# Inertial Parameter Identification in Robotics: A Survey
## 8 Introducing the BIRDy Matlab Toolbox: A Benchmark for Identification of Robot Dynamics
### Hardware Description and Experiment Setup  
This work takes the form of a _case study_, carried out on two different robots, both in simulation and on the real systems. These robots are the 6-DoF **RV2 SQ** industrial manipulator from Mitsubishi, depicted in Figure 8b and the 6-DoF **TX40** robot from Staubli, depicted in Figure 8a. Both are described using the _proximal_ DH convention. Widely used for industrial and research purposes, these systems are ideal test platforms for having a similar kinematic structure but somewhat different communication interfaces and control characteristics. Generally speaking, evaluating the performance of multiple identification methods on different robot models within the same framework is relevant. It allows observing the influence of system-specific factors, such as the sampling rate or the control structure's knowledge, on the overall algorithm performance. This, in turn, makes it possible to infer guidelines regarding the selection process of an identification algorithm depending on the experimental context. In practice, while the TX-40 has a high-speed communication interface allowing the joint position and torque to be sampled at rates of up to \(f=5\) kHz, the data acquisition process on the RV2 SQ is achieved at a much lower frequency, namely \(f=140\) Hz. Moreover, although the low-level control characteristics of the TX40 are known with a sufficient level of accuracy (see in particular [6]), it must be emphasized that no prior knowledge of control structure, gains nor bandwidth of the RV2 SQ is available. In this work, the low-level control structures are assumed to be of cascaded PD type--as described in Section 2.3--with a control bandwidth \(f_{c}=5\) kHz. Please note that during the simulation experiments the control structure and gains used for data generation and identification are the same. Although hardly verifiable in practice, this hypothesis has critical implications as to the convergence properties of identification algorithms that are based on successive closed-loop DDM simulation runs such as DIDIM, CLIE, CLOE or NKF. We considered an integrated Viscous-Coulomb friction model for both data generation and parameter identification processes. This choice is deliberate and justified by the results exposed in [6; 106]. In this model, the \(j^{th}\) component \(\zeta_{j}\) of the friction force vector \(\mathbf{\zeta}\) is expressed in the form of a linear function of two parameters, namely the Coulomb friction force \(Fc_{j}\in\mathbb{R}_{+}\) and of the viscous friction coefficient \(Fv_{j}\in\mathbb{R}_{+}\) as  
\[\zeta_{j}(\chi_{j},\dot{q}_{j})=\underbrace{Fc_{j}\cdot\text{sign}(\dot{q}_{ j})}_{\text{Coulomb friction}}+\underbrace{Fv_{j}\cdot\dot{q}_{j}}_{\text{Viscous friction}} \tag{68}\]  
Figure 7: Detail of the “_Simulation Engine_” of Figure 6.  
As a result, the friction coefficients can be directly included within the link's standard dynamic parameter vector \(\chi_{j}\in\mathbb{R}^{13}\), as shown in Equation (2). A specificity of the TX40 is the coupling existing between the joints 5 and 6 of the robot. As explained in [75], this can be accounted for using two additional friction parameters denoted \(Fvm_{6}\) and \(Fcm_{6}\). Although it was decided to neglect this coupling during the simulation experiments, this was later taken into account during the validation phase on the real robot. In the context of Monte Carlo Simulation (MCS) experiments, the model generation step resulted in a vector \(\beta\) of 52 base dynamic parameters for each robot. During the validation experiments on the TX40, this base parameter vector was of dimension 54 due to \(Fvm_{6}\) and \(Fcm_{6}\). It is worth noting that in the more general case where joint friction is nonlinear, provided that the friction model is not _load dependent_, the IDM given by (1) can be identified using a separable approach as suggested by [59; 106].