Kuka servo use VDC?

which controller?

in KRC1 it is PM6-600
in KRC2 it is KSP600
in KRC4 it is KPP
...

in ALL servos (regardless if they are part of robot system or not) energy is converted few times:
1. line supply (usually 3phase AC) is converted to DC; this is few hundred volts (largely depends on line input)
2. this DC is called bus or intermediate stage and includes filter, voltage monitoring, etc. it is used to power servo amplifier(s)
3. servo amplifiers use energy from bus and produce 3phase AC to power motor. type of control may differ in details but the point is that the units are just some sort of amplifier - they read weak control signal computed by motion controller and produce equivalent "big" signal that actually power motor.
Since produced AC is product of digital circuit, result is not smooth sine wave but series of pulses of different length and polarity. if this is run through filter, you would get pure AC (sinewaves).

so all servo will have those function - how exactly those functions are divided (packaged into hardware) is up to manufacturer.
KRC1 has all of those functions for all 6 robot axes in one box (PM6-600).
KRC1A and KRC2 have those functions divided into several components (one KPS is powering 6 servo amplifiers)
KRC4 can have several options. there are three servo amplifiers packed into one KSP (kuka servo pack). KPP is working as power supply (KPP0) but there are also versions of KPP that also have one, two (or now also three) servo amplifiers. number of servo amplifiers is indicated by part number (KPP1, KPP2 or recently also KPP3).

position feedback is coming from some sensor (encoder, resolver or whatever).
in case of KRC, all feedback is handled by RDC (in German it is called RDW).

Motion controller uses inputs such as position feedback and required speed and position from motion planer and then produces output which controls amplifiers.

In KRC1, KRC1A, KRC2 motion controller was DSE board. Motion planer was PC.

In KRC4 things are implemented a bit differently - DSE functionality (and many other things) are done completely in software on PC (new PCs are much more powerful and can do significant work without bunch of specialized hardware "cards").

MR-J2S is a Mitsubishi servo drive for single axis. it is one unit that includes:
- AC/DC converter producing DC bus voltage,
- feedback input (for encoder)
- servo amplifier (single axis)
- motion controller with motion planer (optional, used if working standalone for very simple functionality)
- interfaces to get for example external commands from higher level controller (if controlled by PLC or doing more complicated things such as interpolation etc.).

through motor cable

you may want to use complete sentences and be more descriptive.

robots and motors are different things.

as mentioned above, robot controllers are powered by AC (3phase for standard and 1phase for small robots).
AC power is obtained from mains, not from batteries.

is it possible to use batteries? well, yes...
https://www.youtube.com/watch?v=LcZJA3XyVjQ