Robust arm configuration of manipulator mounted on flexible base

In this paper, the robustness of a manipulator mounted on a flexible base with a task-space feedback control to a fixed desired point is considered. We define the robust arm configuration (RAC), which is a special configuration where the linearized system is positive real. Lyapunov indirect method and the passivity theory guarantee a local asymptotic stability of the original nonlinear system. A finite but high closed-loop gain can be applied in the neighborhood of the RAC without considering the base flexibility, i.e., an additional sensor or a solution of whole inverse dynamics is not necessary. Considering the positive semidefiniteness of the residue matrices, a measure is proposed that measures the distance from the RAC. This measure represents the controllability of the manipulator itself, and does not depend on the underlying control law. The validity of the proposed approach is confirmed by a numerical example and experiments.

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