ORIGINAL ARTICLE Online modeling and adaptive control of robotic manipulators using Gaussian radial basis function networks Rajesh Kumar 1 • Smriti Srivastava 1 • J. R. P. Gupta 1 Received: 3 May 2016 / Accepted: 3 November 2016 Ó The Natural Computing Applications Forum 2016 Abstract Radial basis function network (RBFN) is used in this paper for predefined trajectory control of both one-link and two-link robotic manipulators. The updating equations for the RBFN parameters were derived using the gradient descent principle. The other advantage of using this prin- ciple is that it shows the clustering effect in distributing the radial centres. To increase the complexity, the dynamics of robotic manipulator is assumed to be unknown, and hence, simultaneous control and identification steps were per- formed using the RBFNs. The performance of the RBFN is compared with the multilayer feed-forward neural network (MLFFNN) in terms of mean square error, tolerance to disturbance and parameter variations in the system. The efficacy of RBFN as a controller and identification tool is verified by performing the simulation study, and the results obtained reveal the superior performance of RBFN over MLFFNN in both identification and control aspects for one-link and two-link robotic manipulators. Keywords Radial basis function networks  One-link and two-link robotic manipulators  Identification and adaptive control  Multi layer feed-forward neural network  Robustness 1 Introduction The fact that most systems are inherently nonlinear with partially known or unknown dynamics makes the use of conventional techniques like PID control difficult. This has laid to development and use of intelligent control techniques. There has been a rapid growth seen in the research efforts during the past decades for developing systematic methods for the predefined trajectory control of one-link and two-link robotic manipulators [26]. The robotic manipulators found numerous applications in industries like manufacturing, assembly, space and medical in which they are used for the purpose of pick and place, positioning and path following, etc. Various control methods have been explored as the suitable al- ternatives to enhance the deficiencies of the traditional PID-type controllers [13, 25]. An adaptive-learning control scheme was proposed by Sun and Mills [25] for improving the trajectory performance, but for this scheme to work, system dynamics details are required. A model-based PID controller was introduced by Li et al. [13] to accomplish the time-varying tracking control of a robot controller. In any case, it is hard to build up a fitting numerical model for the design of a model-based control system. On the other hand, the conventional intelligent control schemes have the capacity to com- pensate the effects of structured parametric uncertainty and unstructured disturbance by using their powerful learning ability without requiring the prior knowledge about the mathematical model of system (plant) under consideration. In the past decade, considerable attention is given to the use of intelligent control techniques (fuzzy logic-based control or artificial neural-network- based control) for the motion control of robotic manip- ulators [5, 6, 9, 14]. A stable self-organizing fuzzy & Rajesh Kumar rajeshmahindru23@gmail.com Smriti Srivastava smriti.nsit@gmail.com J. R. P. Gupta jairamprasadgupta@gmail.com 1 Department of Instrumentation and Control Engineering, Netaji Subhas Institute of Technology, Sector 3, Dwarka, New Delhi 110078, India 123 Neural Comput & Applic DOI 10.1007/s00521-016-2695-8