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A robustness bound of computed torque linearization for control of a manipulator in contact task

This paper suggests a robustness bound of modeling errors in computed torque linearization for control of a manipulator in a contact task. Modelling errors due to sensing and estimation errors can cause instability of the overall control. A stability condition for the modelling errors is derived from the error dynamics using the operator theory and the small gain theorem. The result is a single equation, which gives an allowable bound in a combined form of the inertia modelling error and Jacobian estimation error. It shows that the Jacobian estimation errors degrade the stability when the force feedback is used in the computed torque linearization. Especially for control of a manipulator in a stiff environment, the Jacobian should be estimated accurately. The Coriolis and nonlinear terms are not as critical factors as inertia and Jacobian estimation. The bound can be used in controller design, which is insensitive to the modelling errors.