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Nonlinear Parameter Identification in Multibody Systems Using Homotopy Continuation

“…Note that there may be fewer independent coordinates in the mathematical model than there are in the experimental system (i.e., m < n), which is often the case when identifying parameters using reduced-order models. The objective is to identify the parameters p ¼ p 1 ; p 2 ; …; p l ½ T and the initial conditions rð0Þ ¼ q 2 ð0Þ; q 3 ð0Þ; …; q m ð0Þ ½ T in the mathematical model (5) such that the error between the predicted response q 1 ðtÞ and the experimental response q 1e ðtÞ is minimized. We assume zero velocity initial conditions throughout, which is reasonable since the experimental systems presented herein can all be started from rest for identification purposes.…”

“…Since the shape of the objective function J p; rð0Þ; 0 ð Þ is unknown, we introduce the homotopy transformation into the equations of motion (5), not directly into the objective function:…”

“…8is motivated by the theory of high-gain observers for mechanical systems [31], where the gains are c 1 and c 2 . Thus, the governing dynamic equation (5) have been augmented with terms that couple the experimental data to the mathematical model. The observer-like terms force the mathematical model to generate solutions that are close to those generated by the experimental system, even if the system parameters used by these two models differ.…”

“…If only the inertial parameters are to be identified, an absolute coordinate formulation can be used so that the parameters appear linearly in the equations of motion. Linear least-square methods (linear regression) can then be used to estimate the inertial parameters given experimental data [2][3][4][5]. In many robotic and multibody applications, however, it is beneficial to formulate the equations of motion in terms of joint coordinates, in which case the geometric and inertial parameters appear nonlinearly in the equations of motion-that is, the entries in the mass matrix and force vector contain products and sums of the unknown parameters.…”

Dynamic modelling, identification and simulation of industrial robots: for off-line programming of robotised laser welding

“…Decompositions such as the Singular Value Decomposition (SVD) of matrix A are commonly used to analyse and solve linear least squares problems with rank deficiency of the regression matrix A, see Lawson and Hanson (1974); Golub and Van Loan (1983). The application of the singular value decomposition in the dynamic identification has been demonstrated by An et al (1988); Gautier (1990); Sheu and Walker (1991); Shome et al (1998); Khalil and Dombre (2002). In this thesis, the singular value decomposition will also be employed to solve and analyse the rank deficient least squares problem.…”