From the Super Mario Wiki
The Robot Princess was a robotic double of Princess Toadstool that was built and programmed by Kooky von Koopa. Although the differences between Princess Toadstool and the Robot Princess were noticeable to the Koopas (and television viewers), other characters were completely fooled.
In The Adventures of Super Mario Bros. 3 episode "Reign Storm", Kooky built the Robot Princess when the real Princess Toadstool went on vacation in Hawaii, so that Bowser could take over the Mushroom Kingdom.
A few days after Princess Toadstool left, Bowser and Kooky unleashed the Robot Princess on Mario and Luigi, who couldn't handle the responsibility of temporarily running the kingdom. Having complete control over all the decisions made in the Mushroom Kingdom, the Robot Princess made several crazy demands, including ordering a new highway to be built out of quicksand, and getting the Mushroom Kingdom Fire Department to extinguish all the Fire Flowers in the kingdom.
When Mario and Luigi went to pay the Robot Princess a visit, they found her planning on giving the Mushroom Kingdom over to Bowser, and she demanded them to leave. The Robot Princess nearly succeeded in crowning Bowser as the new ruler of the Mushroom Kingdom, but the real Princess Toadstool showed up to reclaim her crown.
After Princess Toadstool returned, the Koopas all ran off, leaving the Robot Princess behind. It is unknown what happened to the Robot Princess afterwards, but it's likely that she was destroyed.