Rodin, a towering ego even in a century of mythomaniacs, hated to show with anyone else. Pressurised into the landmark Monet Rodin exhibition in 1889 — the sculptor was already a celebrity, the painter not yet so famous — Rodin arranged to sneak into the gallery just before the opening and have “The Burghers of Calais” positioned to obliterate the strongest wall of Monet’s canvases: “I don’t give a damn about Monet . . . the only thing I’m worried about is me.”

Today it is Rodin who needs company: few exhibitions show him alone. Among 2017’s homages on the centenary of his death, Rodin at the Met reunited him with Monet, and Philadelphia staged Kiefer Rodin. Now Picasso Rodin, due to open in Paris in February, sets the sensuous, supple, spiralled bodies of “The Kiss”, icon of young erotic ecstasy, against Picasso’s 1969 painting of the same name: disfigured, grizzled old lovers enacting desire as black comedy. In Basel, Switzerland, at the Beyeler Foundation’s Rodin Arp, the gloomy “Thinker” pondering the circles of hell is challenged, in a majestic introductory pairing, by German-French artist Jean Arp’s optimistic “Ptolemy III”, all harmonious interlocking shapes, balanced volumes and voids, positive and negative spaces (launched in December, reopening expected in March). Rodin Giacometti, among the pandemic’s first online exhibitions in 2020, subsequently at Madrid’s Mapfre, sought to tilt Rodin towards existential ambiguity.

It is pretty obvious why Rodin exhibitions are on the rise: the 19th-century master for anguished times brought a new expressive realism, connected to Impressionist rendering of light and shade and movement, to give pathos and intimacy to figurative sculpture. It is not just the downcast heads, faltering gait, slumped shoulders, oversized bare feet of the Calais Burghers walking out to presumed death; in their thin joints, emaciated flesh, agonised twisting fingers, Rodin told how the body feels in every nerve and muscle. He reinvigorated cold academic sculpture — but with a Romantic excess, a refusal of comedy, irony, detachment. Modernism has separated us from that sensibility; Rodin’s emotionalism accords with moments of trouble, yet we cannot fully accept his weight and ostentation. That may be why curators partner him with modernity.

When Rodin died in 1917, Serge Diaghilev’s Ballets Russes performance of “Parade”, with its characters dressed as Picasso’s colourful sculptural assemblages, had just been shrieked off the stage in Paris, and Arp was orchestrating Dada subversions at Zurich’s Cabaret Voltaire. Still, the young Picasso had a photograph of “The Thinker” pinned to his studio wall, and in 1938 Arp called his strange anthropomorphic composition of curving, downward-pulsing fluid forms “Automatic Sculpture (Homage to Rodin)”: it resembles an abstracted “Thinker”.

The Beyeler compellingly situates Arp’s playful metamorphoses — the human/vegetal “Flower Nude” and “Torso-Sheaf”, the upright female figure/tree trunk “Kore” — as a formal development, yet a departure in spirit, from Rodin’s flexible, undulating, dynamic bodies. In 1887 Rodin provocatively feminised and sexualised the equestrian monument in “Centauress”, a woman fused to a horse’s body — “an image of the soul whose ethereal impulses remain miserably imprisoned in the corporeal mire,” Rodin explained.

In 1952 Arp’s sinuous woman/snake “Cobra-Centaur”, referring back to Rodin, by contrast lyrically blends human and natural. Rodin thunders, Arp proceeds lightly, slyly. Compare Rodin’s pessimistic bronze “Three Shades”, so anatomically distorted that necks and shoulders form a continuous horizontal barrier — they were conceived to look down on spectators from atop “The Gates of Hell” — with Arp’s soaring, wavy aluminium columns “The Three Graces”. Arp’s abstraction is a language of postwar hope.

If Arp is Rodin’s temperamental opposite, in Picasso, Rodin meets his match as a godlike creator of forms. The year-long joint extravaganza at Paris’s Musée Rodin, where the focus is on representational strategies, and Musée Picasso, which compares creative processes, benefits from numerous in situ greats. Death and sex are the motors: two charnel houses, “The Gates of Hell” and a tapestry rendering of “Guernica”; Picasso’s rapturous post-cubist bodies, unfolded and reassembled like cutouts — “The Swimmer”, “The Blue Acrobat” — from 1929, his early days with his sporty teenage muse Marie-Thérèse Walter, and Rodin’s leaping, open-legged fin-de-siècle shocker “Iris, Messenger of the Gods”.

Rodin’s late obsession with extreme acrobatic dance poses, as in the terracotta, footless “Dance Movement” group (1911), gains interesting context as contemporaneous with Picasso’s high point of cubist deconstruction. And some true rarities provide counterpoints of delicacy: Picasso’s collage of insect, leaf, twine, wood, “Composition with Butterfly”, and an extraordinary plaster version of Rodin’s “Eternal Idol”, a nude sitting on a rock sprouting a real holly branch.

It is the artist of assemblage and experiment which Tate will highlight in The Making of Rodin, scheduled for April: an anti-monumental presentation focused on the plaster originals rather than the polished bronzes and marbles. “Study for The Thinker”, perched on a metal pole, has only one leg and one arm, surfaces gnarled and pitted, eye gouged. All the expressive force of a body in tension is distilled into the fragment, studded with the pressure of the kneading, pummelling hand, in “Study for Torso of John the Baptist”.

Tate’s mise-en-scène will evoke the atmosphere of Rodin’s studio, with its piles of plaster fragments to be reiterated, varied, interchangeable in figures, or parts of figures, across the decades. Rodin’s strategies of multiplication and repetition — evolved in parallel to Monet’s series paintings — are a conceptual legacy to sculptors sharing little else with him, such as minimalists Donald Judd and Carl Andre. Tate’s destabilising, improvisational Rodin also accords with the art of process which Tate strongly prioritises in displays of its 20th- and 21st-century permanent collection around the themes “In the Studio” and “Materials and Objects”. Rodin here is in dialogue with the contemporary.

In “Rodin: Le Livre du Centenaire” (2017) Catherine Chevillot, director of the Musée Rodin, argues that plaster was “the material most crucial to his aesthetic, giving the impression of sculptures that are never finished, always becoming”. There is a Rodin for every age, and curators are persuasively shaping ours into the prophet of mutability and uncertainty.

While we wait for these museums to open, and also for the many people who seek art outside during the pandemic, the old, larger-than-life Rodin however remains on view in spectacular outdoor settings. Londoners can always see, free, the etiolated suffering medieval Burghers of Calais appropriately framed by Westminster Palace’s Gothic revival architecture. The Musée Rodin reopened its gardens alone last weekend: “The Thinker” thinks against the backdrop of the Dôme des Invalides, “Ugolino” sits in the pool, “Orpheus” tunes his lyre half-hidden in the thickets. Rodin’s most satisfying conversation of all, and the most affirmative for now, is with nature.

Picasso Rodin, Musée Rodin and Musée Picasso, Paris, February 9-January 2 2022; Rodin Arp, Fondation Beyeler, Basel, March to May 16; The Making of Rodin, Tate Modern, London, April 29-October 31