From that map though, it looks like they got a bit up into Scotland. A fair part of the South. There is Hadrian’s wall and my friends tell me, there is a 2nd wall as well. I’ve seen Hadrian’s, beautiful scenery around it.
The history of the Roman empire in what is now the UK is utterly fascinating. We were just discussing some other story on it a few months ago.
Southern Scotland was culturally more like northern England compared to Highland Scotland.
Antoninus Pius ordered the building of the Antonine Wall further north, across the narrowest part of Scotland, roughly from Glasgow to the Firth of Forth. It was abandoned shortly after and some time later again occupied by Septimus Severus. Hadrian’s Wall was the border through almost the entire Roman occupation.