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.

Integral Line-of-Sight Path Following Control of Magnetic Helical Microswimmers Subject to Step-Out Frequencies