Characterization of a Novel Magnetic Tracking System

Abstract

A tracking system for determining the five-degrees-of-freedom position and orientation of a cylindrical permanent magnet was developed. The system consists of a planar array of 27 Hall effect magnetic sensors, interface electronics, and computer. A magnet is modeled by an ideal magnetic dipole. The closed-form solution for the magnetic flux density of the magnetic dipole was used with a Levenberg-Marquardt optimization algorithm to determine the coordinates of the dipole. The system was characterized using Nd-Fe-B magnets (n=5,B <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">r</sub> =14.25plusmn0.25 kG, 2.00-mm diameter D, and 5.00-mm length L and n=5,B <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">r</sub> =13.1plusmn0.1 kG, 4.55-mm D, and 6.35-mm L). The axis of each magnet was first aligned perpendicular to the center of the sensor array, and an automated positioner moved the magnet away from the array perpendicular to its face. Voltage data was collected from the 27 sensors at each 1-mm interval along this direction out to 150 mm for the smaller magnets and 300 mm for the larger magnets. Sensor offset and environmental magnetic flux density were measured after each test. A coordinate measurement machine verified the position and orientation of the magnets. A useful range of 100 mm from the array was determined for all magnets tested. Within this range, the position of smaller magnets along the axis of motion were determined with maximum error of 1.8 mm, while their position in the two orthogonal directions perpendicular to the axis of motion were determined with maximum error of 5.3 mm; the position of larger magnets along the axis of motion were determined with maximum error of 0.8 mm, while their position in the two orthogonal directions were determined with maximum error of 3.8 mm; and the maximum error in orientation for all magnets tested was 4.2deg