A motion system for moving objects in a space, e.g., for moving virtual reality (VR) participants about space used to provide a VR environment. The system includes a controller and a position monitoring assembly. The system has a modular floor including a plurality of tile assemblies defining a support surface for a first and a second object. Each of the tile assemblies includes: (a) a planar tile with an upper surface for supporting the first and second objects; and (b) a drive system. The drive system includes a vibration-inducing assembly operable to oscillate the planar tile in a horizontal plane and further includes a preferential friction assembly operable to selectively reduce friction between the upper surface and any supported object. The controller generates control signals, based on position information, to independently control the tile assemblies of the modular floor to move the first and second objects on the support surface.