Self-Driving Cars are cars that are driven by computers. Assuming you set your destination before Shabbat (or can otherwise direct it without performing any Melacha), can one ride in such a car on Shabbat?
I could see parralels between this and the shabbat elevator, going on a boat ride from before shabbos untill after shabbos, and riding a bicycle on shabbas.
Elevator According to the tzomet institute, the following criteria are required to make an elevator "kosher" for shabbat usage. What is needed for an elevator to operate as a "Shabbat elevator?"
A timer to schedule automatic operation Disconnecting the manual buttons (except for the emergency button) Automatically stopping at every floor or two, leaving enough time for safe entry and exit Neutralizing any electrical effects connected to entry or exit from the elevator while it stops at a floor Sounding a warning buzzer before the doors close Taking care of the weighing mechanisms – either by disconnecting them or by neutralizing the effect of a person's entry into the elevator Proper operation of re-leveling Turning off unnecessary signal lights and taking care of floor indicator lights Appropriate signs in the elevator and at all floors
Some of the concerns that are addressed here that may be relevant to our current question.
by boats and bikes there are additional issues with tchum shabbos and a gezera on transport means that are usually used to transport out of the tchum.
just a few points but clearely only scratching the surface