Dynamic Modeling of Flexible Manipulators without their Mass Matrices Inversion

Abstract

In recent scientific literature, much attention is paid to the optimal modeling of elastic dynamical systems. The relevance of these studies is dictated by the ever-increasing demand in the control theory of high-precision robotic manipulators and automatic mechanisms, which consists in the need for continuous adjustment of the movement of their executive bodies in real time, with account for the flexibility of the constituent links of these systems. The generalized Newton --- Euler method formulated in this regard served as a reliable platform for a subsequent progressive modification of dynamic analysis for a wide class of elastodynamic systems. The purpose of the study is to improve the existing computational algorithms to accelerate the computational process of dynamic analysis of flexible manipulators. In this regard, relying on symbolic-iterative calculus, we formulated and solved the mixed dynamic problem of the manipulators without inverting their mass matrices. Furthermore, we modified the Newton --- Raphson method, intended for a numerical integration of the Newton --- Euler equations of motion. Finally, we dynamically calculated the spatial five-elastic link manipulator by comparing the speed of computational processes carried out at constant accuracy of the problem modeling, and assessed the efficiency of the method of dynamic analysis of the manipulators. In this study, we introduce an advanced method of dynamic modeling of flexible manipulators without the well-known procedure of their mass matrices inversion

Please cite this article in English as:

Gevorkian H.A. Dynamic modeling of flexible manipulators without their mass matrices inversion. Herald of the Bauman Moscow State Technical University, Series Natural Sciences, 2022, no. 1 (100), pp. 4--21 (in Russ.). DOI: https://doi.org/10.18698/1812-3368-2022-1-4-21

References

[1] Medvedev V.S., Leskov A.G., Yushchenko A.S. Sistemy upravleniya mani-pulyatsionnykh robotov [Control system of a robot manipulator]. Moscow, Nauka Publ., 1978.

[2] Luh J.Y.S., Walker M.W., Paul R. On-line computational scheme for mechanical manipulators. J. Dyn. Sys., Meas., Control., 1980, vol. 102, iss. 2, pp. 69--76. DOI: https://doi.org/10.1115/1.3149599

[3] Boyer F., Coiffet P. Generalization of Newton --- Euler model for flexible manipulators. Int. J. Robot. Syst., 1996, vol. 13, iss. 1, pp. 11--24. DOI: https://doi.org/10.1002/(SICI)1097-4563(199601)13:1<11::AID-ROB2>3.0.CO;2-Y

[4] Boyer F., Khalil W. An efficient calculation of flexible manipulators inverse dynamics. Int. J. Rob. Res., 1998, vol. 17, no. 3, pp. 282--293. DOI: https://doi.org/10.1177/027836499801700305

[5] Sarkisyan Yu.L., Stepanyan K.G., Azuz N., et al. Dynamic analysis of a flexible manipulator by Newton --- Euler general method. Izvestiya NAN RA i GIUA. Ser. T.N., 2004, vol. 57, no. 1, pp. 3--10 (in Russ.).

[6] Gevorkian H.A. [Dynamic analysis of spatial flexible manipulators by Newton --- Euler general method]. Sb. tr. Mezhdunar. nauch.-tekh. konf. [Proc. Int. Sci.-Tech. Conf.]. Erevan, GIUA Publ., 2010, pp. 126--128 (in Russ.).

[7] Sarkisyan Yu.L., Stepanyan K.G., Gevorkian H.A., et al. Dynamic analysis of flexible tree-like systems without external links. Izvestiya NAN RA i GIUA. Ser. T.N., 2006, vol. 59, no. 1, pp. 3--9 (in Russ.).

[8] Gevorkian H.A. Application of Newton --- Euler general method to the problems of optimum control on flexible mechanics. Izvestiya NAN RA i GIUA. Ser. T.N., 2010, vol. 63, no. 2, pp. 133--138 (in Russ.).

[9] Gevorkian H.A. Principles of formal and methodological optimization of multistage systems dynamic analysis. Izvestiya NAN RA i GIUA. Ser. T.N., 2017, vol. 70, no. 4, pp. 401--410 (in Russ.).

[10] Verlinden O. Simulation du comportement dynamique de systemes multicorps flexibles comportant des membrures de forme complexe. These de doctorat de la Faculte Polytechnique de Mons, 1994.

[11] Verlinden O., Dehombreux P., Conti C., et al. A new formulation for the direct dynamic simulation of flexible mechanisms based on the Newton --- Euler inverse method. Int. J. Numer. Methods, 1994, vol. 37, iss. 19, pp. 3363--3387. DOI: https://doi.org/10.1002/nme.1620371910

[12] Dombre E., Khalil W. Modelisation et commande des robots. Edition Hermes, 1988.

[13] Dombre E., Khalil W. Modelisation, identification et commande des robots. Edition Hermes, 1999.

[14] Featherstone R. The calculation of robot dynamics using articulated-body inertias. Int. J. Rob. Res., 1983, vol. 2, no. 1, pp. 13--30. DOI: https://doi.org/10.1177/027836498300200102

[15] Fisette P., Samin J.C. Symbolic generation of large multibody system dynamic equations using a new semi-explicit Newton --- Euler recursive scheme. Arch. Appl. Mech., 1996, vol. 66, no. 3, pp. 187--199. DOI: https://doi.org/10.1007/BF00795220

[16] Avello A., De Jalon J.G., Bayo E. Dynamics of flexible multibody systems using Cartesian coordinates and large displacement theory. Int. J. Numer. Methods Eng. Special Issue: Adaptive Meshing, 1991, vol. 32, iss. 8, pp. 1543--1563. DOI: https://doi.org/10.1002/nme.1620320804

[17] Kim S.-S., Haug E.J. A recursive formulation for flexible multibody dynamics, part I: open-loop systems. Comput. Methods Appl. Mech. Eng., 1988, vol. 71, iss. 3, pp. 293--314. DOI: https://doi.org/10.1016/0045-7825(88)90037-0

[18] Jing Xie. Dynamic modeling and control of flexible manipulators: a review. MECS, 2017, pp. 270--275. DOI: https://dx.doi.org/10.2991/mecs-17.2017.50

[19] Bascetta L., Ferretti G., Scaglioni B. Closed form Newton --- Euler dynamic model of flexible manipulators. Robotica, 2017, vol. 35, iss. 5, pp. 1006--1030. DOI: https://doi.org/10.1017/S0263574715000934

[20] Gevorkian H.A. Simulation of elastic tree-like dynamic systems in presence of external holonomic constraints. Herald of the Bauman Moscow State Technical University, Series Natural Sciences, 2020, no. 2 (89), pp. 4--24 (in Russ.). DOI: http://doi.org/10.18698/1812-3368-2020-2-4-24