This article presents a novel strategy for two-dimensional (2-D) feedbackless automatic locomotion on a liquid surface by magnetic milli/microrobots, using only one coil. By exploiting the tendency of a magnet to move toward and remain at the point of maximum magnetic field, we created a “trapping point” (TP) located at the axis of the coil to confine a magnetic millirobot within it. The TP is created by balancing the gravity, buoyancy, and magnetic forces acting on the millirobot to confine it to the surface of the liquid at the position of the local point of maximum magnetic field. Then, by using a parallel manipulator, the location of the TP along the fluid surface is changed through a set of rotations of the coil, resulting in changes to the position of the magnetic millirobot. Owing to the use of a TP, this new magnetomechatronic system with a single coil can perform 2-D control of individual magnetic millirobots and swarms of magnetic millirobots without position feedback from the robot. This results in a relatively small, cheap, and low-power system with simple, feedbackless automatic control that can achieve precise position control.