Natalia Osipova was standing in a queue at Moscow airport recently, waiting for her flight back to London, when she overheard a woman mention her name. “She was talking about the show,” says Osipova, who had just finished performing The Mother, a contemporary dance drama. “The woman said, ‘She could have danced another classical ballet. Why is she spending her time on this?’” Osipova sighs. “I felt quite vulnerable. Why am I not understood?”

Some of her fans might not be ready to accompany the Russian ballerina on her odyssey into experimental dance, but Osipova is an artist who trusts her instincts: from her 2001 decision to walk out of one of the world’s most prestigious ballet companies, the Bolshoi, in favour of a second-tier institution, the Mikhailovsky Theatre, to launching a parallel career in contemporary dance while still one of the top classical ballerinas.

Now a principal with the Royal Ballet, and boasting a nonstop freelance schedule on the side, Osipova is a powerful dancer of explosive jumps and dramatic intensity. Her passion and self-belief give the title to Force of Nature Natalia, a new documentary by director Gerry Fox that follows Osipova as she rehearses for three shows: La Bayadère at the Royal Ballet; The Mother, Arthur Pita’s dark retelling of the Hans Christian Andersen story; and a new duet created with dancer and Osipova’s fiance Jason Kittelberger, more of whom later.

We meet at her flat in Little Venice, London – smart modern decor and the feel of someone who’s not home much – where we are joined by an interpreter and two over-excited dogs. Osipova, 33, is very straightforward, not starry or effusive – unlike when she gets on stage, when she’ll propel herself towards dramatic extremes. The Mother, a two-hander based on the bleak tale of a woman desperately trying to save her dying baby, often leaves Osipova bloodied and bruised from its physical floorwork and emotionally tested trying to reach the heart of the character.

“I’m not a mother myself yet,” she says, “so I was anxious that it wouldn’t be a realistic portrayal because I don’t know what it’s like.” It’s similar to how you feel about your dogs, I tell her, but times a hundred. “It’s funny you make that comparison,” she laughs, “because when we got them, they were just puppies, two months old. And in a way, my feeling about them fed into the part.”

We talk about how rare it is in dance to depict something other than romantic love. “Traditionally in ballet,” she says, “you are expressing love for a man and there are very few exceptions. In my career, I can only think of Kenneth MacMillan’s Anastasia.” (Premiered in 1967, Anastasia is about a woman who claimed to be the daughter of tsar Nicholas II.) “In contemporary,” Osipova adds, “it’s different. Sometimes we speak just about physiology, sexuality …” She pauses and laughs. “But the men are always there somewhere!”

Of course, two people, two bodies connecting, is something dance can express well. But Osipova is as interested in showing the realities of relationships as well as the fairytale ideals. Last year, in her self-curated programme Pure Dance, she and Kittelberger performed Roy Assaf’s Six Years Later, a portrait of a tired and tetchy relationship, in which, the noted New York Times critic Siobhan Burke, Kittelberger emerged as an equal to the charismatic Osipova on stage.

Dancing with Kittelberger was a revelation for Osipova. “It was so, so different to dancing with a classical dancer,” she says. “It was like a real person, really touching me, and it was like, ‘Mmmm!’” Her bright eyes widen with mischief at the memory. “It was electrifying. He really showed me a different way of experiencing dance.”

Gerry Fox, who filmed the couple dancing in the studio, talks about their “sensual tension, two people giving their all through their bodies and being so free with each other”. Osipova has danced with many notable partners, including former boyfriends Ivan Vasiliev and Sergei Polunin, but this was different. “So different,” she says. The film sees them working on a new creation, I’m Fine, about the ups and downs of a relationship. “The title comes from me personally, when I’m irritated or angry – saying ‘I’m fine!’ when it’s clear I’m not.” Kittelberger created the steps (“That’s not my strong point”) and Osipova was dramaturg. “I’m more sensitive to the story,” she says. “I’m strong on interpretation. That’s the gift I have.”

Kittelberger provides Osipova with essential support off stage as well as on. “If I’m in an intense project, I become more needy,” she says. “I need more comfort, and if I don’t get it I become resentful. I need a lot of attention, especially from men – maybe because my father had such a comforting, amazing energy. Jason really gets it and gives me everything I need.

“He does see a bit of the child in me, in a good way. I’m very aware of my own power. Physically and emotionally, I’m a really strong person, in art and in life. But there are times when you want to totally give it away and be helpless, and he’s somebody who can allow me to do that.”

As well as exploring her adventures in contemporary dance, Fox’s documentary discusses one of Osipova’s most feted classical roles: Giselle, the beautiful young peasant girl who falls for a deceitful nobleman. “Giselle,” Osipova tells the camera at one point, “it’s me.” What did she mean? “It’s the most natural part for me,” she says. “The second act is so close to me, as if I have it somewhere in my DNA.”

Osipova is not the ghostly spirit of a wronged woman, as Giselle becomes in act two, but her entire physicality alters as she embodies the role – a more vivid, chilling and unhuman Giselle than any I’ve seen. “When I started dancing it, I was 19 or 20, and I was doing it in a very non-traditional way. My teachers would be telling me off, but I had such an inner certainty that it was impossible to knock it out of me.” Where does that confidence come from? “From my deep connection to the part – and my peaceful certainty that this is how it should be.”

When Osipova began her career at the Bolshoi, the director was Alexei Ratmansky, “who gave quite a lot of freedom”. But when he was succeeded by Sergei Filin, Osipova found herself unhappy in Moscow, her opportunities restricted. She’s content now at the Royal Ballet, a company with a healthier culture than most she has experienced. “The first time I came I was surprised there was no intrigue or conflict, and people were nice to each other,” she says. “It’s my fifth season now and I’ve had not a single conflict. Sometimes people say I just don’t get enough of the language to know!” She laughs. “But in other companies, you can sense it, when people are envious, or don’t want you to be there, or they’re talking behind your back. I can’t work like that.”

Does something about the nature of ballet companies engender a dysfunctional atmosphere? Filin was the victim of an acid attack orchestrated by a disgruntled dancer, and New York City Ballet has been rocked by accusations of harassment and abuse. “It all depends on who is leading, and what they encourage and what they cut off,” says Osipova. “I can think of two situations when [Royal Ballet director] Kevin O’Hare said, ‘This is not happening’, otherwise something unpleasant might have started.”

The pressure, the egos, the intensity of a dancer’s life have certainly been blamed for more than one artistic outburst. Osipova’s ex, Polunin, is a case in point, with his recent macho and fat-shaming tirades online. The controversial dancer had this to say about male dancers: “Females now trying to take on the man role because you don’t f––– them and because you are an embarrassment.” He also wrote: “Let’s slap fat people.”

Osipova has gone on record saying Polunin is a good guy who should be judged only on his dancing. Why does she think he is so frequently self-destructive? “No one but him can answer your question,” she says. “He’s clearly gifted, and I really wish that he nurtures it rather than undermines it.”

Osipova seems able to harness all the drama and drive for her dancing and thinks she has another five years of performing at her peak. “At the moment, I feel very mature and capable, emotionally and physically,” she says. “Contemporary dance is making my body feel and move differently. It’s a really good time for me now.”

• The Mother is at Queen Elizabeth Hall, London, 20-22 June. Force of Nature Natalia is out now and will be broadcast on Sky Arts on 18 June.