ANN Based Inverse Dynamic Model of the 6-PGK Parallel Robot Manipulator

Liviu Moldovan, Horațiu-Ștefan Grif, Adrian Gligor


This paper presents an inverse dynamic model estimation based on an artificial neural network of a complete new parallel robot manipulator prototype 6- PGK with six degrees of freedom, built at Petru Maior University of Tirgu-Mures. The model estimation of the parallel robot manipulator is performed with a feedforward artificial neural network. In the control engineering domain there are control structures that need the direct or inverse model of the process for ensuring the process control at the imposed performances. Usually, the determination of the direct/inverse mathematical model is a difficult or impossible task to be achieved. In these cases different non-parametric or parametric, off-line or on-line identification methods are used. A solution that may support the on-line parametric methods is represented by the feedforward artificial neural networks. By implementing feedforward artificial neural networks as a nonlinear autoregressive model with exogenous inputs, the authors investigate the possibility of choosing the optimum parameters that characterize the neural network so that it approximates as better as possible the model of the 6-PGK prototype robot. Finally an innovative algorithm is developed for obtaining the optimal configuration parameters set of the feedforward artificial neural network. The proposed algorithm helps in setting the optimal parameters of the neural network that offer high opportunities to provide satisfactory identification of the robot model. Experimental results obtained by a structure derived from the proposed solution demonstrate a good approximation related to the studied system, which is characterized by nonlinearities and high complexity.


6-DOF parallel robot manipulator, inverse dynamics, nonlinear model, unmodeled dynamics, feed-forward artificial neural network

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Hamlin, G.J.; Sanderson, A.C. (1997); TETROBOT: a modular approach to parallel robotics, IEEE Robotics & Automation Magazine, ISSN 1070-9932, 4(1): 42-50.

Uzunovic, T.; Golubovic, E.; Baran, E. A.; Sabanovic, A. (2013); Configuration space control of a parallel Delta robot with a neural network based inverse kinematics, IEEE Proc. of 2013 8th Intl. Conf. on EEE (ELECO), 497-501.

Abdellatif H.; Heimann, B. (2010); Experimental identification of the dynamics model for 6-DOF parallel manipulators, Robotica, 28:359-368. doi:10.1017/S0263574709005682.

Yang, Z.; Wu, J.; Mei, J.; Gao, J.; Huang, T. (2008); Mechatronic model based computed torque control of a parallel manipulator, International Journal of Advanced Robotic Systems, 5(1):123-128.

Zhang, J.; Yu, H.; Gao, F.; Zhao, X.; Ma, C.; Huang, X. (2010); Application of a novel 6-DOF parallel robot with redundant actuation for earthquake simulation, IEEE Proc. on Intl. Conf. on Robotics and Biomimetics (ROBIO), 513-518.

Najafi, F.; Sepehri N. (2008); A novel hand-controller for remote ultrasound imaging, Mechatronics, 18: 578-590.

Ibrahim, K.; Ramadan, A.; Fanni, M.; Kobayashi, Y.; Abo-Ismail, A.A.; Fujie, M.G. (2012); Design and workspace analysis of a new endoscopic parallel manipulator, IEEE Proc of 2012 12th Intl. Conf. on Control, Automation and Systems (ICCAS), 688-693.

Jian, X.; Zhiyong, T.; Zhongcai, P.; Shao, H.; Lanbo, L. (2013); Adaptive controller for 6-DOF parallel robot using TS fuzzy inference, International Journal of Advanced Robotic Systems, 10(119):1-9.

Moldovan, L. (2008); Geometrical Method for Description of the 6-PGK Parallel Robot’s Workspace, IEEE Proc. of First Intl. Conf. on Complexity and Intelligence of the Artificial and Natural Complex Systems, Medical Applications of the Complex Systems, Biomedical Computing, 2008. CANS’08, 45-51.

Constantinescu, D.; Salcudean, S.E.; Croft E.A. (2005); Haptic Rendering of Rigid Contacts Using Impulsive and Penalty Forces, IEEE Transactions On Robotics,21(3):309-323.

Le, T. D.; Kang, H. J.; Suh, Y. S.; Ro, Y. S. (2013); An online self-gain tuning method using neural networks for nonlinear PD computed torque controller of a 2-dof parallel manipulator, Neurocomputing, 116: 53-61.

Lu, Y.; Li, X.P. (2014); Dynamics analysis for a novel 6-DoF parallel manipulator I with three planar limbs, Advanced Robotics, 28(16): 1121-1132. DOI: 10.1080/01691864.2014.908743.

Lopes, A.M. (2010); Complete dynamic modelling of a moving base 6-dof parallel manipulator, Robotica, 28:781-793, doi:10.1017/S0263574709990506.

Staicu, S.; Liu X.-J.; Wang, J. (2007); Inverse dynamics of the HALF parallelmanipulator with revolute actuators, Nonlinear Dyn., 50: 1- 12.

Gallardo J.; Rico, J.; Frisoli, A.; Checcacci, D.; Bergamasco M. (2003); Dynamics of parallel manipulators by means of screw theory, Mech. Mach. Theory, 38: 1113-1131.

Miller, K. (2004); Optimal Design and Modeling of Spatial Parallel Manipulators, The Int. J. of Robotics Research, 23(2): 127-140.

Staicu, S.; Zhang, D.; Rugescu, R. (2006); Dynamic modelling of a 3-DOF parallel manipulator using recursive matrix relations, Robotica, 24:125-130, doi:10.1017/S0263574705001670.

Achili, B.; Daachi, B.; Amirat, Y.; Ali-Cherif, A.; Daâchi, M. E. (2012); A stable adaptive force/position controller for a C5 parallel robot: a neural network approach, Robotica, doi:10.1017/S0263574711001354, 30(7):1177-1187.

Peng, Z.; Liu, F.; Yang, L. (2010); Control based on double neural networks-PI for parallel mechanism, Robotics and Computer-Integrated Manufacturing, 26(3): 250-252.

Yu, W. S.; Weng, C. C. (2014); H∞ tracking adaptive fuzzy integral sliding mode control for parallel manipulators; Fuzzy Sets and Systems, ISSN 0165-0114, 248: 1-38.

Obe, O.; Dumitrache, I. (2012); Adaptive Neuro-Fuzzy Controler With Genetic Training For Mobile Robot Control, International Journal od Computers Communications & Control, 7(1): 135-146.

Resceanu, I. C.; Resceanu, C. F.; Bizdoaca, N. G. (2012); Cooperative Robot Structures Modeled After Whale Behavior and Social Structure, International Journal od Computers Communications & Control, 7(5):945-956.

Liu, X.; Wang, Q.; Malikov, A.; Wang, H. (2012); The design and dynamic analysis of a novel 6-DOF parallel mechanism, International Journal of Machine Learning and Cybernetics„ 3(1): 27-37.

Pei, Z.; Zhang, Y.; Tang; Z. (2007); Model reference adaptive PID control of hydraulic parallel robot based on RBF neural network, IEEE Proc. of Intl. Conf.on Robotics and Biomimetics, ROBIO 2007, 1383-1387.

Beji, L.; Pascal, M. (1999); The kinematics and the full minimal dynamic model of a 6-DOF parallel robot manipulator, Nonlinear Dynamics, 18(4): 339-356.

Ayas, M. S.; Sahin, E.; Altas, I. H. (2014); Trajectory tracking control of a Stewart platform, Proc. of IEEE 2014 16th Intl. Conf. and Exposition on Power Electronics and Motion Control

(PEMC), 720-724.

Moldovan, L. (2008); Trajectory Errors of the 6-PGK Parallel Robot, IEEE Proc. of First Intl. Conf. on Complexity and Intelligence of the Artificial and Natural Complex Systems, Medical Applications of the Complex Systems, Biomedical Computing, 2008. CANS’08, 31-37.

Mendes Lopes, A.; Almeida, F. (2009); The generalized momentum approach to the dynamic modeling of a 6-dof parallel manipulator, Multibody System Dynamics, 21(2): 123-146.

Grif, S. (2014); Automatic daylight control system based on neural estimator, Procedia Technology, 12: 759-765.

Demut, H.; Beale, M.; Hagan, M. (2007); Neural Network Toolbox For Use with Matlab. User’s Guide. Version 5, 2007, The MathWorks, Inc.


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