Abstract
Magnetic target tracking is a low-cost, portable, and passive method for tracking materials wherein magnets are physically attached or embedded without the need for line of sight. Traditional magnet tracking techniques use optimization algorithms to determine the positions and orientations of permanent magnets from magnetic field measurements. However, such techniques are constrained by high latencies, primarily due to the numerical calculation of the gradient. In this study, we derive the analytic gradient for multiple-magnet tracking and show a dramatic reduction in tracking latency. We design a physical system comprising an array of magnetometers and one or more spherical magnets. To validate the performance of our tracking algorithm, we compare the magnet tracking estimates with state-of-the-art motion capture measurements for each of four distinct magnet sizes. We find comparable position and orientation errors to state-of-the-art magnet tracking, but demonstrate increased maximum bandwidths of 336%, 525%, 635%, and 773% for the simultaneous tracking of 1, 2, 3, and 4 magnets, respectively. We further show that it is possible to extend the analytic gradient to account for disturbance fields, and we demonstrate the simultaneous tracking of 1 to 4 magnets with disturbance compensation. These findings extend the use of magnetic target tracking to high-speed, real-time applications requiring the tracking of one or more targets without the constraint of a fixed magnetometer array. This advancement enables applications such as low-latency augmented and virtual reality interaction, volitional or reflexive control of prostheses and exoskeletons, and simplified multi-degree-of-freedom magnetic levitation.
Highlights
M AGNETS have been used to track fingers [1], [2], styli [3], jewelry [4], vibrating beams [5], endoscopes [6], [7], catheters [8], tongues [9], jaws [10], bladders [11], heart valves [12], and joints [13]–[15], and have been suggested for tracking other biological tissue such as muscle [16]
While the use of an analytic Jacobian matrix has been demonstrated previously for offline localization of multiple static axisymmetric magnets [29], we focus on the tracking of spherical magnets with the dipole model in order to optimize the speed of evaluation for real-time tracking
We describe below a tracking algorithm, implementing the use of analytic derivatives, to track spherical magnets via an optimization algorithm
Summary
M AGNETS have been used to track fingers [1], [2], styli [3], jewelry [4], vibrating beams [5], endoscopes [6], [7], catheters [8], tongues [9], jaws [10], bladders [11], heart valves [12], and joints [13]–[15], and have been suggested for tracking other biological tissue such as muscle [16] As demonstrated by this extensive formative work on magnet tracking, using permanent magnets as position markers is advantageous because there is no need to power them via wired or wireless power transmission. This model most accurately characterizes the field around a uniformly magnetized spherical object [17], but using the far field of magnetized objects, the dipole model has been used to track and characterize nonspherical permanent magnets, electromagnets [18], and ferromagnetic objects such as cars [19], spacecraft [20], underwater magnetic anomalies [21], and mineral deposits [22]
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