A method for moving a plurality of moveable stages (10,110,210) relative to a stator (30,130,230), the method comprising: providing a stator comprising one or more stator tiles (43,243), each stator tile comprising: an x-trace layer (40,240) comprising a plurality of x-trace groups, each x-trace group comprising a plurality of electrically conductive x-traces which extend in a stator-x direction across the stator tile and into which currents may be independently driven; a y-trace layer (42,242) comprising a plurality of y-trace groups, each y-trace group comprising a plurality of electrically conductive y-traces which extend in a stator-y direction across the stator tile and into which currents may be independently driven; the x-trace layer and the y-trace layer overlapping one another in a stator-z direction; the stator-x direction and the stator-y direction non-parallel to one another; providing a plurality of moveable stages, each moveable stage comprising: a first magnet array (12,112A, 212A) comprising a plurality of first magnetization segments (14,114, 214), each first magnetization segment having a corresponding magnetization direction and at least two of the first magnetization segments having magnetization directions that are different from one another; and driving currents in the x-traces and the y-traces to move a first moveable stage and a second moveable stage relative to the stator where the first magnet array of the first moveable stage overlaps with the first magnet array of the second moveable stage in the stator-x direction, wherein driving currents in the x-traces and the y-traces to move the first moveable stage and the second moveable stage relative to the stator comprises: for at least a first portion of a time where the first magnet array of the first moveable stage overlaps with the first magnet array of the second moveable stage in the stator-x direction, controllably driving first x-trace group currents in a first x-trace group that overlaps with a first portion of the first magnet array of the first moveable stage in the stator-z direction and a first portion of the first magnet array of the second moveable stage in the stator-z direction, the first x-trace group currents determined based at least in part on positions of both the first moveable stage and the second moveable stage and the first x-trace group currents generating first forces on the first magnet array of the first moveable stage and on the first magnet array of the second moveable stage. providing a stator comprising one or more stator tiles (43,243), each stator tile comprising: an x-trace layer (40,240) comprising a plurality of x-trace groups, each x-trace group comprising a plurality of electrically conductive x-traces which extend in a stator-x direction across the stator tile and into which currents may be independently driven; a y-trace layer (42,242) comprising a plurality of y-trace groups, each y-trace group comprising a plurality of electrically conductive y-traces which extend in a stator-y direction across the stator tile and into which currents may be independently driven; the x-trace layer and the y-trace layer overlapping one another in a stator-z direction; the stator-x direction and the stator-y direction non-parallel to one another; an x-trace layer (40,240) comprising a plurality of x-trace groups, each x-trace group comprising a plurality of electrically conductive x-traces which extend in a stator-x direction across the stator tile and into which currents may be independently driven; a y-trace layer (42,242) comprising a plurality of y-trace groups, each y-trace group comprising a plurality of electrically conductive y-traces which extend in a stator-y direction across the stator tile and into which currents may be independently driven; the x-trace layer and the y-trace layer overlapping one another in a stator-z direction; the stator-x direction and the stator-y direction non-parallel to one another; providing a plurality of moveable stages, each moveable stage comprising: a first magnet array (12,112A, 212A) comprising a plurality of first magnetization segments (14,114, 214), each first magnetization segment having a corresponding magnetization direction and at least two of the first magnetization segments having magnetization directions that are different from one another; and driving currents in the x-traces and the y-traces to move a first moveable stage and a second moveable stage relative to the stator where the first magnet array of the first moveable stage overlaps with the first magnet array of the second moveable stage in the stator-x direction, wherein driving currents in the x-traces and the y-traces to move the first moveable stage and the second moveable stage relative to the stator comprises: for at least a first portion of a time where the first magnet array of the first moveable stage overlaps with the first magnet array of the second moveable stage in the stator-x direction, controllably driving first x-trace group currents in a first x-trace group that overlaps with a first portion of the first magnet array of the first moveable stage in the stator-z direction and a first portion of the first magnet array of the second moveable stage in the stator-z direction, the first x-trace group currents determined based at least in part on positions of both the first moveable stage and the second moveable stage and the first x-trace group currents generating first forces on the first magnet array of the first moveable stage and on the first magnet array of the second moveable stage.