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Resolved acceleration control is a method for motion control of robot manipulators in task space where a desired end-effector pose trajectory is specified. We consider the orientation part of the pose given by the Euler parameters or unit quaternion. The main contribution is a novel proof of asymptotic stability based in the use of a strict Lyapunov function. This is a one stage procedure which improves previously reported analysis where two-stage mechanisms are in general invoked: first demonstrating stability and then convergence.