This is the video of the 11+ year old system installed in Århus Denmark by Lödige Industries from Germany.
Lödige Industries more recent solution is actually moving the whole pallet you park on, so you can also plug your car into it:
https://youtu.be/-_ZxnDrfwGk?t=46The system in London Gatwick UK is done by Stanley Robotics from France (which was acquired by HL Robotics from South Korea in 2024), but it could be similar.