Input-Output Boundedness of a Magnetically-Actuated Helical Device

To date, all previous research in the wireless magnetic actuation of untethered helical devices has achieved motion stability using feedback control in vitro. However, feedback control systems are likely to be affected by the increased sensory uncertainty during in vivo trials. In this study we investigate the input-output boundedness of an interconnection between a helical device and a single rotating magnet actuator in low-Reynolds-number regime. Using the resistive-force theory, the interconnection is expressed in terms of all possible input-output pairs. Inputs representing the actuation frequency, pitch angle, lateral speed, and field strength are analyzed numerically and experimentally. We demonstrate input-output boundedness of the states of the helical device during circular and straight runs in open-loop, and we demonstrate bounded input-output propulsion without orienting the angle of attack (the often used input to swim horizontally without vertical drift) of the helical device to counteract gravity. Our results are important for a number of minimally invasive applications and tasks requiring improved control authority for stable runs of helical devices without drift due to gravity and without feedback control and restricted configuration imposed on the helical device's motion.