Numerical calculation of the base inertial parameters of robots

Abstract

This paper presents a new approach to the problem of determining the minimum set of inertial parameters of robots.The calculation is based on numerical QR and SVD factorizations and on scaling procedure of matrices. It proceeds in two steps : -at fmt the number of base parameters is determined, -then a set of base parameters is determined by eliminating some standard parameters which are regrouped to some others in linear relations.Different models, linear in the inertial parameters are used: a complete dynamic model, a simplified dynamic model and an energy model. The method is general, it can be applied to open loop, or graph structured robots. The algorithms are easy to implement. An application for the PUMA 560 robot is given.Exact dynamic model of robot is required to control or simulate its motion. The model is characterized by ten inertial parameters per link, which are called the standard inertial parameters.Because of the redundancy of this representation, there is an infinite sets of standard parameters which satisfies the dynamic model. In order to reduce the computational cost of the dynamic model and to facilitate the identification process, a minimum set of inertial parameters, which are called also base parameters, must be used to determine the dynamic model [l,. . .,a, Dynamic model, using Newton Euler or Lagrange, or energy formulation model, linear in the inertial parameters, can be used to study this problem. From a linear algebra point of view, this problem appears to be a rank deficiency problem.The study is carried out in two steps: -find the rank of a linear system, this gives the number of base parameters.-choose the base parameters from the standard ones by eliminating some of them which are regrouped to the others in linear relations, in this step the regrouping relations will be determined. Previous work;Several authors have studied the problem using two principal approaches: i-Symbolic approach:-In [l, 2, 3, 41 a case by case method using the symbolic expression of the dynamic model have been presented, -In [5, 61, we have presented a general and direct method to aetermine most of the set of minimum inertial parametemof serial or tree structured robots, using the energy formulation. -At the same time similar results concerning the special case of robots whose successive axes are perpendicular or parallel have been given by Mayeda et al.[7,8].ii-Numerical approach: -Atkenson et all [9] used ridge regression and singular value decomposition, SVD, to solve the rank deficiency problem. The dynamic model using Newton Euler formulation was used.-Sheu and Walker [lo] used SVD also on the energy model.These two methods did not give explicitely the minimum set of inertial parameters, nor the linear relations which define them. In this paper we propose to use the QR decomposition, which serve equally well as the SVD and at less cost [l 1, pl l-231, and the SVD itself to solve the deficiency problem. We find the number of base parameters and we give a method to define them. Then we give an algor...

Modeling and Identification of Passenger Car Dynamics Using Robotics Formalism

“…The base parameters are obtained from the standard dynamic parameters by grouping some parameters together and by eliminating those that have no effect on the dynamic model. Two methods are available for the computation of the base parameters, namely 1) a symbolical method [14] and 2) a numerical method based on the QR decomposition [15]. The numerical method allows considering the grouping relations due to the poor excitation properties of the chosen identification trajectory.…”

Online payload identification for quadruped robots

“…the number of linearly-independent columns) represents the number of parameters that are observable [19]. A method to check whether a specific parameter is observable is to compute the observable subspace of regressor matrix, as explained in [20]. Often, only a linear combination of some parameters is observable, rendering these parameters partially observable.…”

Dynamic Parameter Identification for Parallel Manipulators

“…The number of base parameters is equal to the rank of the observation matrix. The base parameter combination can be calculated principally in two ways; analytically (Khalil & Bennis, 1995) or numerically using the Singular Values Decomposition (SVD) or QR factorization (Gautier, 1991). The analytical analysis will not be considered here since for a parallel manipulator its application is not direct.…”

“…These columns correspond to a subset of parameters called the base parameters. Reduction process can be held symbolically (Khalil & Bennis, 1995) or numerically (Gautier, 1991). For experiment design and in order to reduce the sensitivity of the system to the noise signal, procedures have been developed for the trajectories to be executed by the manipulator (Gautier & Khalil, 1992;Swevers et al, 1997).…”