Utilizing Synthetic Data in Supervised Learning for Robust 5-DoF Magnetic Marker Localization

TL;DR

A novel approach that leverages neural networks (NNs) to bypass limitations, directly inferring the marker’s position and orientation to accurately determine the magnet’s five degrees of freedom (5 DoFs) in a single step without initial estimation is introduced.

Abstract

Tracking passive magnetic markers plays a vital role in advancing healthcare and robotics, offering the potential to significantly improve the precision and efficiency of systems. This technology is key to developing smarter, more responsive tools and devices, such as enhanced surgical instruments, precise diagnostic tools, and robots with improved environmental interaction capabilities. However, traditionally, the tracking of magnetic markers is computationally expensive due to the requirement for iterative optimization procedures. Moreover, these methods depend on the magnetic dipole model for their optimization function, which can yield imprecise outcomes due to the model's significant inaccuracies when dealing with short distances between non-spherical magnet and sensor.Our paper introduces a novel approach that leverages neural networks to bypass these limitations, directly inferring the marker's position and orientation to accurately determine the magnet's 5 DoF in a single step without initial estimation. Although our method demands an extensive supervised training phase, we mitigate this by introducing a computationally more efficient method to generate synthetic, yet realistic data using Finite Element Methods simulations. The benefits of fast and accurate inference significantly outweigh the offline training preparation. In our evaluation, we use different cylindrical magnets, tracked with a square array of 16 sensors. We perform the sensors' reading and position inference on a portable, neural networks-oriented single-board computer, ensuring a compact setup. We benchmark our prototype against vision-based ground truth data, achieving a mean positional error of 4 mm and an orientation error of 8 degrees within a 0.2x0.2x0.15 m working volume. These results showcase our prototype's ability to balance accuracy and compactness effectively in tracking 5 DoF.

Figures (12)

• Figure 1: Schematic pipeline overview. We use a Multi-Layer Perceptron (MLP) to output the location and orientation of the magnet directly. During the training phase, the MLP outputs are compared with the ground truth for generating synthetic sensor readings. During the inference, the input to the MLP is the sensor data to track the position and orientation of the magnet.
• Figure 2: Coordinate system overview for Alg. \ref{['algo:coor_trans']}
• Figure 3: Histogram of input values before and after adding feature-engineering function.
• Figure 4: Hall sensor array in a 4x4 grid. The center-to-center distance is 52mm. The array is connected to a Jetson Nano for the complete inference pipeline. The inset shows a rigid-tree to collect Optitrack groundtruth.
• Figure 5: Positional errors of the iterative method in simulation for different number of iterations. (a) We vary the initial orientation mismatch, keeping a fixed distance of $80$ mm to the truth. (b) We vary the initial positional mismatch, keeping a fixed orientation difference of $45^{\circ}$. As our method does not rely on iterations or initialization, it is a single value. The standard deviation of our method is too small to show in the graph.