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.
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.
- Maaris Ayin (this is addressed in having signs)- seemingly the Shabbos car would also need to be clearly labeled for all to see.
- Not causing more energy to be used- with the elevator this is addresed by having weighing mechanisms disconnected. Seemingly by a boat it has to be a significant change in energy usage added due to the weight. I know that a friend who raced cars was very careful to remove anything that weighed down the car to increase speed. Perhaps there is a way to create an indirect response to weight such as is the case with opening the fridge on Shabbos which is allowed but clearly effects energy usage.
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 clearly only scratching the surface.