Before revision:  Using linear programming, we can control the motion of  non-magnetic particles with a predefined trajectory of a line, square, and circle with a precision of 57.4 +/ -33.6 um, 74 +/ -44.4 um , and 67.2 +/ -38.6 um, respectively.
After revision:  Using linear programming, we can control the motion of the non-magnetic particles with a predefined trajectory of a line, square, and circle with a precision of 57.4 +/ -33.6 um, 74 +/ -44.4 um , and 67.2 +/ -38.6 um, respectively.