If, as Wordsworth said, poetry is human emotion recollected in tranquillity, what happens when verses are scrawled in sand on the floor of a shopping centre? When they are left unguarded, to be kicked and scuffed by customers wandering into Costa Coffee or New Look?

We'll find out this week, when a robot called Skryf snakes through the Centre MK in Milton Keynes, spelling out lines by Jackie Kay. The extract from her poem Equinox is rich in significance. The inspiration was Kay's birth mother, whose vascular dementia is slowly scuffing away her memory, just as this poem will eventually be lost to the feet, buggies and shopping bags of the public. "Words are disappearing for her," says Kay, standing in Centre MK's atrium, the robot whirring at her side. "She'll look up and say there's a big biscuit in the sky, when it's the moon. As dementia goes on, you speak in a kind of jagged poetry."

It was outside Boots in this same mall that the pair first met as adults, more than 20 years ago. Kay had been given up for adoption when she was a baby and had subsequently written about her search for her birth mother in a collection called The Adoption Papers. Now they were getting to know each other again. In an odd coincidence, both women turned up with orchids. "In The Adoption Papers, I wrote what I imagined [my birth mother's] voice to be," says Kay. "Now I feel like I'm writing a voice that I hear, that I know."

She recalls: "She was looking at a picture of me the other day and said, 'She's a very nice lady. You can tell her things.' She referred to herself in the third person, too. There was something very liberating about both of us having the third person to speak in. In writing, we tend to think of the third person as less intimate, but in this context it made me see it as the most intimate form. She was able to tell me things in the form of 'she' that she couldn't say in 'I'."

Equinox explores this strange, jagged voice. Although only a single 60-line stanza will be sandwritten by the robot, the larger text explores a network of paradoxes, relationships and memory. Lines like, "I am only half real: my memory is failing me" and "I am writing in the sand: most magic, my hands,/ I seem mechanical and my poem is my own," create an intriguing confusion between subject, poet and robot. As the poem itself says, "Nothing is what it seems." If the combination of poetry and technology appears odd, it in fact speaks volumes about both Kay and Milton Keynes. (If You Want Wonderful Words, as the sandwriting exercise is called, is part of the IF: Milton Keynes international festival.) The poet has her own collection of robots, after being given a tin figurine by her former partner (and poet laureate) Carol Ann Duffy. "I told her I'd always wanted one as a child," says Kay. "I used to think they were half real; I liked that ambivalence. You could give them human thoughts but they seemed to come from a different world."

The Skryf robot – a plough-like collection of wheelbarrow parts, pram wheels, a lampstand and a laptop – is based on a milling machine, which would normally be used to shape wood. Its creator, artist Gijs van Bon, can type any text into the laptop, feed coloured sand into the top of the lampstand, then watch those words get slowly poured out on to the floor. "Usually the words just become shapes to me," says Van Bon, who has been taking Skryf to festivals since 2012. Working with Kay "is much more intimate".

Milton Keynes is a city built on contrasts; it has more green space than any other British city, yet is a grid-like sprawl of huge roads and modern buildings. It has an enormous network of pedestrian and cyclist routes, yet is defined by cars. It looks like a film set, but is home to over 256,000 people.

"It's made me want to explore those oxymorons," says Kay. "The squares and the circles, the sacred and secular, the built landscape and park lands, the ecological and the creative. It's a town built on a green ethos – they had a policy that if there was a well-established tree standing in the way, they would build the roads around it – and yet its public image is a bit of a joke. I like that, too."

Having grown up in Glasgow, Kay is well aware of how a city's image can fluctuate. "Glasgow got a very bad press for years – it was seen as the city where you'd get beaten up on a Saturday night," she recalls. "Then it became the European Capital of Culture in 1990 and transformed. It started to be seen as the home of these beautiful buildings by Charles Rennie Mackintosh, even though they were there all along. It was like they'd suddenly been cleaned up and given back to the public. By taking the dirt off the buildings, we lifted the city out of its past."

Trailing sand through a shopping centre is, of course, very different from cleaning up an old building. "I like the idea that something wise has been left on the pavement – a couple of lines that people can keep in their heads," Kay explains. "Poems can be little nuggets of intense, concentrated thought that, hopefully, make people think differently about their life."

Sometimes it is the very brevity of poetry that cuts straight to our emotional core. "I've got this poem called Darling that people use a lot at funerals," says Kay. "The reason, I think, is just to do with the last two lines, 'The dead don't go till you do, loved ones/ The dead are still here, holding our hands.' For some reason people find those two lines very comforting; people almost just need the two lines."

Each poem needs its own key, says Kay. Something that unlocks an idea and makes the robot walk. In this case, it was both the city and the transient nature of the poem. "I love the theatre of the poem in this context, all the chance that it involves," she says. "You might be walking past, see the poem and a line of it just happens to resonate."

• If You Want Wonderful Words is at the Centre MK on 18 and 19 July, moving to South Willen Lake Park on 20 July. An Audience with Jackie Kay is at the Stables Spiegeltent on 20 July at 4pm. Details: ifmiltonkeynes.org

• This article was amended on 16 July 2014. An earlier version referred to Carol Ann Duffy as the former, rather than current, poet laureate.