This paper initiates a research aimed at developing tools that may have practical significance in contactless position control applications such as, e.g., photolithography. We describe a simple three-magnets planar positioning device, its mathematical model, and design a nonlinear controller that stabilizes it about an equilibrium. Specifically, we derive a feedback transformation mapping for the nonlinear system with three positive inputs into a linear system in Brunovsky normal form with two inputs. Robust and robust adaptive controllers are then designed in the transformed input domain and their effectiveness in handling uncertainties is compared through simulations. An experimental testbed under construction is described. It was used as a benchmark to test the controllers developed here as well as other nonlinear control approaches.