Fig. 5: Alternating open-loop control strategy for 3-DoF orientation manipulation of an anisotropic soft magnet.

In the first step, the orientation path is discretized into small orientation steps and orthogonal magnetic control inputs \({{{{{{\bf{B}}}}}}}_{{{{{{\boldsymbol{i}}}}}}}^{{{{{{\boldsymbol{a}}}}}}}\) and \({{{{{{\bf{B}}}}}}}_{{{{{{\boldsymbol{i}}}}}}}^{{{{{{\boldsymbol{r}}}}}}}\) are generated along a-axis and b-axis of the discretized midway orientations of the anisotropic soft magnet. In the second step, the orthogonal magnetic control inputs \({{{{{{\bf{B}}}}}}}_{{{{{{\boldsymbol{i}}}}}}}^{{{{{{\boldsymbol{a}}}}}}}\) and \({{{{{{\bf{B}}}}}}}_{{{{{{\boldsymbol{i}}}}}}}^{{{{{{\boldsymbol{r}}}}}}}\) are applied alternatingly to control the direction of the longest axis (2 DoFs) and the rotation about the longest axis (1 DoF), respectively, in each discrete orientation step until the soft magnet reaches the target orientation. The green coordinate frames denote the next desired midway orientation. In the last step, alternating orthogonal magnetic fields need to be maintained to “lock” the soft magnet to the desired orientation for disturbance rejection.