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The following is based on Fallout Tactics and some details might contradict canon.
The hover robot is a guard and/or patrol robot. It's very similar to the floating eye bot or the eyebot robot but far more heavily armed. After the War, it was used by the Calculator, the mad cyborg from Vault 0.
It uses a very quiet propulsion system to stealthily approach its target. It's armed with a rocket launcher. When it has exhausted its three rockets. It will make a kamikaze run, smashing into its target as hard as it can.
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