419 APSAEM12 Journal of the Japan Society of Applied Electromagnetics and Mechanics Vol.21, No.3 (2013) (87) Novel Adaptive Forward Neural MIMO NARX Model Application for Modelling of Biped Robot’s Arm Kinematics HO Pham Huy Anh *1 , CHUNG Tan Lam *2 and PHAN Huynh Lam *2 In this paper, a novel forward adaptive neural MIMO NARX model is used for modelling and identifying the forward kinematics of the biped robot’s 3-DOF arm system. The nonlinear features of the forward kinematics of the industrial robot arm drive are thoroughly modelled based on the forward adaptive neural NARX model-based identi- fication process using experimental input-output training data. This paper proposes the novel use of a back propaga- tion (BP) algorithm to generate the forward neural MIMO NARX (FNMN) model for the forward kinematics of the biped robot’s 3-DOF arm system. The results show that the proposed adaptive neural NARX model trained by Back Propagation learning algorithm yields outstanding performance and perfect accuracy. Keywords: forward kinematics model, biped robot’s 3-DOF arm system, back propagation learning algorithm (BP)), adaptive neural MIMO NARX model, modelling and Identification. (Received: 31 May 2012, Revised: 14 June 2013) 1. Introduction The robot control problems can be divided into two main areas, kinematics control (the coordination of the links of kinematics chain to produce desire motion of the robot), and dynamic control (driving the actuator of the mechanism to follow the commanded position velocities). In general the control strategies used in robot involves position coordination in Cartesian space by direct or indirect kinematics methods. Forward kinematics comprises the computation need to find the join angles for a given Cartesian position and orienta- tion of the end effectors. This computation is fundamen- tal to control of robot arms but it is very difficult to calculate an Forward kinematics solution of robot arm. For this solution most industrial robot arms are designed by using a nonlinear algebraic computation to finding the Forward kinematics solution. From the literature it is well described that there is no unique solution for the Forward kinematics. That is why it is significant to apply an artificial neural network models. Novel approach of artificial neural network (ANN) models has been proposed to control the motion of robot arm. In these works two types of ANN models were used. The first kind ANN model is MLP (multi-layer perceptron) which was famous as back propagation neural model. In this network gradient descent type of learning rules are applied. The second kind of ANN model is PPN (polynomial poly-processor neural net- work) where polynomial equation was used. Here, work has been undertaken to find the best ANN configuration for the problem. It was found that between MLP and PPN, MLP gives better result as compared to PPN by considering average percentage error, as the perfor- mance index. Alavandar and Nigam [1] developed ANFIS (Adap- tive Neuro-Fuzzy Inference System) approach for Forward kinematics solution of industrial robot arms- Morris et al. [2] developed artificial neural network for finding Forward kinematics of robot arm using look up table. Mayorga et al. [3] and Kieffe et al. [4] developed precise solution to Forward kinematics problem in robots using neural network. The average error is less than 0.01 radians while maximum error is 0.25 radians. Furthermore various methods using numerical meth- ods and intelligent methods to solve the forward kine- matics of industrial robot arm were investigated in [5]. Recently robust adaptive control approaches combining conventional methods with new learning techniques are realized. During the last decade several adaptive neural network models and learning schemes have been ap- plied to offline and online learning of robot arm dynam- ics [6-8]. Ahn and Anh in [9-10] have successfully optimized a NARX neural and fuzzy model of the forward kinematics of the PAM-based robot arm using genetic algorithm. These authors in [11] have identified the forward kinematics of the PAM-based robot arm based on adaptive neural networks. The drawback of all these results is related to consider the forward kinemat- ics of the industrial robot arm as an independent decou- pling system and the external force variation like negli- gible effect. Consequently, all intrinsic cross-effect features of the Forward kinematics of the industrial robot arm has not represented in its resulting adaptive neural model. This paper proposes the novel use of adaptive neural NARX model to generate the Forward neural MIMO NARX (FNMN) model for a highly nonlinear Forward kinematics of the biped robot’s 3-DOF arm system. The _______________________ Correspondence: HO Pham Huy Anh, Faculty of Electrical and Electronics Engineering, Ho Chi Minh City University of Technology, HCM Ciy, Viet Nam email: hphanh@hcmut.edu.vn *1 HCMUT, VietNam *2 DCSELAB, HCMUT, VietNam Regular Paper