Optimization algorithm to generate a robust magnetic force of the magnetic navigation system against position error of a magnetic robot

We propose an optimization algorithm to generate a robust magnetic force against position error to achieve good controllability of the magnetic robot in the region of interest of a magnetic navigation system comprising electromagnets. We formulate an optimization problem that minimizes the norm of the spatial derivatives of the magnetic force subject to the constraints of the magnetic flux density and magnetic force. The robust magnetic force generated by the proposed algorithm was compared with conventional pseudo-inverse matrix method and verified through an experiment in which a magnetic robot was successfully steered along a bifurcated glass tube to reach a target position.