It's a little disappointing. It's just one of those automated disc vacuum cleaners that scoots around the floor, with sensors to avoid walls and a system to prevent it going over the same ground twice.
But for Vestergaard, an enthusiastic proponent of technology in old-age care, the robots mean fewer cleaners at the Rosenborg Centre – the home she helps to manage in central Copenhagen. This means more personnel available to care for residents.
Over the last six years Denmark has cut the amount it spends on care for each person over 65 by nearly a fifth, according to figures from Statistics Denmark – an average cut of 10,851 Danish kroner (£1,200) per elderly person every year.
The robots are a key part of the "welfare modernisation strategy", Denmark announced last September. The aim is to use technology to cut 12bn kroner (£1.3bn) from the government's welfare budget by 2020.
According to a survey by DaneAge, which represents elderly people in Denmark, 84% of managers responsible for elderly care in the country's municipalities either already use or are about to start using robot vacuum cleaners.
"We normally only use them at night, because otherwise the residents trip over them," says Vestergaard.
It doesn't stop there. The centre has installed special coffee machines that make it easier for old people with shaky hands to pour their own drinks and transfer them onto their walking aids.
"At the start, there were complaints from people who were used to just getting coffee given to them," she says. "But now we say, 'the coffee machine is out in the kitchen, you can just get a coffee yourself if you want one'."
"Of course there's a change in the amount of coffee being spilt," she adds. "But that's life."
The centre identifies the capabilities of the more able-bodied and alert residents, and asks them to help the others, and also encourages friends and family of residents to come in and lend a hand.
"It's a good idea," Vestergaard says. "People like to know that there are still people who need them."
The philosophy has had an even bigger impact in the homes of elderly Danes who have not yet gone into full-time care.
According to Jens Hoejgaard at DaneAge, government spending on practical help for the aged at their homes has been cut by a third since 2008, while personal care has only been cut by 12%.
"The new trend is everyday rehabilitation or training, where you say to citizens, 'there are some things that you can't do any more, but we will train you so that you can do it yourself'," Hoejgaard says.
So instead of a nurse or helper coming in once a week, cleaning their apartment and helping them have a bath, older people in Denmark now get a trainer.
"You get training for a month, or two months and then after that you must do it yourself," Hoejgaard says. "That's the official reason why we have been able to cut so many hours from home help."
DaneAge fears, however, that the policy leaves the most vulnerable elderly people inadequately cared for.
"It is good for some people, but it is also used as an excuse to cut back on people who really need help," Hoejgaard says. "There are a lot of people who are simply too old and too weak to manage for themselves, and we think that the municipalities are not good enough at separating these two groups."
He added: "Weekly visits from helpers are about more than just giving old people a bath and a quick clean of their flat.
"It's also a person who comes into your home to see how it's going. They are meant to check that things are not getting worse, and you lose that element when you only get help once every two to three months."
During a bitter row over the country's budget last year, Johanne Schmidt-Nielsen, the leader of the left-wing Red-Green Alliance, tried to force the centre-left coalition government to guarantee all over-65s at least two baths a week.
But rather than make such a commitment, the prime minister, Helle Thorning-Schmidt, struck a budget deal with the centre-right opposition, opening the way for a raft of new cuts which came into force on 1 January.
Some people have argued it is the beginning of the end for the Danish universal welfare state.
But rather than grumble, many Danes seem keen to try and make the welfare system deliver the same or at least comparable services, for less money.
"I've been in the system for 25 years, and I think it's getting better," says Vestergaard. "I believe Denmark will continue to give the Danish people what they need, but I also believe that we will try to make people who have resources use them."