Control of a direct drive robot using fuzzy spiking neural networks with variable structure systems-based learning algorithm Yesim Oniz a,n , Okyay Kaynak a,b a Bogazici University, Electrical & Electronics Engineering Department, Istanbul, Turkey b Harbin Institute of Technology, China article info Article history: Received 15 May 2014 Received in revised form 16 July 2014 Accepted 29 July 2014 Communicated by H.R. Karimi Available online 11 August 2014 Keywords: Direct drive robot Spiking neural networks Variable structure systems based learning algorithm Robot trajectory control abstract In this work, a sliding mode theory based supervised training algorithm that implements fuzzy reasoning on a spiking neural network has been developed and tested on the trajectory control problem of a two-degrees-of-freedom direct drive robotic manipulator. To describe the generation of a new spike train from the incoming spike trains Spike Response Model has been utilized and the Lyapunov stability method has been adopted in the derivation of the update rules for the neurocontroller parameters. The results of the real-time experiments indicate that stable online tuning and fast learning speed are the prominent characteristics of the proposed algorithm. & 2014 Elsevier B.V. All rights reserved. 1. Introduction Because of the highly nonlinear and coupled dynamics involved, the trajectory control of robotic manipulators has been usually considered as a challenging engineering problem. Further- more, the variations in the system parameters with time hamper the development of an accurate model and there are very often uncertainties associated with the load that the gripper carries. Consequently, traditional model-based approaches have become impractical as their performance is directly related to the accuracy of the mathematical model of the system [1,2]. The tracking control of complex nonlinear systems subject to uncertainties has been thoroughly investigated in numerous research works [3–7], and model-free control methodologies based on computational intelligence techniques have been widely utilized in the trajectory control of manipulators to overcome the shortcomings stemming from the lack of model- ing information and inaccuracies in the measurements. Artificial neural networks (ANNs) are generally considered among the most common and effective approaches to model-free design. McCulloch–Pitts neurons [8] constitute the first generation of artificial neural networks. In this early model, a neuron fires if the sum of its weighted incoming signals is above a threshold value. In the subsequent generation, the step threshold activa- tion function of the first generation is replaced by a continuous one to promote the use of artificial neural networks in systems with analog inputs and outputs [9]. Hyperbolic tangent and sigmoid functions are typical activation functions of this generation. Recent research has shown that neurons encode information in the timing of single spikes and not just in their average firing frequency [10]. Unlike the first two generations, in which the outputs of the network can be considered as the normalized firing rates of the neuron within a particular time interval, the third generation of ANNs consisting of spiking neurons (SNs) further improves the level of biological realism by attempting to make direct use of the temporal information of the individual spikes. In this new generation, similar to their biological counterparts, neurons encode the information in the exact timing of the spikes rather than the magnitude of the spikes [11]. In one of the leading works on the spiking neural networks (SNNs) [12], it is stated that SNNs can be applied to any problem that is solvable by the first two generations and this network has at least the same computational power as the neural networks consisting of perceptrons or sigmoidal neurons. Furthermore, it has been shown that these networks are capable of processing a considerable amount of data with a relatively small number of spikes [13]. The above-mentioned advantages and an increasing interest in temporal computation promote the use of SNNs in a Contents lists available at ScienceDirect journal homepage: www.elsevier.com/locate/neucom Neurocomputing http://dx.doi.org/10.1016/j.neucom.2014.07.061 0925-2312/& 2014 Elsevier B.V. All rights reserved. n Corresponding author. Tel.:+90 212 3596855. E-mail addresses: yesim.oniz@boun.edu.tr (Y. Oniz), okyay.kaynak@boun.edu.tr (O. Kaynak). Neurocomputing 149 (2015) 690–699