US Patent 9945222 Closed loop control of drilling curvature

A downhole closed loop method for controlling a curvature of a subterranean wellbore while drilling includes drilling the subterranean wellbore using a drilling tool. A set point curvature is received at a downhole controller. Sequential attitude measurements made at a single axial location on the drilling tool and a rate of penetration of drilling are processed to compute a curvature of the wellbore being drilled. The drilling direction is adjusted such that the computed curvature is substantially equal to the set point curvature.