The CyberWalk is a large size 2D omni-directional platform that allows unconstrained locomotion possibilities to a walking user for VR exploration. In this paper we present the motion control design for the platform, which has been developed within the homonymous European research project. The objective is to compensate the intentional motion of the user, so as to keep her/him always close to the platform center while limiting the perceptual effects due to actuation commands. The controller acts at the acceleration level, using suitable observers to estimate the unmeasurable intentional walker's velocity and acceleration. A moving reference position is used to limit the accelerations felt by the user in critical transients, e.g., when the walker suddenly stops motion. Experimental results are reported that show the benefit of designing separate control gains in the two orthogonal directions (lateral and sagittal) of a frame attached to the walker.