Jean-Claude Samin

Identification of the barycentric parameters of robot manipulators from external measurements

An original procedure for the estimation of the barycentric parameters of a robot is presented. This procedure requires only the processing of measurements provided by an external experimental set-up. The procedure is based on the property that the relations between the robot motion and its reactions on the bedplate are completely independent of the internal joints forces. A convincing validation experiment on a PUMA 562 is reported.

Minimal dynamic characterization of tree-like multibody systems

The dynamic model of tree-like multibody systems is linear with respect to the parameters of mass distribution for instance when barycentric parameters are used. Thus, assuming that the parameters related to the kinematics are perfectly known, these quantities can be estimated through linear regression techniques. The necessary data are obtained by measuring the joint forces and/or torques and the resulting motion given in terms of positions, velocities and accelerations. An alternative method uses measurements of the reaction forces and torques applied to the bedplate.The linearity of the dynamic and reaction models with respect to the barycentric quantities does not however imply that the latter constitute the minimum set of parameters characterizing the mass distribution of the system. In other words, some barycentric parameters may disappear from the models or may be redundant in the sense that they appear only via linear combinations. In the first case they are not identifiable, while in the second case the linear regression technique leads to estimated values which are correct for the combinations but can be erroneous for the individual parameters.The various options taken to derive the dynamic and reaction models by use of the ROBOTRAN programme are briefly reviewed. Then the rules leading to the minimal parametrization are presented and illustrated by means of a practical example related to a robot calibration problem.

Recursive formalism with a minimal dynamic parameterization for the identification and simulation of multibody systems. Application to the human body

This paper presents a multibody formalism using a minimal set of dynamicalparameters, based on the barycentric approach. Using relative jointcoordinates, we show that it is possible to generate recursively the inverseand direct dynamics in terms of this minimal set, rather than using theclassical ones (mass, centre of mass and inertia matrix). More thanproviding a very compact scheme in terms of flops, the proposed formalism,in which the independent dynamical parameters appear linearly, is a precioustool for identification purpose; indeed, the recursive nature of theformalism and its symbolic implementation allows us to deal with very large models, such as the human body for instance. The approach is then applied to the identification of some of the human bodys dynamical parameters, on the basis of a trajectory issuing from a volleyball typical movement.

Comparison of Various Techniques for Modelling Flexible Beams in Multibody Dynamics

The modelling of flexible elements in mechanical systems has been widely investigated through several methods issuing from both the area of structural mechanics and the field of multibody dynamics. As regards the latter discipline, beside the problem of the generation of the multibody equations of motion, the choice of a spatial discretization method for modelling flexible elements has always been considered as a critical phase of the modelling. Although this subject is abundantly tackled in the open-literature, the latter probably lacks an objective comparison between the most commonly used approaches.This contribution presents an extensive investigation of several discretization techniques of flexible beams, in a pure multibody context. In particular, it is shown that shape functions based on power series monomials are very suitable and versatile to model beams being part of a multibody system and thus constitutes an interesting alternative to finite element analysis. For this purpose, a symbolic multibody program, in which various discretization techniques were implemented, was generalized to compute the equations of motion of a general multibody system containing flexible beams.

Fully symbolic generation of complex multibody models

*Communicated by J. McPhee

Symbolic generation of large multibody system dynamic equations using a new semi-explicit Newton Euler recursive scheme

SummaryThe aim of this paper is to show that multibody systems with a large number of degrees of freedom can be efficiently modelled, taking conjointly advantage of a recursive formulation of the equations of motion and of the symbolic generation capabilities.Recursive schemes are widely used in the field of multibody dynamics since they avoid the “explosion” of the number of arithmetical operations in case of large multibody models. Within the context of our field of applications (railway dynamics simulation), explicit integration schemes are still prefered and thus oblige us to compute the generalized accelerations at each time step. To achieve this, we propose a new formulation of the well-known Newton/Euler recursive method, whose efficiency will be compared with a so-called “O(N)” formulation.A regards the symbolic generation, often decried due to the size of the equations in case of large systems, we have recently implemented recursive multibody formalisms in the symbolic programme ROBOTRAN [1]. As we shall explain, the recursive nature of these formalisms is particularly well-suited to symbolic manipulation.All these developments have been successfully applied in the field of railway dynamics, and in particular allowed us to analyse the dynamic behaviour of several railway vehicles. Some typical results related to a completely non-conventional bogie will be presented before concluding.

A new wheel/rail contact model for independent wheels

SummaryThe classical multibody approach in railway vehicle dynamics considers as rolling element a rigid wheelset, for which the geometrical problem associated with the wheel/rail contact and the formulation of the dynamic equations are well known at the present time. New designs of non-conventional bogies led us to develop a new model for independent wheels in which each wheel/rail contact must be treated separately due to the absence of an axle between left and right wheels. This model constitutes an additional feature of the multibody approach for this type of application. The classical multibody formalism is first briefly reviewed and the wheel/rail contact model is then developed in the case of a straight track. The way the model has been extended to curved track is also explained. Finally, numerical results related to classical and non-conventional bogies will be presented before concluding.ÜbersichtDie klassische Mehrkörper-Annäherung in der Dynamik der Eisenbahnfahrzeuge betrachtet als Rollelement das steife Achse-Räder-System, dessen geometrisches Problem des Kontaktes zwischen Rad und Gleis sowie dessen Formulierung der dynamischen Gleichungen heutzutage allbekannt sind. Neue Konzepte von unkonventionellen Drehgestellen führte die Autoren zur Entwicklung eines neuen Modells für unabhängige Räder, in welchem aufgrund des Fehlens einer gemeinsamen Achse zwischen linkem und rechtem Rad jeder Rad-Gleis-Kontakt getrennt betrachtet werden soll. Dieses Modell bildet einen zusätzlichen Gesichtspunkt der Mehrkörper-Methode für die Lösung solcher Probleme. Nach kurzer Betrachtung des klassischen Mehrkörper-Formalismus wird ein Modell des Rad-Gleis-Kontaktes für eine gerade Strecke entwickelt. Weiter folgt die Ausweitung des Modells auf ein gekrümmtes Gleis und schließlich werden die numerischen Ergebnisse für klassische und nicht-konventionelle Drehgestelle vorgelegt.

Linearity of Multibody Systems with Respect to Barycentric Parameters: Dynamics and Identification Models Obtained by Symbolic Generation

Abstract The aim of the paper is to produce the equations of motion of a multibody system in symbolic form. The formulation permits emphasis of the linearity of the equation with respect to barycentric parameters. Dynamic and identification models for manipulators are derived in an easy-to-read symbolic form by use of the ROBOTRAN program, which is also described.

A fully symbolic generation of the equations of motion of multibody systems containing flexible beams

The modelling of flexible elements in mechanical systems has been investigated via several methods issuing from both the field of multibody dynamics and the area of structural mechanics and vibration theory. A multibody approach using a recursive formalism in relative coordinates is adopted here. While leading to a highly non-linear system with a dense mass matrix, relative coordinates allow the setting up of the minimal set of equations of motion for open-loop systems. As for the recursive technique, the latter was proved to be a very good candidate for an optimized symbolic generation in the case of rigid multibody systems. These two assertions have led us to generalize such a formalism for a general multibody system containing flexible beams, in order to make its fully symbolic generation possible within the stand-alone program ROBOTRAN [1]. Several validation examples are presented to illustrate the method and to highlight the efficiency and the user-friendliness of this fully symbolic model, even when dealing with beams undergoing large motions.

Minimal Parametrization of Robot Dynamic Models

This paper presents systematic rules for determining the minimum set of inertial parameters that are relevant for the dynamic model of serial and tree-like manipulators. In particular, it is shown, starting from the barycentric definition of inertial parameters, that a limited number of additional rules are necessary to obtain this minimum set. Moreover, the value of these parameters can be identified experimentally either from the dynamic model or from a reaction model that relates the robot motion to the reaction forces and torques transmitted to its bedplate.