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Table 1 Comparison of damping ratios and natural frequencies of the Panda robot performing Cartesian impedance control using two different damping matrices \({\mathbf {C}}_1\) and \({\mathbf {C}}_2\)

From: Analytical methodology for the analysis of vibration for unconstrained discrete systems and applications to impedance control of redundant robots

\({\mathbf {C}}_1\) \(\lambda _{1,2}\) \(\lambda _{3,4}\) \(\lambda _{5,6}\) \(\lambda _{7,8}\) \(\lambda _{9,10}\) \(\lambda _{11,12}\)
\(\omega _n\) 20.25 10.98 9.755 73.17 90.89
\(\zeta\) 0.0255 0.0316 0.0294 0.2483 0.4075 1
\({\mathbf {C}}_2\) \(\lambda _{1,2}\) \(\lambda _{3,4}\) \(\lambda _{5,6}\) \(\lambda _{7,8}\) \(\lambda _{9,10}\) \(\lambda _{11,12}\)
\(\omega _n\) 20.23 10.95 11.17 125.45
\(\zeta\) 0.2235 0.2032 0.2288 1 1 0.94
  1. Data from all six pairs of eigenvalues in the modal space are tabulated