This invention is a vending machine and components parts that include a sophisticated positioning system, gripper and trays for improved efficiency in product retrieval and delivery. A unique initialization and calibration system is implemented at start up to determine the positions of shelves and trays of product containers in the machine, and may be implemented at other times if trays or shelves are added or removed, or if tray or shelf positions change. These positions are then used by the positioning and gripping systems to accurately and efficiently retrieve products from the trays. Related methods are also disclosed.