Robotic assembly systems and methods of assembling products using planar robots. Planar movers cooperate magnetically with stators to pick products provided on an infeed and place them in a pattern on an outfeed system, wherein the movers having a clamp having at least two opposing clamping surfaces whose relative positions are continuously adjustable by a force from an object external to the mover and the stator. Sensors and controllers cooperate to precisely move the movers on the stator, particularly as a group, for the movers to pick respective products at respective picking locations. Some systems permit packaging of multiple products.