This  is a surprisingly difficult problem.

The general idea is to not add heat to the environment where it’s so cold that the moon has saved up ice for us over billions of years.  Add heat, and the goodies evaporate.  Industrial scale engines and machines which create lots of waste heat may be out. In turn that means that a self contained rover might be a problem.  What mechanical machine could we make that would work at 80 kelvin?

Here’s one take on the matter.  A medium power laser is positioned on a hill overlooking the areas where the ice is.  Either a natural path exists nearby or a rail is laid alongside.  Line of sight, the laser is aimed at the rover and heats the stirling engine up to operating capability.  Rover shoots red guidance laser; power station responds with power laser. Whenever the power station can operate, the rover and ice extraction operations can be done.  That’s whenever solar rays hit the hill where the power station is at.

Microwave sintering is used to create a linear gear rail leading to the areas where ice mining will occur.  The rover rides this rail, it’s wheels riding a transmission wheel attached to the bucket.  The transmission is just a small gear moving a big gear, maybe about a 20:1 speed reduction.  This allows the lightly powered rover to move a bucket of ore, ice, or whatever up the side of the crater while riding the rail.

To explore the eternally dark crater, the power system on the peak simply must continually hit the heat absorption disk of the rover with it’s laser beam.  Perhaps there is a flywheel for energy storage which allows some limited movement without power.

After you have the ice, the fun is just beginning.  Perhaps by establishing temperature gradients – areas cut into the moon where the temperature is established and is the same always – the ice can be boiled off fractionally.  This creates an issue of storage of raw materials.  Perhaps the separated materials can be moved back into the crater, or perhaps the separation can be done in the crater itself.

Here is a camera shot of one such crater where the rim sees sunlight a fair amount of the time, but the interior never does.  This is 10 km across crater Erlander, near the N Pole.  Depending on how filled in the interior is, a cog rail slanting down to the floor or base would be one to four km in length.