LAUSR

This article presents the optimal current allocation and the magnetic force production associated with the hexapole electromagnetic actuation, wherein six electromagnets are used to control the magnetic field and exert the 3-D magnetic force on a specified microscopic magnetic particle in the 3-D workspace of the actuating system. It addresses four major issues in the inverse modeling of the multipole electromagnetic actuation, i.e., 1) redundancy; 2) coupling; 3) nonlinearity; and 4) position-dependency, and leads to the accurate and effective 3-D magnetic force production within the specified workspace. Specifically, the optimal inverse modeling of the hexapole electromagnetic actuation is derived to minimize the 2-norm of the $6 \times 1$ input current vector when applied to produce the desired 3-D magnetic force to propel the magnetic particle in aqueous solutions. The inverse model is implemented in a high-speed field programmable gate array system to realize the real-time current allocation, which is used to render the feedback stabilization of the magnetic trap. The accurate and effective 3-D force production through the optimal current allocation is experimentally validated.