From Wikipedia:
Britannia
In the spring of 40, Caligula tried to extend Roman rule into Britannia.[4] Two legions had been raised for this purpose, both likely named Primigeniae in honour of Caligula's newborn daughter. Ancient sources depict Caligula as being too cowardly to have attacked or as mad, but stories of his threatening a decimation of his troops indicate mutinies. Broadly, "it is impossible to judge why the army never embarked" on the invasion. Beyond mutinies, it may have simply been that British chieftains acceded to Rome's demands, removing any justification for war.[184][185] Alternatively, it could have been merely a training and scouting mission[186] or a short expedition to accept the surrender of the British chieftain Adminius.[187][188] Suetonius reports that Caligula ordered his men to collect seashells as "spoils of the sea"; this may also be a mistranslation of musculi, meaning siege engines.[185][189] The conquest of Britannia was later achieved during the reign of Caligula's successor, Claudius.
A difference with The Dotard is that nobody was calling him Caligula while he was in power. And if anyone did, it was certainly not to his face and likely not in any public space. He probably wasn't as crazy as portrayed in surviving accounts, but he probably was as vicious.
Also, the single word names we now use for convenience for prominent Romans were not necessarily what anyone would have called them in their daily life. But the names overlap and are reused like crazy, AND elite Romans' names changed throughout their lifetime, so for clarity and brevity we call the guy Caligula now. One reason why: he as born Gaius Julius Caesar (incidentally so was the guy we call Julius Caesar), soon after called Gaius Caesar Germanicus, then his regnal name was Gaius Julius Caesar Augustus Germanicus. To find a brief identifier, writers had to resort to a childhood nickname (Germanicus already being taken, and earned, by his father).
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