An on-the-fly robotic system and method for unloading glass sheets of mixed sizes, including jumbo-sized sheets, from or onto a conveyor onto or from unloading platforms. The system comprises at least one traverse unit extending along the conveyor in parallel to the longitudinal axis thereof and at least two programmable industrial robots movably mounted on the traverse unit. The robots may be operated in a full synchronized mode for handling sheets too large or to heavy to be handled by a single robot or in an individual operation mode where each robot handles a single sheet.