International Journal of Innovative Computing, Information and Control ICIC International c ⃝2011 ISSN 1349-4198 Volume 7, Number 2, February 2011 pp. 965–976 REAL-TIME DECENTRALIZED NEURAL BACKSTEPPING CONTROL: APPLICATION TO A TWO DOF ROBOT MANIPULATOR R. Garcia-Hernandez 1,3,∗ , E. N. Sanchez 1 , E. Bayro-Corrochano 1 M. A. Llama 2 and Jose A. Ruz-Hernandez 3 1 Departamento de Ingenieria Electrica CINVESTAV Unidad Guadalajara Avenida Cientifica 1145, Zapopan, Jalisco, Mexico { rhernand; sanchez; edb }@gdl.cinvestav.mx 2 Division de Estudios de Posgrado Instituto Tecnologico de la Laguna Apartado Postal 49, Adm. 1, C.P. 27001, Torreon, Coahuila, Mexico mllama@itlalaguna.edu.mx 3 Facultad de Ingenieria Universidad Autonoma del Carmen Avenida 56, No. 4, Cd. del Carmen, Campeche, Mexico jruz@pampano.unacar.mx * Corresponding author: rghernandez@pampano.unacar.mx Received October 2009; revised May 2010 Abstract. This paper presents a discrete-time decentralized control scheme for tra- jectory tracking of a two degrees of freedom (DOF) robot manipulator. A high order neural network (HONN) is used to approximate a decentralized control law designed by the backstepping technique as applied to a block strict feedback form (BSFF). The neural network learning is performed on-line by Kalman filtering. The controllers are designed for each joint using only local angular position and velocity measurements. These simple local joint controllers allow trajectory tracking with reduced computations. The proposed scheme is implemented in real-time to control a two DOF robot manipulator. Keywords: Decentralized control, High-order neural networks, Extended Kalman filter, Backstepping 1. Introduction. Recently, control of robot manipulators has become a significant re- search area for different applications due to the relevancy that they have acquired in performing tasks classified as dangerous, or which require higher accuracy. In this context, different control schemes have been proposed to guarantee efficient trajectory tracking and stability [1,2]. Fast advances in computational technology offer different possibilities for implementing control algorithms within the approach of a central- ized control design [3]. However, there is a great challenge to obtain an efficient control for these systems, due to their highly nonlinear complex dynamics, with strong inter- connections, parameters difficult to be measured and unmodeled dynamics. Considering only the most important terms on the mathematical model, control algorithms with great number of mathematical operations are required, which affect real-time implementation feasibility. In [4], the authors presented a control approach based on open-loop optimization us- ing a genealogical decision tree (GDT), which can be used for solving both tracking and regulation. A novel task-space robust control approach with suitable tracking perfor- mance under imperfect transformation was presented in [5]; the proposed control law is 965