A downhole closed loop method for controlling a curvature of a subterranean wellbore while drilling includes controlling a direction of drilling such that the drilling attitude is substantially equal to a setpoint attitude. A setpoint rate of penetration is processed in combination with a setpoint dogleg severity to compute a setpoint attitude increment. The setpoint attitude may be adjusted by the setpoint attitude increment. The setpoint attitude may be incremented at some interval to control the curvature of the wellbore while drilling.