Discrete-Time Optimal Control of Miniature Helical Swimmers in Horizontal Plane

Abstract

Microswimmer and miniswimmer toward precision-targeted medicine have attracted extensive attention recently. We have developed an autonomous manipulation approach for magnetic-driven helical miniswimmer at low Reynolds number in the horizontal plane (<inline-formula> <tex-math notation="LaTeX">$H$ </tex-math></inline-formula>-plane). Different from our previous work which just makes the barycenter of miniswimmer on the reference path as well as takes the swimming direction not into consideration in planar path following, our control policy in this article can make the miniswimmer to follow the reference path and, at the same time, its swimming direction is also along the reference path. A robust tracking method is employed to locate the helical miniswimmer in real time. Due to different external disturbances, an angle compensating model in the global coordinate frame is developed by radial basis function (RBF) networks trained by backpropagation algorithms, which is used to express the swimming model of the helical miniswimmer facing the gravity and lateral disturbances. A discrete-time optimal controller is formulated based on the linear-quadratic feedback control. Simulations and experiments are conducted to quantitatively validate the autonomous manipulation, and the results show the control performance with submillimeter accuracy in the <inline-formula> <tex-math notation="LaTeX">$H$ </tex-math></inline-formula>-plane. <i>Note to Practitioners:</i> This article is motivated by the potential application of precision-targeted medicine using magnetic-driven microswimmer/miniswimmer. The formulated controller employs the error model in the horizontal plane to design the control law. Simulations and experiments validate the effectiveness of the proposed discrete-time optimal control scheme using magnetic-driven miniswimmers.