An automated guided vehicle is equipped with a stabilization system for precisely locating, leveling, or otherwise positioning the AGV and its payload with respect to a work piece. The stabilization system includes one or more extension members that extend away from the AGV to engage the ground or a locating assembly installed in the ground. Each extension member may be part of a locating assembly or a leveling assembly. The locating assembly extension member may extend at least partially into an opening of another locating assembly to align the two locating assemblies. The locating assembly may also be configured to provide a leveling function.