A multi-dimensional automated storage and retrieval system is provided herein that enables the space-efficient storage of containers within a three-dimensional lattice structure. Each container includes one or more drivers to engage with rails of the three-dimensional lattice structure, enabling the container to slide along the rails based on a propulsion system. A control device is provided to selectively engage each container to a desired rail of the lattice structure, and to provide power to the propulsion system, thereby moving the container to a desired location within the lattice structure. Due to the high storage efficiency of the disclosed automated storage and retrieval system, the system may be utilized in space-sensitive applications, such as vending machines for physical goods or in cargo vehicles such as trailers.