The "4 people's escape, 2 children and woman and a man" part made me thought of Spartakus and the Sun Beneath the Sea, (Les Mondes engloutis in french). But I don't remember the rest of the series well enough to say if it fit with the rest of the description.

Reading further (both on English and French sites) didn't gives me more clues, there is some robots, but there is also others humans survivors. Spartacus was not a soldier but a gladiator and I don't think he was a cyborg, but he did had a magical gauntlet. But since you were dubbing about those details, it may be a good start. You may have seen a single episode of the series.

The "four people's escape, two children and woman and a man" part made me thought of Spartakus and the Sun Beneath the Sea, (Les Mondes engloutis in french). But I don't remember the rest of the series well enough to say if it fit with the rest of the description.

Reading further (both on English and French sites) didn't gives me more clues, there is some robots, but there is also others humans survivors. Spartacus was not a soldier but a gladiator and I don't think he was a cyborg, but he did had a magical gauntlet. But since you were dubbing about those details, it may be a good start. You may have seen a single episode of the series.