An autonomous robotic transport system has been developed in which the individual robot vehicles are able to move in multiple directions, such as vertically as well as around curves. Through the use of a unique rail system, the vehicle is able to move around corners and turns without the need for expensive modifications. This eliminates the need for various differentials or multiple electric motors to provide the difference between inner and outer wheels in a turn. Moreover, a number of switches have been developed that allow the vehicles to move not only vertically but also horizontally as well as transition between vertical and horizontal movement. A technique for operating the robotic vehicles is also described.