  This paper investigates the problem of straight-line path following for
magnetic helical microswimmers. The control objective is to make the helical
microswimmer to converge to a straight line without violating the step-out
frequency constraint. The proposed feedback control solution is based on an
optimal decision strategy (ODS) that is cast as a trust-region subproblem
(TRS), i.e., a quadratic program over a sphere. The ODS-based control strategy
minimizes the difference between the microrobot velocity and an integral
line-of-sight (ILOS)-based reference vector field while respecting the magnetic
saturation constraints and ensuring the absolute continuity of the control
input. Due to the embedded integral action in the reference vector field, the
microswimmer will follow the desired straight line by compensating for the
drift effect of the environmental disturbances as well as the microswimmer
weight.
