Here's to you, Mrs Robinson: The First Lady Michelle Obama's mother plays a crucial role in the White House

It was a rare, almost intimate scene, between Michelle Obama and her mother, played out before the world. When a group of Chinese girls invited the First Lady to skip rope at an event on the ancient city wall during her recent visit to Xi'an, China, she kicked her heels off to slide on a pair of flats. Before an aide could swoop in and pick up her daughter's shoes, Marian Robinson bent down to grab them.

Then, the 76-year-old grandmother beamed as Obama jumped. Obama's daughters, Sasha and Malia, stood nearby, shyly hanging back as their mother took centre stage. Robinson clapped and smiled.

For six days in China, the least-public resident of the White House was a central figure on the public stage. Overseas trips such as the one Robinson took with her daughter and granddaughters last month provide an uncommon glimpse into their family dynamic and the critical role she has continued to play in the first family. In Washington, Mrs Robinson – or Mrs R, as she is sometimes called – is anonymous enough to go around town undetected.

Her private life is carefully guarded by the Obamas: she has only given a handful of interviews – to friendly media outlets – since her son-in-law became President and she stays away from the West Wing. In China, Michelle Obama proudly showed off her mother, and their bond was obvious. Max Baucus, the newly appointed US ambassador to China, tasked with introducing the First Lady to Chinese students at Peking University, offered, "She's so devoted to her mother, Mrs Robinson."

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When Robinson left Chicago for Washington, she told an interviewer, "They're dragging me with them, and I'm not that comfortable, but I'm doing exactly what you do. You do what has to be done." Five years in, Robinson seems to have settled into life in the White House, where she sometimes spends afternoons reading in a great hall that serves as the family's living room on the second-floor residence. Her children have said she has built a busy social life, but she still remains a go-to person for ensuring her granddaughters, who've grown up as household names, maintain some normality. It was this role she played in China, walking with her granddaughters as their mother drew the world's attention, or taking them to dinner when the First Lady had other obligations.

It is a space in which Robinson has grown comfortable. She smiled brightly at China's president, Xi Jinping, and outstretched her hand to him during a brief, formal meeting between the two first families. She greeted China's First Lady, Peng Liyuan, with a wave, and she strolled along as their group toured the Forbidden City, where emperors once dwelled. She chatted with Baucus while walking through the Summer Palace, an enchanting park of gardens, lakes and pavilions in Beijing.

During the meeting with Xi, Michelle Obama thanked him for welcoming her family – especially her mum. "Being able to see my mother, who doesn't get to travel internationally often, walk through that ancient city, and to see her excitement and wonder, is a moment that I will treasure forever," she told him. Robinson, seated three chairs away from her daughter, quietly said "Awwww".

Marian Shields Robinson moved into the White House in 2009 after a lifetime in Chicago, where she was raised by a painter and a stay-at-home mother in a small house with seven siblings. She married and became a stay-at-home mother herself, raising two Ivy League graduates. Before retiring to help care for her granddaughters, she worked as a bank secretary and took yoga classes. When her daughter asked her to move from her Chicago apartment block to the museum that is the White House, Robinson agreed, recognising the enormous transition the family faced at the time. Still, Robinson drew lines between herself and what she called "Michelle's family".

She considered taking an apartment in Washington, but ultimately moved into a room with a four-poster bed and sitting area on the third floor of the White House. The rest of the first family lives on the second floor. "There are many times when she drops off the kids, we hang out and talk and catch up, and then she's like, 'I'm going home.' And she walks upstairs," the First Lady told Oprah Winfrey early on.

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"I don't believe she is living in that house like a prisoner, as lovely as it is," says Anita McBride, Laura Bush's former chief of staff and now an executive-in-residence at American University in Washington. "I'm sure she has enjoyed a lot of what Washington and the world have to offer, but it demonstrates to me that there is a privacy about her and the circle of people she is spending time with." A senior administration official, who asked not to be identified out of respect for Robinson's privacy, adds that "She really enjoys the fact that she can walk out of the White House by herself". Officials in Michelle Obama's office declined to comment

Only the outlines of Robinson's life are known, picked up from scant mentions in interviews given by the President and First Lady. She doesn't grant interviews but wrote an essay published in Essence magazine during the 2012 campaign describing her life as relatively typical. "One of my biggest blessings is getting to see my granddaughters grow up before my eyes. My job here is the easiest one of all: I just get to be Grandma."

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One part of the job description in the early White House years: when Sasha and Malia were younger, Robinson would ride with them to and from school. And while Robinson is now part of the Obamas' daily routine, she deliberately carves out time to visit her son Craig's family as well. When the first family travels to Hawaii for the Christmas holidays, she has sometimes gone to see her son, daughter-in-law and their three children in Oregon.

Robinson's care-giving duties have not stopped her from creating a life of her own or making new friends, among whom is Betty Currie, who served as President Bill Clinton's personal secretary. The Obamas have said they sometimes have to plan their schedule around Mrs Robinson's. Unlike other members of the first family, she moves about without Secret Service detail. If she is recognised, the President has said she just demurs, saying she gets that a lot. She occasionally attends cultural events at the White House, such as music concerts or holiday and birthday parties, especially when her granddaughters are in attendance. At a state dinner in 2010, Robinson turned to the person sitting next to her to excuse herself so that she could tuck in her granddaughters. She then returned to the soirée. Outside the White House gates, she takes trips to Las Vegas with her friends, as the President enviously noted in a 2010 speech there. "She comes quite frequently... maybe I shouldn't say that in front of the press," Obama said.

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Robinson has been spotted at Washington restaurants dining with relatives, taking in an Aretha Franklin concert with her daughter and mingling at a book party hosted by family friends. "She's definitely very down-to-earth and receptive to engaging in conversations with anyone," said one guest at the party, celebrating the 2012 release of Harvard Law professor Randall Kennedy's The Persistence of the Color Line: Racial Politics and the Obama Presidency, who asked not to be named, "She was somebody who you could walk up to without pretence."

Still, Robinson is as much of a perfectionist as her daughter. She started running in her 50s and became a gold medallist in both the 50 and 100 metres in the 1997 Illinois Senior Olympics. But she abandoned the sport after an injury that made her less competitive. "If I can't do it fast, I'm not doing it," she said in Oprah Winfrey's magazine O in 2007. "You don't run just to be running – you run to win."

But being a perfectionist doesn't necessarily mean she's perfect, as her daughter has pointed out. The First Lady revealed that her mother, whom she has called her role model, is a smoker and can be "pretty stubborn" ."She taught us that you can be open and honest about your own shortcomings and it doesn't necessarily mean your kids are going to adopt them," Michelle Obama has said, describing one of the many lessons she has learnt from her mother. The First Lady also told People magazine this year that her mother "speaks her mind". "She does exactly what she wants to do every single day without apology," she added.

A case in point is that when Michelle and her daughters hiked the Great Wall in Beijing, pausing to be photographed by a couple of dozen journalists, Robinson stayed behind. On a plateau just below the high walkways, Robinson took in the scenic view. With her sunglasses propped on top of her head and a bottle of water in her hands, she looked like she was exactly where she wanted to be.

A version of this article has appeared on washingtonpost.com