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The Robot Princess was a robotic double of Princess Toadstool that was built and programmed by Kooky von Koopa. The Koopa Troopas protested that this would not work, citing obvious differences between the gynoid and the real Princess. However, denizens of the Mushroom Kingdom were successfully deceived, as were Mario and Luigi.
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, Mario and Luigi, failed to handle the responsibility of temporarily running the kingdom (as Bowser and the Koopalings were instigating trouble wherever they could). This caused the subjects of the Mushroom Kingdom into demanding the Mario Brothers recall the Princess from Hawaii. Bowser and Kooky sent the Robot Princess to Mario and Luigi, who fail to notice an impostor, instead overjoyed to have the Princess reclaim her leadership role. 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 shown that she was accidentally destroyed by Kooky while trying to warn Koopa about Toadstool.