# Inertial Parameter Identification in Robotics: A Survey
## 1 Introduction  
### Motivation and Related Works  
The growing popularity of adaptive, predictive, and passivity-based control strategies in robotic applications raises new challenges for researchers and engineers. Since these methods rely on an explicit formulation of system dynamics, substantial research efforts are being made in the field of inertial parameter identification to improve their performance and robustness, see for example [1] and the references therein. In the context of rigid robots, techniques for identifying the inertial parameters are generally based on a rigorous analysis of joint movements and torque signals over a predefined time horizon. A given robot is tracking a trajectory that _excites_ the different components of its dynamic model and the residuals in terms of motion and torque are used to refine the parameters estimates. The most common approach to offline or batch dynamic parameter identification is the Inverse Dynamic Identification Model with ordinary Least-Squares estimation (referred toas IDIM-OLS in [2; 3]). This method is based on the assumption that the mapping between joint torques and the inertial parameters of a robot is linear (this holds provided that the robot links are rigid, that friction nonlinearity is negligible and that the joints are not subject to backlash). Both efficient and easy to implement, IDIM-OLS and its variants--including Weighted Least-Squares (IDIM-WLS) and Total Least-Squares (IDIM-TLS) methods described in [4]--however lack noise immunity and exhibit a strong dependence on the conditioning of the robot's trajectory, as depicted in [5; 6]. As a matter of fact, whether due to measurement noise, incorrect data-filtering, or insufficient excitation, IDIM-OLS parameter estimates may eventually prove to be highly biased, to the point of losing all physical coherence, yielding, for example, negative link masses, friction coefficients, or non-positive-definite rotational inertia. Over the past two decades, much research effort has focused on solving these issues, and multiple promising methods were proposed. These approaches can generally be divided into two distinct classes, whether the objective is to improve the statistical consistency of the estimates - physical consistency naturally stemming from statistical consistency (although the opposite is not true.) --or to more explicitly enforce physicality by means of dedicated constrained optimization techniques. In both cases, performance evaluation is generally carried out through direct comparison with unconstrained IDIM-OLS or IDIM-WLS. For instance, ref. [7] compared the performance of the IDIM-WLS method with that of an Extended Kalman Filter (EKF) estimator, on a 2 degree of freedom (DoF) SCARA robot. The results indicate that unlike IDIM-WLS, the EKF estimator has convergence issues and exhibits a strong dependence to both initial conditions and tuning parameters. In [8] the authors presented an approach based on Set Membership Uncertainty (SMU). This approach was tested on a 2 DoF SCARA robot and compared to IDIM-OLS but did not show significant improvement. In [9; 10; 11], the authors compared IDIM-WLS with a Maximum Likelihood (ML) estimator on 2- and 3 DoF robots. The results suggest that ML techniques may reduce the bias of the parameter estimates in the case of noisy joint measurements, at the price however, of a much greater computational effort. Interestingly, only a few studies have actually performed a formal comparison between more than two identification approaches at the same time, and on robots with many degrees of freedom, such as industrial manipulators or humanoids. In [5; 12], the authors used a 6 DoF TX40 industrial robot manipulator to compare the Direct and Inverse Dynamic Identification Model (DIDIM) method, the Closed-Loop Output Error (CLOE) method, the Closed-Loop Input Error (CLIE) method and the IDIM-WLS. In [6] the same research team compared the Instrumental Variable approach (IDIM-IV) with IDIM-WLS, the Total Least-Squares approach (IDIM-TLS) and CLOE.