  The engineering space for magnetically manipulated biomedical microrobots is
rapidly expanding. This includes synthetic, bioinspired, and biohybrid designs,
some of which may eventually assume clinical roles aiding drug delivery or
performing other therapeutic functions. Actuating these microrobots with
rotating magnetic fields (RMFs) and the magnetic torques they exert offers the
advantages of efficient mechanical energy transfer and scalable
instrumentation. Nevertheless, closed-loop control still requires a
complementary noninvasive imaging modality to reveal position and trajectory,
such as ultrasound or x-rays, increasing complexity and posing a barrier to
use. Here, we investigate the possibility of combining actuation and sensing
via inductive detection of model microrobots under field magnitudes ranging
from 0.5 mT to 10s of mT rotating at 1 Hz to 100 Hz. A prototype apparatus
accomplishes this using adjustment mechanisms for both phase and amplitude to
finely balance sense and compensation coils, suppressing the background signal
of the driving RMF by 90 dB. Rather than relying on frequency decomposition to
analyze signals, we show that, for rotational actuation, phase decomposition is
more appropriate. We demonstrate inductive detection of a micromagnet placed in
distinct viscous environments using RMFs with fixed and time-varying
frequencies. Finally, we show how magnetostatic gating fields can spatially
isolate inductive signals from a micromagnet actuated by an RMF, with the
resolution set by the relative magnitude of the gating field and the RMF. The
concepts developed here lay a foundation for future closed-loop control schemes
for magnetic microrobots based on simultaneous inductive sensing and actuation.
