Utilizing Field Gradient Measurements for Object Tracking in Permanent Magnet Based Manipulation Systems

Advancements in magnetically actuated medical instruments have led to the development of sophisticated systems that manipulate magnetic fields within the body to control surgical instruments. A prominent approach involves the use of large external permanent magnets (EPMs), offering a high workspace and potential for full-rank magnetic manipulation. For clinical applications, precise localization of these instruments is critical. Previous studies have used single-field sensors and accelerometers while applying complex external fields (which are not used for actuation) to localize. This article explores an alternative approach by incorporating multiple field sensors where the field gradients are estimated through finite differences. The presented approach effectively addresses the significant issue of workspace singularities, allowing for accurate six-degree-of-freedom (6-DoF) localization and tracking. Analysis of the systems’ observability and sensitivity along with experimental validation confirms the method’s accuracy and robustness. These findings suggest that field-gradient-based localization (along with accelerometer data) can counter workspace and singularities constraints, while accurately tracking instruments under permanent magnet based manipulation, without the need for specific or time-varying external fields.