Connecting two "makes" together: can I leave one out?
Solution 1:
I think the issue here is that make is two different verbs in your second sentence, or at least has two distinct meanings.
I make robots = I manufacture robots.
I make them move = I force them to move.
Consequently you have to repeat the verb, just as you would if you were to use the equivalents:
I manufacture robots and force them to move.
In your first sentence, both instances of make mean manufacture, so you don't have to repeat the verb.
The answer is yes: you do have to repeat it if the sense is different.