What kind of power supply do TARS and CASE and other such automatons use? How do they recharge? Radioisotope Thermoelectric Generator? Solar power? Eating small rodents?
It appears they can operate for decades (TARS on the ship with Romilly), and they could probably spend years helping the astronauts build the new colony. Do they consume anything? Do they ever need to rest? (these are all variations of "where do they get their energy?")
I suspect this isn't explained at all, since Interstellar wasn't that kind of sci-fi, but perhaps it was discussed in BTS interviews or the novelization. It's also possible that they are shown recharging on the ship, so if the ship's power source was ever explained that would count. The actual screenplay has the following allusions:
TARS powers up a second articulated machine, CASE.
Dr Mann indicates a DEFUNCT ARTICULATED MACHINE.
TARS: What’s wrong with him?
DR MANN: Degeneration. He misidentified the first organics we found as ammonia crystals. We struggled on for a time, but ultimately, I decommissioned him and used his power source to keep the mission going.
Romilly watches Tars crouch down beside Kipp and connect Kipp to his own power. Kipp shows signs of life ...
Cooper looks over the kitchen. Cooper sees a familiar-looking articulated machine
COOPER: Is that ...?
ADMINISTRATOR: The machine we found out near Saturn when we found you, yes. Its power source was shot, but we could get you another if you want to try and get it up and running again.