Geodesic
On control for double-link manipulator with elastic joints
Russian journal of nonlinear dynamics, Tome 11 (2015) no. 2, pp. 267-277.

Voir la notice de l'article provenant de la source Math-Net.Ru

In the paper the problem on stabilization of program motion for two-link manipulator with elastic joints is solved. Absolutely rigid manipulator links are connected by elastic cylindrical joint and via the same one the first link is fixed to the base. Thus, the manipulator can perform motion in a vertical plane. Motions of the manipulator are described by the system of Lagrange equations of the second kind. The problem on synthesis of motion control of such a system consists in the construction of the laws of change of control moments that allow the manipulator to carry out a given program motion in real conditions of external and internal disturbances, inaccuracy of the model itself. In this paper the mathematical model of controlled motion of the manipulator is constructed for the case of the control actions in the form of continuous functions. Using vector Lyapunov functions and comparison systems on the base of the cascade decomposition of the system we justified the application of these control laws in the problem of stabilization of the program motion of the manipulator. The novelty of the results is to solve the problem of stabilization of nonstationary and nonlinear formulation, without going to the linearized model. The graphs for the coordinates and velocities of the manipulator links confirm the theoretical results.
Keywords: multi-link manipulator, elasticjoint,stabilization, programmotion, comparisonsystem, Lyapunov vector-function. 
@article{ND_2015_11_2_a4,
     author = {A. S. Andreev and O. A. Peregudova},
     title = {On control for double-link manipulator with elastic joints},
     journal = {Russian journal of nonlinear dynamics},
     pages = {267--277},
     publisher = {mathdoc},
     volume = {11},
     number = {2},
     year = {2015},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ND_2015_11_2_a4/}
}
TY  - JOUR
AU  - A. S. Andreev
AU  - O. A. Peregudova
TI  - On control for double-link manipulator with elastic joints
JO  - Russian journal of nonlinear dynamics
PY  - 2015
SP  - 267
EP  - 277
VL  - 11
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/ND_2015_11_2_a4/
LA  - ru
ID  - ND_2015_11_2_a4
ER  - 
%0 Journal Article
%A A. S. Andreev
%A O. A. Peregudova
%T On control for double-link manipulator with elastic joints
%J Russian journal of nonlinear dynamics
%D 2015
%P 267-277
%V 11
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/ND_2015_11_2_a4/
%G ru
%F ND_2015_11_2_a4
A. S. Andreev; O. A. Peregudova. On control for double-link manipulator with elastic joints. Russian journal of nonlinear dynamics, Tome 11 (2015) no. 2, pp. 267-277. http://geodesic.mathdoc.fr/item/ND_2015_11_2_a4/

[1] Andreev A. S., Peregudova O. A., “O stabilizatsii programmnykh dvizhenii golonomnoi mekhanicheskoi sistemy”, XII Vserossiiskoe soveschanie po problemam upravleniya (VSPU-2014, Institut problem upravleniya im. V. A. Trapeznikova RAN), Institut problem upravleniya im. V. A. Trapeznikova RAN, Moskva, 2014, 1840–1843

[2] Matrosov V. M., Metod vektornykh funktsii Lyapunova: Analiz dinamicheskikh svoistv nelineinykh sistem, Fizmatlit, Moskva, 2001, 380 pp.

[3] Khalil Kh. K., Nelineinye sistemy, NITs «Regulyarnaya i khaoticheskaya dinamika», Institut kompyuternykh issledovanii, Moskva–Izhevsk, 2009, 832 pp.

[4] Brogliato B., Ortega R., Lozano R., “Global tracking controllers for flexible-joint manipulators: A comparative study”, Automatica, 31:7 (1995), 941–956. | MR | Zbl

[5] De Luca A., “Dynamic control of robots with joint elasticity”, Proc. of the IEEE Internat. Conf. on Robotics and Automation, Philadelphia, Pa.,, 1988, 152–158

[6] De Luca A., “Feedforward/Feedback laws for the control of flexible robots”, Proc. of the IEEE Internat. Conf. on Robotics and Automation, San Francisco, Calif., 2000, 233–240

[7] De Luca A., Siciliano B., Zollo L., “PD control with on-line gravity compensation for robots with elastic joints: Theory and experiments”, Automatica, 41:10 (2005), 1809–1819 | MR | Zbl

[8] Moberg S., On modeling and control of flexible manipulators., Linkoping Univ., Linkoping, 2007, 148 pp.

[9] Palli G., Melchiorri C., De Luca A., “On the feedback linearization of robots with variable joint stiffness”, IEEE Internat. Conf. on Robotics and Automation, Pasadena, Calif., 2008, 1753–1759