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In this paper, we consider the state estimation problem for flexible joint manipulators that involve nonlinear characteristics in their stiffness. The two key ideas of our design are that (a) an accelerometer is used in order that the estimation error dynamics do not depend on nonlinearities at the link part of the manipulators and (b) the model of the nonlinear stiffness is indeed a Lipschitz function. Based on the measured acceleration, we propose a nonlinear observer under the Lipschitz condition of the nonlinear stiffness. In addition, in order to effectively compensate for the estimation error, the gain of the proposed observer is chosen from the ARE (algebraic Riccati equations) which depend on the Lipschitz constant. Comparative experimental results verify the effectiveness of the proposed method.

Position and Velocity Estimation for Two-Inertia System with Nonlinear Stiffness Based on Acceleration Sensor