Nihon Kikai Gakkai ronbunshu (Jun 2024)
Stability assessment method based on actual measurements for a cable-driven continuum robot
Abstract
In order to experimentally determine the controlled variable values realizing a quasi-zero stiffness of a cable driven continuum robot, this paper presents an experimental method for quantitatively and accurately assessing the stability of a robot in a static equilibrium state with the controlled variables being kept at their target values. Experimental stability assessment requires consideration of the difficulty for an actual robot to achieve the unstable static equilibrium states and the fact that measurement errors can greatly affect stability assessment. Thus, the proposed experimental method assesses the stability of a robot by determining the smallest eigenvalue of the Hessian matrix of the total potential energy through measuring the relationship betweensmalldisplacementandworkdonebyexternalforcesfromastaticequilibriumstatetobeassessed. This measurement sets the controlled variables on an experimental robot that stably achieve the static equilibrium state instead of the controlled variables to be assessed. Moreover, an additional small displacement is given in the same direction as the eigenvector of the smallest eigenvalue of the Hessian once obtained. Then the stability of a planar 3-DOF continuum robot consisting of a variable-length elastic rod and two cables with the controlled variables set as the rod length and the cable tensions was assessed by the derived stability analysis and the proposed experimental method. The experimental results showed that the stability of both stable and unstable static equilibrium states was quantified, with a high repeatability of the results. Additionally, the stability assessment value decreased from positive to negative with the increasing cable tensions, consistent with the theoretical results. Furthermore, giving the additional small displacement enables a more accurate assessment of the stability. Finally, an approximation of the experimental results successfully determined the controlled variable values that allow the experimental robot to realize the neutral static equilibrium state.
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