Magnetically actuated tools (MATs) that utilize rotating magnetic fields for propulsion, such as active capsule endoscopes and magnetic microrobots, have typically been controlled using either arrangements of electromagnets or permanent-magnet systems operated in limited configurations. It was recently shown that a rotating magnetic field for MAT actuation can be generated using a single rotating permanent magnet (RPM) from any position in space with a unique axis of rotation. The method has potential benefits for clinical systems, but it requires knowledge of the MAT position with respect to the RPM. In any application, MAT localization will be subject to uncertainty caused by sensor noise, slow update rates, and/or localization failure. In this paper, we develop and experimentally verify worst-case bounds on properties of the rotating dipole field, given a worst-case bound on localization error, which can be used to design operating procedures that mitigate undesired MAT behavior in the presence of known localization uncertainty. The results are important for the robust operation of rotating MATs actuated using a single rotating permanent magnet in a clinical setting.
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