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Two types of asymptotic observer are constructed for constrained robot systems in this paper. Since a constrained robot, in general, involves a set of differential equations and a set of algebraic equations, both differential and algebraic variables should be estimated. This gives arise to difficulty in estimating the algebraic variables which are the contact forces. The difficulty is eased by introducing a nonlinear transformation. Although the transformation causes nonlinear coupling on the input, asymptotic observers can be constructed in terms of the transformed system by a special treatment. Since both the contact force and the motion of the robot can be directly estimated, the observers may be useful for the controller design of the constrained robot system.

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