A finishing apparatus for performing an automated finishing operation on a surface of a workpiece is disclosed. The finishing apparatus may include a platen fabricated from a magnetic material and having a platen surface, and a finishing module disposed on the platen surface and having a finishing operation end effector. The finishing module may generate a magnetic field that biases the finishing module toward the platen, and may be operable to generate a magnetic flux to control movement of the finishing module over the platen surface to perform the automated finishing operation on the surface of the workpiece.