Mahmoodabadi, M., Taher-Khorsandi, M. (2018). Pareto design of fuzzy tracking control based on particle swarm optimization algorithm for a walking robot in the lateral plane on slope. AUT Journal of Modeling and Simulation, 50(2), 157-164. doi: 10.22060/miscj.2018.14327.5103

M.J. Mahmoodabadi; M. Taher-Khorsandi. "Pareto design of fuzzy tracking control based on particle swarm optimization algorithm for a walking robot in the lateral plane on slope". AUT Journal of Modeling and Simulation, 50, 2, 2018, 157-164. doi: 10.22060/miscj.2018.14327.5103

Mahmoodabadi, M., Taher-Khorsandi, M. (2018). 'Pareto design of fuzzy tracking control based on particle swarm optimization algorithm for a walking robot in the lateral plane on slope', AUT Journal of Modeling and Simulation, 50(2), pp. 157-164. doi: 10.22060/miscj.2018.14327.5103

Mahmoodabadi, M., Taher-Khorsandi, M. Pareto design of fuzzy tracking control based on particle swarm optimization algorithm for a walking robot in the lateral plane on slope. AUT Journal of Modeling and Simulation, 2018; 50(2): 157-164. doi: 10.22060/miscj.2018.14327.5103

Pareto design of fuzzy tracking control based on particle swarm optimization algorithm for a walking robot in the lateral plane on slope

^{1}Department of Mechanical Engineering, Sirjan University of Technology, Sirjan, Iran

^{2}Department of Mechanical Engineering, University of Texas at San Antonio, San Antonio, USA

Abstract

Many researchers have controlled and analyzed biped robots that walk in the sagittal plane. These robots require the capability of walking merely laterally when they are faced with the obstacles such as a wall. In this field of study, both nonlinearity of the dynamic equations and also having a tracking system cause an effective control has to be utilized to address these problems. Therefore, this paper presents a nonlinear fuzzy tracking control for the walking robots that step in the lateral plane on a slopes. When fuzzy control is utilized to track the desired trajectories of the joints, there has to be a trade-off between tracking errors and control efforts. Consequently, a particle swarm optimization algorithm is used to obtain the Pareto front of these non-commensurable objective functions to determine the fuzzy control parameters. In this paper, normalized summation of angle errors and normalized summation of control efforts are considered as the objective functions. These objective functions have to be minimized simultaneously. A vector which contains the control parameters is considered as the vector of selective parameters with positive constant values. The obtained Pareto front by the proposed multi-objective algorithm is compared with three prominent algorithms, modified NSGAII, Sigma method and MATLAB Toolbox MOGA. The result dramatizes the superiority of innovative particle swarm optimization over the algorithms.

[1] Z. Liu, Y. Zhang, Y.J.I.T.o.S. Wang, Man,, P.C. Cybernetics, A type-2 fuzzy switching control system for biped robots, 37(6) (2007) 1202-1213.

[2] T.-H.S. Li, Y.-T. Su, S.-W. Lai, J.-J.J.I.T.o.S. Hu, Man,, P.B. Cybernetics, Walking motion generation, synthesis, and control for biped robot by using PGRL, LPI, and fuzzy logic, 41(3) (2011) 736-748.

[3] G. Dip, V. Prahlad, P.D.J.R. Kien, Genetic algorithm-based optimal bipedal walking gait synthesis considering tradeoff between stability margin and speed, 27(3) (2009) 355-365.

[4] P.N. Mousavi, C. Nataraj, A. Bagheri, M.A.J.A.M.M. Entezari, Mathematical simulation of combined trajectory paths of a seven link biped robot, 32(7) (2008) 1445-1462.

[5] S. Ito, S. Amano, M. Sasaki, P. Kulvanitt, In-place lateral stepping motion of biped robot adapting to slope change, in: 2007 IEEE International Conference on Systems, Man and Cybernetics, IEEE, 2007, pp. 1274-1279.

[6] M.T. Khorsandi, B. Miripour-Fard, A. Bagheri, Optimal tracking control of a biped robot walking in the lateral plane, in: 2011 International Symposium on Innovations in Intelligent Systems and Applications, IEEE, 2011, pp. 560-564.

[7] D.A. Shook, P.N. Roschke, P.-Y. Lin, C.-H.J.E.s. Loh, GA-optimized fuzzy logic control of a large-scale building for seismic loads, 30(2) (2008) 436-449.

[8] H. Shayeghi, A. Jalili, H.J.E.C. Shayanfar, Management, Multi-stage fuzzy load frequency control using PSO, 49(10) (2008) 2570-2580.

[9] Z. Bingül, O.J.E.S.w.A. Karahan, A Fuzzy Logic Controller tuned with PSO for 2 DOF robot trajectory control, 38(1) (2011) 1017-1031.

[10] R. Eberhart, J. Kennedy, Particle swarm optimization, in: Proceedings of the IEEE international conference on neural networks, Citeseer, 1995, pp. 1942-1948.

[11] P.J. Angeline, Using selection to improve particle swarm optimization, in: 1998 IEEE International Conference on Evolutionary Computation Proceedings. IEEE World Congress on Computational Intelligence (Cat. No. 98TH8360), IEEE, 1998, pp. 84-89.

[12] R.C. Eberhart, Y. Shi, Comparison between genetic algorithms and particle swarm optimization, in: International conference on evolutionary programming, Springer, 1998, pp. 611-616.

[13] H. Yoshida, K. Kawata, Y. Fukuyama, S. Takayama, Y.J.I.T.o.p.s. Nakanishi, A particle swarm optimization for reactive power and voltage control considering voltage security assessment, 15(4) (2000) 1232-1239.

[14] X. Hu, R. Eberhart, Multiobjective optimization using dynamic neighborhood particle swarm optimization, in: Proceedings of the 2002 Congress on Evolutionary Computation. CEC’02 (Cat. No. 02TH8600), Ieee, 2002, pp. 1677-1681.

[15] J.E. Fieldsend, S. Singh, A multi-objective algorithm based upon particle swarm optimisation, an efficient data structure and turbulence, (2002).

[16] S. Mostaghim, J. Teich, Strategies for finding good local guides in multi-objective particle swarm optimization (MOPSO), in: Proceedings of the 2003 IEEE Swarm Intelligence Symposium. SIS’03 (Cat. No. 03EX706), IEEE, 2003, pp. 26-33.

[17] K.E. Parsopoulos, D.K. Tasoulis, M.N. Vrahatis, Multiobjective optimization using parallel vector evaluated particle swarm optimization, in: Proceedings of the IASTED international conference on artificial intelligence and applications, Acta Press, 2004, pp. 823-828.

[18] D.A. Winter, Biomechanics and motor control of human movement, John Wiley & Sons, 2009.

[19] L.-X. Wang, L.-X. Wang, A course in fuzzy systems and control, Prentice Hall PTR Upper Saddle River, NJ, 1997.

[20] R. Eberhart, P. Simpson, R. Dobbins, Computational intelligence PC tools, Academic Press Professional, Inc., 1996.

[21] A.P. Engelbrecht, Fundamentals of Computational Swarm Intelligence, John Wiley & Sons, Inc., 2006.

[22] A. Ratnaweera, S.K. Halgamuge, H.C.J.I.T.o.e.c. Watson, Self-organizing hierarchical particle swarm optimizer with time-varying acceleration coefficients, 8(3) (2004) 240-255.

[23] M.J. Mahmoodabadi, A. Bagheri, S.A. Mostaghim, M.J.M. Bisheban, C. Modelling, Simulation of stability using Java application for Pareto design of controllers based on a new multi-objective particle swarm optimization, 54(5-6) (2011) 1584-1607.

[24] M. Mahmoodabadi, A. Bagheri, N. Nariman-Zadeh, A.J.E.O. Jamali, A new optimization algorithm based on a combination of particle swarm optimization, convergence and divergence operators for single-objective and multi-objective problems, 44(10) (2012) 1167-1186.

[26] Z.-H. Zhan, J. Zhang, Y. Li, H.S.-H.J.I.T.o.S. Chung, Man,, P.B. Cybernetics, Adaptive particle swarm optimization, 39(6) (2009) 1362-1381.

[27] J.J. Durillo, J. García-Nieto, A.J. Nebro, C.A.C. Coello, F. Luna, E. Alba, Multi-objective particle swarm optimizers: An experimental comparison, in: International conference on evolutionary multi-criterion optimization, Springer, 2009, pp. 495-509.

[28] M. Reyes-Sierra, C.C.J.I.j.o.c.i.r. Coello, Multi-objective particle swarm optimizers: A survey of the state-of-the-art, 2(3) (2006) 287-308.

[29] K. Deb, S. Agrawal, A. Pratap, T. Meyarivan, A fast elitist non-dominated sorting genetic algorithm for multi-objective optimization: NSGA-II, in: International conference on parallel problem solving from nature, Springer, 2000, pp. 849-858.

[30] R.J.J.o.p.c. Toscano, A simple robust PI/PID controller design via numerical optimization approach, 15(1) (2005) 81-88.

[31] F. Golnaraghi, B.C. Kuo, Automatic Control Systems, Wiley Publishing, 2009.

[32] K. Atashkari, N. Nariman-Zadeh, M. Gölcü, A. Khalkhali, A.J.E.C. Jamali, Management, Modelling and multi-objective optimization of a variable valve-timing spark-ignition engine using polynomial neural networks and evolutionary algorithms, 48(3) (2007) 1029-1041.