Nonlinear Ultimate Boundedness Control and Stabilization of a Flexible Robotic Arm

We treat the question of control of an elastic robotic arm of two links. Of course, this approach can be extended to other elastic arms. A nonlinear ultimate boundedness controller (UBC) is synthesized such that in the closed-loop system the joint angle tracking error is uniformly bounded and tends to a certain small neighborhood of the origin. The controller includes a reference joint angle trajectory generator and integral error feedback. Although the joint angles are controlled using the UBC, elastic modes are excited. A feedback stabilizer is designed for the linearized model including the UBC about the terminal state that is switched only in the vicinity of the equilibrium state for stabilization. Simulation results are presented to show that in the closed-loop system including the UBC and the stabilizer accurate joint angle trajectory following and elastic mode stabilization are accomplished in the presence of uncertainty

Dynamic Modeling,simulation And Nonlinear Analysis Of Rigid And Flexible Robot Manipulators

The need for fast and precise robots in the industrial environment, capable of attending the productivity and quality demands and that allow a high volume of work, needs the usage of manipulators with flexible links. Besides this, aeronautic applications demand the usage of long and thin arms, which leads to remarkable structural changes. Therefore, the development of manipulators with structural flexibility and its automatic control has become an important research area. The main goal of this work is to model the dynamic behavior of flexible manipulators. It is also presented a comparative study with rigid robots. It is possible to use the model for computer simulations to aid the development of efficient control. © ECCOMAS.Book, W.J., Recursive Lagrangian dynamics of flexible manipulator arms (1984) The International Journal of Robotics Research, 3 (3), pp. 87-101Craig, J.J., (1986) Introduction to Robotics: Mechanics and Control, , Addison Wesley P. CompanyDavid, S.A., Rosário, J.M., Dynamic modeling and simulation of robot manipulator with two flexible links (1999) Proceedings of Sixth Pan American Congress of Applied MechanicsDavid, S.A., (1996) Modelagem, Simulação E Controle de Robôs Flexíveis, , MSc Thesis, State University of Campinas (in Portuguese)Farid, M., Lukasiewicz, S.A., Dynamic modeling of spatial flexible manipulators (1997) Computational Methods and Experimental Measurements, 3, pp. 255-264Li, C.J., Sankar, T.S., A systematic method of dynamics for flexible robot manipulators (1992) Journal of Robotic Systems, 9 (7), pp. 861-891Nathan, P.J., Singh, S.N., Nonlinear ultimate boundedness control and stabilization of a flexible robotic arm (1992) Journal of Robotic Systems, 9 (3), pp. 301-326Nayfeh, A.H., Mook, D.J., (1979) Nonlinear Oscillations, , John Wiley & Sons, New YorkRosário, J.M., (1987) Modelisation Dynamique Dún Robot Industriel, , Ministère de l'Education Nationale. Institut Supérieur des Matériaux et de la Construction Mécanique. FranceSchielen, I.W., Technische Dynamik, p. 106. , s.l.p.s.c.p. s.d.