Paludamentum

In Republican and Imperial Rome, the paludamentum was a cloak or cape fastened at one shoulder, worn by military commanders (e.g., the legatus) and rather less often by their troops. As supreme commander of the whole Roman army, Roman emperors were often portrayed wearing it in their statues and on their coinage. After the reign of Augustus, the paludamentum was restricted to the Emperor. Children would also wear it sometimes, when there was bad weather and they needed protection.

The paludamentum was generally crimson, scarlet, or purple in colour, or sometimes white. It was fastened at the shoulder with a clasp, called a fibula, whose form and size varied through time. Putting on the paludamentum was a ceremonial act on setting out for war.

Etymology
According to Varro in De lingua latina L VII,37: