Virtual Frame Rotation: A Novel Two-Stage Pose Estimation Scheme of Permanent Magnet Marker for Medical Applications

Permanent magnetic marker (PMM) has the potential to broaden the scope of medical robots by facilitating the localization of target points even in environments where vision-based methods cannot operate. However, conventional approaches rely on the accuracy of the modeling equations and are not adaptable to changes in the magnet's properties, which can occur due to factors like non-uniformity in the marker material or temperature fluctuations within the PMM. These constraints make it challenging to apply the PMM across diverse medical techniques. In this work, we introduce a novel two-stage PMM localization scheme, called Virtual Frame Rotation (VFR), designed to address this issue. VFR employs an approach that virtually rotates the observation frame of the Hall sensors' output vector and checks the symmetry of the magnetic field in the rotated frame. This approach allows for robust pose estimation of the condition with variance in magnetic properties, as verified by comparing its localization performance with the conventional approach in the simulation and the real-world environments with temperature variance conditions. Based on these characteristics, VFR can expand the scope of medical applications that involve changes in the properties of magnetic markers, such as the in-body localization of magnetic macro particles for hyperthermia treatment.