In this study, we consider the null-space control problem of redundant robot manipulators. Specifically for robot manipulators with kinematically redundancy where at least one extra degree of freedom is present, we introduce a sub-task controller that will ensure the use of the extra degrees of freedom for possible control purposes while still ensuring the main objective. The stability of the main (end-effector tracking) and sub-task objectives are obtained via Lyapunov based arguments. Extension to adaptive controller formulation for robotic devices with uncertain system dynamics is also presented. Numerical studies for the adaptive controller are presented to illustrate the liability of the proposed method.