Controllable: Yes (Only to guide it between Hydra Marshes and Gaea's Navel.)
Parameters: The party summons it using the Beeba Flute in Hydra Marshes. The first time, it leads to a boss battle. Later, when they have the Ancient Fruit, it carries them to Gaea's Navel.
First Seen: During the quest to save Kid, when the party uses the Beeba Flute in Hydra Marshes.
First Used: During the quest to meet the six dragons, when the party uses the Beeba Flute in Hydra Marshes and has an Ancient Fruit.
Wingapedes are explained as an ancient method of travel for the Beeba species, who dwell in the Hydra Marshes. They are summoned through the use of a crude flute, and then given fruit for domestication. While the party's travel is limited to Gaia's Navel, the Beeba may be able to harness Wingapedes for travel to other destinations.
The Wingapede appears to be, appropriately enough, a centipede with wings. The "Pede" suffix means "Feet."