Despite an icy wind the 53-year-old easily climbed -- bare-handed and without ropes -- up the 187-metre (614-feet) building in less than 45 minutes, delighting passers-by.
"I am happy because yesterday it was grey all day. Now it is cold, there will be wind, but at least it will not rain," Robert said before heading up the tower, which he has previously climbed.
The urban climber has scaled more than 100 structures without ropes or other safety equipment, setting a record for "most buildings climbed unassisted" according to Guinness World Records.
While known for climbing with nothing but his bare hands and a bag of chalk, he used suction devices and a safety rope on the Burj Khalifa, the world's tallest building, which had no hand or footholds.
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As usual the location of his climb was kept secret until the last minute.
"I have never seen him in person, too bad for work," said Marie, 43, a Total employee.
Security officials stood by helplessly.
"What do you want us to do? We are less strong than him, we can't climb the facade," said the head of Total's building security.
Robert has suffered several severe falls while climbing and estimates his accidents have left him 66 percent disabled.
"Climbing is my passion, my philosophy of life. Although I suffer from vertigo, although my accidents left me disabled up to 66 percent, I have become the best solo climber," he wrote on his website.