[shadowgovt]

Acoustic signalling for control (which would have to be done very carefully to account for echo, motor noise, etc), with a great deal of onboard navigation via LIDAR and onboard cameras. Signalling would be high-level.

It's entirely possible data couldn't be delivered back to the parent machine until a physical connection could be established; not sure if acoustic signalling can be made high-bandwidth enough for video. Line-of-sight laser modulation could be used for high-bandwidth once the ROV is out of the bulk of the ship.

[jandrese]

Remote control with acoustics is undoubtedly feasible. Getting a return picture so you're not doing it blind is probably not. It would be much easier to make the drone autonomous and self pathfinding, but even that's quite state of the art and would be placing a lot of faith in your code to not get confused/lost/crash in the process.

[constantly]

Something like this maybe? The website claims 6,000m depth (20,000ft), which is more than enough to do the job.

https://www.anduril.com/hardware/dive-ld/