The classic formula R + X + b + a assumes pallets as wide as the robot. With wide pallets the front pallet corner sweeps a larger arc, so its real radius is used:

Lt = √(R² − (Wv/2 + e)²)
X  = (L − Lf) − Lt + d
Rp = √((X + b)² + (Wp/2 + e)²)
Rn = √(X² + (Wp/2 + e)²)        only if X < 0
R* = max(R, Rn)

Turn  = R* + Rp + a
Line  = max(Wv, Wp) + 2·s
RASA  = max(turn, line)

R: robot turning radius · X: fork face relative to the turning center (negative when the center sits under the pallet) · e: lateral turning-center offset · a: total clearance to racks · s: side clearance per side.

A lifting robot slides under the cart and turns in place with it. The cart sweeps a circle as large as its diagonal, and the robot only needs its own turning diameter. The minimum aisle is the larger of the two plus the same clearance as the forklifts: a fixed 200 mm + extra clearance (200 mm by default).

Dc = √(Wc² + Lc²)
Aisle   = max(Dc, Dr) + a

Wc, Lc: cart width and length · Dc: cart diagonal · Dr: robot turning diameter (data sheet) · a: clearance (fixed 200 mm + extra).