetic fields generated by the electromagnets of an eMNS is crucial for the precise control of these devices. Existing methods assume a linear behavior of these systems, leading to significant modeling errors within nonlinear regions exhibited at higher magnetic fields, preventing these systems from operating at full capacity. In this paper, we use a random forest (RF) and an artificial neural network (ANN) to model the nonlinear behavior of the magnetic fields generated by an eMNS. Both machine learning methods outperformed the state-of-the-art linear multipole electromagnet model (MPEM). The RF and the ANN model reduced the root mean squared error (RMSE) of the MPEM when predicting the field magnitude by approximately 40% and 87%, respectively, over the entire current range of the eMNS. At high current regions, especially between 30 and 35 A, the field-magnitude RMSE improvement of the ANN model over the MPEM was 37 mT, equivalent to 90% error reduction. This study demonstrates the feasibility of using machine learning to model an eMNS for medical applications, and its ability to account for complex nonlinear behavior at high currents. The use of machine learning thus shows promise in developing accurate field predicting models, and ultimately improving surgical procedures that use magnetic navigation.

In this paper, the design of a new variable stiffness spherical joint for MR-compatible robotics is presented. It is based on the use of prestressed cable-driven mechanisms in singular configurations to provide large stiffness variation ranges, including zero stiffness configuration as required by the medical context. An original implementation is proposed, with a prestress adjustment system using pneumatic energy and taking advantage of multimaterial additive manufacturing. The proposed component combines compactness, MR-compatibility and is lightweight. The system is evaluated on a dedicated experimental setup with validation of the expected behavior, with in particular a very large achievable range of stiffnesses. The approach is effective for the design of such device and constitutes a novel solution for the design of variable stiffness devices with complex motions.