Not intending to sound harsh, but if you need to ask that question then really you should be looking up both basic electronics and the FRA rules.
Fuses are basic electronic safety devices, to put it in simple terms if you get a runaway of power demand then the fuse breaks the circuit by failing in a fail-safe way below the level where other more critical components would do the same. Fuses hence protect your house, and i believe by law are built into the plug of every standard UK appliance - so should they ever have a short, electrocute someone ect - instead of blowing up they just burn the fuse instead.
Similarly the question of "do all robots need them" is answered in the FRA rules. Read them, because otherwise there may be some other safety information youve missed.
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