# Inertial Parameter Identification in Robotics: A Survey
## 8 Introducing the BIRDy Matlab Toolbox: A Benchmark for Identification of Robot Dynamics
### Validation Experiments on the Real TX40 and RV2 SQ  
A set of validation experiments were conducted on the real Staubli TX-40 and Mitsubishi RV2 SQ robots. These experiments aimed at assessing the performance of the different identification algorithms presented in this paper on real systems, with unknown sensor characteristics, unknown control structure, and potentially non-negligible model errors stemming from nonlinearities in the joint friction. During these experiments, the coupling between the fifth and sixth joint of the TX40 was considered for better precision resulting in 54 base parameters as opposed to the 52 considered during the MCS experiments. In both cases, the robot drive gains were identified following the Least-Squares approach developed by [104; 105], which consists of having the robot track a permanently exciting trajectory, both with and without a well-known external payload, rigidly attached to the end-effector as depicted in Figure 8c in the case of the RV2 SQ. Drive-gain identification is made possible by analyzing variations in the control current, sampled along the same excitation trajectories, both with and without the external payload attached to the end-effector. Good prior knowledge of the payload parameters is, of course, essential to the quality of the estimation. In practice, this is made possible either by direct measurements or through modern CAD software, given the generally simple geometry of the payload. During the experiments, the benchmark was executed a _single time_ for each robot, along a dedicated validation trajectory. The joint position and drive current data were sampled at a rate of 1 kHz on the TX40 and at a rate of 140 Hz on the RV2 SQ. The detailed results of these experiments in terms of the values of the different figures of merit defined in Section 9.2, are presented in the table section of the supplementary material for the real TX40 and the real RV2 SQ. The different links to the supplementary material are made available to the reader in the Data Availability Statement, Section 11. Finally, the reconstructed torque signals for the IDIM-IV and DIDIM methods are displayed in Figure 9 for the TX40 and in Figure 10 for the RV2 SQ.  
\begin{table}
\begin{tabular}{l l l l} \hline
**MCS Experimental Conditions** & **TX40 Decimation 1** & **TX40 Decimation 4** & **RV2 SQ Decimation 1** \\ \hline \(\sigma_{q}=10^{-4}\) rad, \(\sigma_{\mathbf{\tau}}=5\times 10^{-2}\) N\(\cdot\)m & MCS-TX40-1-1 & MCS-TX40-4-1 & MCS-RV2 SQ-1-1 \\ \(\sigma_{q}=10^{-3}\) rad, \(\sigma_{\mathbf{\tau}}=5\times 10^{-2}\) N\(\cdot\)m & MCS-TX40-1-2 & MCS-TX40-4-2 & MCS-RV2 SQ-1-2 \\ \(\sigma_{q}=10^{-2}\) rad, \(\sigma_{\mathbf{\tau}}=5\times 10^{-2}\) N\(\cdot\)m & MCS-TX40-1-3 & MCS-TX40-4-3 & MCS-RV2 SQ-1-3 \\ \(\sigma_{q}=10^{-3}\) rad, \(\sigma_{\mathbf{\tau}}=10^{-1}\) N\(\cdot\)m & MCS-TX40-1-4 & MCS-TX40-4-4 & MCS-RV2 SQ-1-4 \\ \(\sigma_{q}=10^{-2}\) rad, \(\sigma_{\mathbf{\tau}}=10^{-1}\) N\(\cdot\)m & MCS-TX40-1-5 & MCS-TX40-4-5 & MCS-RV2 SQ-1-5 \\ \hline \end{tabular}
\end{table}
Table 1: Overview and naming convention of the different experiments performed during the MCS. The first row of the table refers to noise conditions that are close to what can be encountered on an industrial robot manipulator. The four other rows explore the performance of identification in the case of substantially higher joint position and torque noise levels.