Helical Propulsion in Low-Re Numbers with Near-Zero Angle of Attack

One approach to the wireless actuation and gravity compensation of untethered helical magnetic devices (UHMD) is through swimming with a non-zero angle of attack (AoA). This configuration allows us to counteract gravity, so that for a given desired path, we can move the UHMD controllably without drifting downward under its own weight. This study seeks to investigate the use a reduced-order model of the complex 6-degrees-of-freedom model of UHMDs in low Reynolds-number regime. A one-dimensional model representing the relative position of the UHMD with respect to an actuator rotating permanent magnet is used to predict a gap which yields bounded behavior of the open-loop system. Using geometric representation of the reduced-order model, the local bounded behavior of the UHMD with near-zero AoA is attributed to periodic active magnetic suspension, which dominates near-zero AoA. Our numerical results are verified experimentally and bounded behavior of the UHMD demonstrates the capability to swim with near-zero AoA (6.3° ± 2.2°) without drifting downward. With this actuation strategy, it is unlikely that the orientation of the UHMD will be needed during noninvasive localization, making the control system dependent on only its position with respect to a prescribed trajectory. This strategy will also provide a computational advantage in adjusting the gap between the UHMD and a robotically controlled rotating permanent magnet actuator.