I seemed to go round in circles, not sure if that's the designed way or perhaps i got mixed up by the symmetry. Nice puzzle and i liked the way B could hurdle the sweeper.
I have a feeling I used a shortcut, but finding it was plenty of fun. Spoiler B climbed on the ground floor slider at the right. Then he walked one block past where the two balls are balanced. The arm then pushed B over that gap to knock the ball down to access the back stairs. B then walked back and let the arm knock him down and got back on ground floor slider. Walked to the back stairs, up, over and down to the win.