Right, this is similar to a paragraph from an article I read
YES, THEY DO - but not in the sense we understand sleep. Research conducted by James and Cottell into sleep patterns of insects (1983) showed that ants have a cyclical pattern of resting periods which each nest as a group observes, lasting around eight minutes in any 12-hour period. Although this means two such rest periods in any 24-hour period, only one of the rest periods bears any resemblance to what we would call sleep. Mandible and antennae activity is at a much lower level (usually up to 65 per cent lower) than during the other rest period in one 24-hour period, indicating a much deeper "resting" phase. Basing and McCluskey in 1986 used brain activity recorders on black, red, and soldier ants to determine whether the deeper resting period constituted actual "sleep". A steep decline in brain wave fluctuations supported the "sleep" hypothesis in black and red ants, but surprisingly showed a higher level of brain activity in soldier ants in a deep resting phase.
source - https://www.theguard...3,-1967,00.html
Another one
Since ants live underground, their sleep patterns are not affected by light and dark. Instead, workers just nap when they’re tired. And they get tired a lot. A worker fire ant takes about 250 naps a day, each averaging one minute in length. That’s one power nap every 6 minutes, adding up to more than 4 hours of sleep every day. But the naps do not unfold like clockwork; the ants sleep at irregular intervals and 80 percent of the workers are awake at any given time. That keeps the nest humming when things are busy. During slow periods, the workers sleep longer.
As for the 3 queens in Cassill’s colony, they slept for 6-minute intervals around 90 times a day. That equals 9 hours of sleep every day. And the 3 queens synchronized their naps so they all dozed off at the same time. As Cassill explains, “It’s very cozy. The synchrony of queens occurs because, like hound dogs, they pile atop each other when they sleep. When awake, they separate.”
Source - http://www.combatbug...-sleep.cky.html
So I gather from this that they do sleep at irregular intervals, but it doesn't seem like anyone has looked at whether they just nap where they are, or return to the nest first.