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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 \({\mathbf {C}}_2\)

\({\mathbf {C}}_1\) | \(\lambda _{1,2}\) | \(\lambda _{3,4}\) | \(\lambda _{5,6}\) | \(\lambda _{7,8}\) | \(\lambda _{9,10}\) | \(\lambda _{11,12}\) |
---|---|---|---|---|---|---|

\(\omega _n\) | 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 |