# Inertial Parameter Identification in Robotics: A Survey
## 10 Results, Discussion and Perspectives
### Analysis and Discussion of the Results
#### 10.1.2 Estimation Accuracy  
The results of the three Monte Carlo Simulation (MCS) experiments indicate that the DIDIM and IDIM-IV methods generally tend to provide the most accurate parameter estimates, and accordingly the best torque tracking performance in the context of standard joint position noise levels (i.e., MCS-RV2 SQ-1-1, MCS-RV2 SQ-1-2, MCS-TX40-1-1, MCS-TX40-1-2, MCS-TX40-4-1 and MCS-TX40-4-2 in the supplementary material). Note that by accuracy, we here refer to the error \(\beta_{err}\) between the estimated parameter vector \(\hat{\mathbf{\beta}}\) and the reference \(\beta_{ref}\) used for experiment data generation. This is visible in the experiment reports, provided alongside with this paper (c.f. Section 11). One may of course argue that these performances are noticeably similar to that of AdaNN, HTRNN, IDIM-OLS, -WLS, -IRLS, ML with filtered or decimated data as well as CLIE and--to a lower extent--CLOE. Interestingly, IDIM-IV and DIDIM does not perform as well on the real RV2 SQ robot although the resulting torque tracking performance remains satisfactory as shown in the _attached experiment reports_. This can be explained by the rather constraining hypothesis made during the simulation experiments, namely that the control law is well known and that these are not model errors (e.g., friction or coupling). One may also notice that CLIE provides better results than CLOE, which can be mainly explained by the lack of sensitivity of the simulated joint positions and velocities against parameters' variations due to the control. When developing a controller, the following approximation \(\mathbf{q}\approx\mathbf{q}_{d}\) is expected which means that the controller must be robust enough against parameters' variations. This result agrees with those published in [5]. Please note that when badly initialized or in the presence of modeling errors, iterative methods such as IDIM-IV, DIDIM, CLIE, CLOE, NKF or AdaNN usually fail to converge to the objective values as the internal DDM or IDM simulation process converge to an inconsistent state. In practice, a reasonable initialization value for the parameters can be obtained from a modern CAD software or from filtered IDIM-OLS. Although AdaNN and IDIM-OLS are asymptotically equivalent, one may note that the results in chapters 2.1 and 22.1 of the _attached experiment reports_ suggest that AdaNN is less efficient than IDIM-OLS - statistically speaking - as the variance of the AdaNN estimate appears to be at least one order of magnitude higher than that of the IDIM-OLS estimate. Finally, although the NKF identification methods provide good results in the case of the TX40 robot with undecimated data (c.f. Table MCS-TX40-1-1), the performance of the estimator sharply deteriorates when fed with decimated or sub-sampled data (c.f. Table MCS-TX40-4-1 and Table MCS-RV2 SQ-1-1). Nevertheless, Kalman filtering techniques generally tend--as with the CLOE method--to suffer from the same lack of sensitivity with respect to parameters' variations since the controller of the simulated robot is robust against these variations as demonstrated in [7]. 10.1.3. Convergence and Computational Complexity  
The convergence of the DIDIM iterative process is fast, similar to IDIM-IV, with an average computation time of 1 second, as a result of 4 (resp. 3) iterations on average and as many model simulations. This is consistent with the results of [6; 43]. Please note that this is approximately five times higher than IDIM-OLS, which can be explained by the process of DDM integration occurring during the simulation step within DIDIM and IDIM-IV. As expected, physically consistent identification methods, based on semi-defined programming algorithms, take about three times longer than their unconstrained counterparts, which is consistent with the performance of current SDP solvers (in our case CVX with MOSEK) and aligned with the results of [92].