A Fuzzy Algorithm to Study the Inverse Kinematics Problem of a Serial Manipulator

Abstract:

This paper presents a fuzzy logic to solve the inverse kinematics problem. As the complexity of robot increases, obtaining the inverse kinematics solution requires the solution of non linear equations having transcendental functions are difficult and computationally expensive. This study focuses on a serial manipulator modelled as a serial chain of rigid bodies connected by joints. A new fuzzy interactive algorithm is developed and the effectiveness is compared with other methods on a SCARA robot. It converge in all the developed simulations showing a robust performance.

• Periodical: Applied Mechanics and Materials (Volume 783)
• Pages: 77-82
• DOI: https://doi.org/10.4028/www.scientific.net/AMM.783.77
• Online since: August 2015
• Authors: Francesco Aggogeri, Nicola Pellegrini*, Riccardo Adamini
• Keywords: Fuzzy Algorithm, Inverse Kinematics Problem, Numerical Simulations

References

[1] A. D'Souza, S. Vijayakumar, S. Schaal: Learning inverse kinematics, International Conference on Intelligent Robots and Systems, IROS, IEEE, Maui, Hawai, USA, (2001), pp.298-303.

[2] M. Raghavan M., B. Roth: Inverse Kinematics of the General 6R Manipulator and Related Linkages, ASME Trans. J. of Mechanical Design 115 (1993) pp.502-508.

DOI: 10.1115/1.2919218

[3] A. Borboni, F. Aggogeri, R. Faglia: Fast Kinematic Model of a Seven-Bar Linkage With a Single Compliant Link, Proceeding of 12th Biennial Conference on Engineering Systems Design and Analysis, Volume 3, (2014).

DOI: 10.1115/esda2014-20076

[4] S. Kumar, N. Patel, L. Behera: Visual motor control of a 7 dof robot manipulator using function decomposition and sub-clustering in configuration, Neural Processing Letters 28 (1), (2008), pp.17-33.

DOI: 10.1007/s11063-008-9079-8

[5] F. Aggogeri, F. Al-Bender, B. Brunner, M. Elsaid, M. Mazzola, A. Merlo, D. Ricciardi, M. de la O Rodriguez, E. Salvi: Design of piezo-based AVC system for machine tool applications, Mechanical Systems and Signal Processing, Vol. 36 (2013), pp.53-65.

DOI: 10.1016/j.ymssp.2011.06.012

[6] F. Aggogeri, A. Borboni, R. Faglia, A. Merlo, S. De Cristofaro: Precision Positioning Systems: An overview of the state of art, Applied Mechanics and Materials 336-338 (2013), pp.1170-1173.

DOI: 10.4028/www.scientific.net/amm.336-338.1170

[7] T.C. Hsia, Z.Y. Guo: New inverse kinematic algorithms for redundant robots, Journal of Robotics Systems 8 (1), (1991), pp.117-132.

DOI: 10.1002/rob.4620080108

[8] G. Tevatia, S. Schaal: Inverse kinematics of humanoid robots, in: Proc. of IEEE Int. Conf. on Robotics and Automation, San Francisco, CA, (2000), pp.294-299.

DOI: 10.1109/robot.2000.844073

[9] A. Borboni, R. Faglia, G. Resconi, M. Tiboni: Kinematic Synthesis and Analysis in robotics by the morphogenetic neuron, Proceedings of EuroCast 2001 Conference, (2001).

DOI: 10.1007/3-540-45654-6_28

[10] F. Aggogeri, A. Borboni, R. Faglia: Reliability roadmap for mechatronic systems, Applied Mechanics and Materials 373-375 (2013), pp.130-133.

DOI: 10.4028/www.scientific.net/amm.373-375.130

[11] A. A. H. Sallam, W. M. F. Abouzaid: NXT* SCARA Model Based Design Controlled by Neural Network, International Journal of Control Science and Engineering 3(3) (2013), pp.86-94.

[12] P.J. Alsina, N.S. Gehlot: Robot inverse kinematics: a modular neural network approach, Proceedings of 38th Midwest Symposiumon Circuits and Systems,vol.2,(1995), p.631–634.

DOI: 10.1109/mwscas.1995.510169

[13] Y.Xia, J.Wang: A dual neural network for kinematic control of redundant robot manipulators, IEEE Transactions on Systems, Man, and Cybernetics, Part B 31(1), (2001), p.147–154.

DOI: 10.1109/3477.907574

[14] M.L. Husty, M.Pfurner and H.P. Schrocker: A new and efficient algorithm for the inverse kinematics of a general serial 6r manipulator, Mechanism and Machine Theory 42, (2007), pp.66-81.

DOI: 10.1016/j.mechmachtheory.2006.02.001

[15] P.J. Angeline, G.M. Saunders, J.B. Pollack: An evolutionary algorithm that constructs recurrent neural networks, IEEE Transactions on Neural Networks 5 (1), (1994), p.54–65.

DOI: 10.1109/72.265960

[16] S.Alavandar, M.J. Nigam: Neuro-fuzzy based approach for inverse kinematics solution of industrial robot manipulators, Int. J. of Computers, Communications & Control, 3, (2008), pp.224-234.

DOI: 10.15837/ijccc.2008.3.2391

[17] S.García, A.Fernández, J.Luengo, F.Herrera: Advanced nonparametric tests for multiple comparisons in the design of experiments in computational intelligence and data mining: experimental analysis of power, Information Sciences 180, (2010), p.2044–(2064).

DOI: 10.1016/j.ins.2009.12.010

[18] T.D. Pham: An optimally wieghted fuzzy k-NN algorithm, Proceedings of the Third International Conference on Advances in Pattern Recognition, Part I, Bath, UK, (2005), p.239–247.

[19] Y.Qu, C.Shang, Q.Shen, N.M. Parthaláin, W.Wu: Kernel-based fuzzy-rough nearest neighbour classification, IEEE International Conference on Fuzzy Systems, Taipei, Taiwan, (2011), p.1523–1529.

DOI: 10.1109/fuzzy.2011.6007401

[20] R.J. Hathaway, J.C. Bezdek, W. Pedrycz: A Parametric Model for Fusing Heterogeneous Fuzzy Data, IEEE Trans. On Fuzzy Systems 4(3) (1996), pp.270-281.

DOI: 10.1109/91.531770

[21] S.S. Rao, L.Chen: Numerical solution of fuzzy linear equations in engineering analysis, Internat.J. Numer. Methods Eng. 43, (1998), p.391–408.

DOI: 10.1002/(sici)1097-0207(19981015)43:3<391::aid-nme417>3.0.co;2-j

[22] A.S. Balu, B.N. Rao: Efficient explicit formulation for practical fuzzy structural analysis, Sadhana 36 (4), (2011), p.463–488.

DOI: 10.1007/s12046-011-0035-3