Compliant Hall-Effect Sensor Array for Passive Magnetic Instrument Tracking

Minimally invasive surgical procedures can strongly benefit from nonvisual magnetic instrument tracking. Most state-of-the-art sensor systems for magnetic tracking, however, are rigid and bulky or depend on multimodal sensor technologies. In this work, we investigate a compliant, wearable 2-D Hall-effect sensor array with self-sensing ability and a minimal spatial footprint. Our tracking algorithm is based on a permanent magnet model and a least squares optimization. For evaluation of self-sensing, we tested the sensor array attached to 3D-printed circular frames with known geometries. Tracking was experimentally evaluated moving the target magnet on a preset path utilizing a robotic actuator. Results show that stronger bending radii lead to larger errors of the shape estimation with an overall absolute error of $8.33^{\circ }$ . However, larger radii eventually lead to a decreased Euclidean distance error in the actual tracking procedure between 1.31 mm and 3.38 mm. Thus, the additional efforts due to shape estimation appear fair, since the overall performance of the tracking improves and the spatial footprint can be minimized with our approach. Future work will address performance improvement and implementation of a machine learning approach, aiming for real-time capability.