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We present an adaptive version of the computed torque method for the control of manipulators with rigid links. The algorithun estimates parameters on-line which appear in the non-linear dynamic model of the manipulator, such as load and link mass parameters and friction parameters, and uses the latest estimates in the computed torque servo. We present what we believe is the first golbally convergent, rigorous proof of the stability of such a scheme in its non-linear setting, as well as its asymptotic properties and conditions for parameter convergence. We illustrate the theory with some simulation results.