The Police Cruisers are alien pod hovering vehicles designed for pursuit and patrol. They were chasing Experiment 626 in Lilo & Stitch because he had stolen the Red One. The fleet then proceeded to attack the ship, damaging it, but Stitch used the Red One's Hyperdrive to escape. However, the damage the fleet caused to the Red One had disabled its navigation system. They follow the Federation Ship.
In the Lilo & Stitch: The Series episode "Finder", Dr. Hämsterviel broke out of prison and hijacked one of the "Police Cruisers" to escape with, he flew the cruiser back to Earth at Kauia but crashed it on impact due to his small size and was unable to reach the controls.