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This paper describes a magnetic levitation system that uses a planar array of 16 cylindrical coils to levitate a platform containing two permanent disk magnets. Position and orientation feedback for closed-loop levitation control is provided by an optical rigid-body motion tracker and wireless LED markers. The actuation model for the levitation system across the full translation and rotation ranges was calculated using electromagnetic finite element analysis and validated with force and torque measurements between a single magnet and coil using motion stages and a six-axis force sensor. The transformation from the set of coil currents to the force and torque generated on the levitated body is recalculated in real time at each update of the levitated platform position and orientation obtained from the motion tracker using a precomputed single magnet and coil actuation model, and redundant kinematic control methods are used to find the least squares set of coil currents to generate the forces and torques needed to stabilize the levitated platform by proportional-derivative feedback control. The approximately 80 × 80 × 25 mm translation range of the implemented levitation system is comparable to the dimensions of the levitated magnet platform. The rotation ranges are ±40° in roll and ±15° in pitch, with unlimited yaw. The horizontal translation ranges can be extended by adding coils to the array, and the vertical translation and tilt rotation ranges are limited by heat dissipation in the coils. Analysis and control methods of the system are described, and large range translation and rotation trajectory following experimental results are given.