A planar-drive system includes a rotor and stator module with a housing, a stator assembly for driving the rotor, and a sensor module for detecting the rotor position. The sensor module has a 2D arrangement of magnetic-field sensors arranged on a carrier in first and second periodic grids, extending in first and second directions. Adjacent magnetic-field sensors are arranged at first and second distances in the first and second directions. The grids are shifted by a vector having first and second components smaller than the respective first and a second distances. The rotor has first and second magnet units, each with an arrangement of magnets with first and second periodic lengths aligned in the first and second directions. The first and second components of the vector, and a difference between the first and second distances and the respective components, are each smaller than the respective first and second periodic lengths.