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A pair of mobile robots acting on opposite sides of a thin plate is developed for a class of tasks where robots have to work together, carrying a pair of end-effectors and traversing across a plate surface. Using powerful magnets, the paired robots attract each other, support themselves against gravity, and generate traction force to move across the panel. First, the design concept of paired mobile robots is presented, followed by dynamic modeling and magnetic analysis. Conditions for preventing the robot from falling as well as from slipping on the plate surface are examined. Time-optimal control of the paired robots subject to the no-fall, no-slip conditions is formulated and solved numerically. Precision positioning control using a laser beacon is designed and tested. A prototype of the paired robots using Halbach array permanent magnets and Lorentz force actuators is developed, and the control methods are implemented and tested on the prototype.