Based on the Lyapunov theory, a new principle of synthesizing robot tracking control of the ‘resolved acceleration’ type is developed. A general Lyapunov-like tracking concept is used as the basis for the control algorithms derived via two different forms of Lyapunov functions. The main contribution is a result for (robust) tracking end-effector (cartesian) motion which obviates the need to invert the jacobian matrix or otherwise solve for desired joint-space coordinates from the given cartesian-space coordinates. Another advantage of the presented algorithms is that they guarantee tracking with a finite prescribed time.