# Inertial Parameter Identification in Robotics: A Survey
## 1 Introduction
### Problem Formulation and Proposed Contributions  
Although it seems possible from the previous studies to infer specific tendencies as to the performance and context of application of the different identification algorithms [29], it is worth noting that no study currently provides a general guideline, based on quantitative arguments, such as encoder noise level, sampling frequency or knowledge of the control law. To be valid, such a study should be carried out within the same framework, on a wide range of methods, under well-defined experimental conditions and using a Monte Carlo analysis scheme to provide statistically significant results. Although benchmarking is common practice in the automatic control community--see e.g., [30; 31; 32] among others--it is less common in robotics, with some notable exceptions [33; 34; 35]. In practice, evaluating the performance of an identification method on a real system proves to be a difficult task since the latter can never be perfectly modeled. This is a direct consequence of the wide variety of complex physical phenomena--such as backlash or nonlinear friction--that have a significant influence on the system behavior while being relatively challenging to model. On the contrary, the identification of a simulated system allows a rigorous quantification of an algorithm's performance since the characteristics and parameters of the simulated model are well known and can therefore be used as a reference. The simulation also makes it possible to highlight the influence of specific physical phenomena--e.g., joint friction or measurement noise--on the estimates' quality. Therefore, our first contribution is to propose a dedicated framework, in the form of an open-source Matlab toolbox, which makes it possible to formally evaluate the performance of multiple identification algorithms on the same robot model and under the same conditions or assumptions. We use this benchmark to formally evaluate the performance of a set of algorithms among the most widely used offline computational approaches to robot dynamic parameter identification. These methods are the IDIM-LS (including the WLS, IRLS and TLS variants), ML, IDIM-IV, Output Error methods (CLOE, CLIE, DIDIM), the Extended Kalman Filter (EKF) as well as several of its Sigma-Point and Square-Root alternatives (SPKF), the Adaline Neural Network (AdaNN), the Hopfield-Tank Recurrent Neural Network (HTRNN) and finally a set of Semi-Definite Programming (SDP) approaches with Linear Matrix Inequalities to enforce physical consistency (PC-IDIM-OLS, PC-IDIM-WLS, PC-IDIM-IRLS, PC-DIDIM). The reader can find a summary of the evaluated identification methods in Appendix A Table A1. Though it is always interesting to formally compare different methodologies, the usefulness of such a comparison remains questionable if no conceptual relationship can ultimately be established between these approaches. For instance, stating that IDIM-IV or DIDIM outperforms IDIM-OLS in the case of improper data-filtering and/or too noisy data is not really helpful nor constructive for practitioners since this gain of robustness against noises is expected from IDIM-IV, and Output Error approaches. Instead, it is more interesting to show how the data-filtering helps IDIM-OLS to provide results that match those provided by IDIM-IV and Output Error approaches. Therefore, our second contribution is to establish some relationships between different methods to emphasize their similarities and differences. Finally, establishing relationships allows providing some _guidelines_ to practitioners non-expert in robot identification to help them to choose an identification method among all the available approaches: this is the third and last contribution of this work. The paper is organized as follows: Section 2 provides a theoretical overview of how simulated robot modeling and control are achieved in the context of identification.