Robust Feedback Linearization for Noncontact Manipulation of Magnetic Particles by a Hexagonal Array of Electromagnets

This paper develops a robust feedback control law for planer steering of magnetic particles in a circular workspace using a hexagonal arrangement of electromagnets encircling the workspace. The electromagnets are actuated independently by a feedback loop to control their aggregate magnetic field flexibly, which is then exploited to exert magnetic force on the particles as needed for steering them along desired reference trajectories. This magnetic force is a highly nonlinear function of both the position of magnetic particles and the control voltages actuating the electromagnets. The control strategy in this work is to cancel this nonlinearity using a nonlinear inverse map, which in effect, realizes the concept of feedback linearization. Such an inverse map is developed in this paper in a specific way that drastically enhances its robustness against inherent modeling errors and uncertainty in the magnetic field. The resulting robust inverse map notably improves the performance of feedback control, as demonstrated by experiments in this paper.