PUMA 560 Optimal Trajectory Control using Genetic Algorithm, Simulated Annealing and Generalized Pattern Search Techniques

Authors: Sufian Ashraf Mazhari, Surendra Kumar

Abstract:

Robot manipulators are highly coupled nonlinear systems, therefore real system and mathematical model of dynamics used for control system design are not same. Hence, fine-tuning of controller is always needed. For better tuning fast simulation speed is desired. Since, Matlab incorporates LAPACK to increase the speed and complexity of matrix computation, dynamics, forward and inverse kinematics of PUMA 560 is modeled on Matlab/Simulink in such a way that all operations are matrix based which give very less simulation time. This paper compares PID parameter tuning using Genetic Algorithm, Simulated Annealing, Generalized Pattern Search (GPS) and Hybrid Search techniques. Controller performances for all these methods are compared in terms of joint space ITSE and cartesian space ISE for tracking circular and butterfly trajectories. Disturbance signal is added to check robustness of controller. GAGPS hybrid search technique is showing best results for tuning PID controller parameters in terms of ITSE and robustness.

Keywords: Controller Tuning, Genetic Algorithm, Pattern Search, Robotic Controller, Simulated Annealing.

Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1081289

References:

[1] Chul-Goo Kang Online "Trajectory Planning for a PUMA Robot," International Journal of Precision Engineering and Manufacturing, vol. 8, vo.4, pp.16-21, Oct. 2007.
[2] Francisco Valero and Vicente Mata, Antonio Besa "Trajectory planning in workspaces with obstacles taking into account the dynamic robot behavior," Journal of Mechanism and Machine Theory, vol. 41, issue 5, pp. 525-536,May. 2006.
[3] Chia-Yu E. Wang, Wojciech K. Timoszyk, and James E. Bobrow "Payload Maximization for Open Chained Manipulators: Finding Weightlifting Motions for a Puma 762 Robot," IEEE Transactions on Robotics and Automation, vol. 17, no. 2, Apr. 2001.
[4] Shadia Elgazzar "Efficient Kinematic Transformations for the PUMA 560 Robot," IEEE Journal Of Robotics And Automation, vol. Ra-1, no. 3, Sept. 1985.
[5] Said M. Megahed "Inverse Kinematics of Spherical Wrist Robot Arms Analysis and Simulation," Journal of Intelligent and Robotic Systems, vol. 5, pp. 211-227, 1992.
[6] Jean Cote, C1ement M. Gosselin and Denis Laurendeau "Generalized Inverse Kinematic Functions for the Puma Manipulators," IEEE Transactions on Robotics and Automation, vol. 1 I, no. 3, Jun. 1995.
[7] Fan-Tien Cheng, Tzung-Liang Hour, York-Yin Sun, and Tsing-Hua Chen "Study and Resolution of Singularities for a 6-Dof Puma Manipulator "IEEE Transactions on Systems, Man, and CyberneticsÔÇö Part B: Cybernetics, vol. 27, no. 2, Apr. 1997.
[8] Frederic Chapelle and Philippe Bidaud, "Closed form solutions for inverse kinematics approximation of general 6R manipulators," Journal of Mechanism and Machine Theory, vol. 39, issue. 3, pp. 323-338, Mar 2004.
[9] Brian Armstrong, Oussama Khatib, Joel Burdick,"The explicit dynamic Model and Inertial Parameters of the Puma 560 Arms," IEEE International conference on Robotics and Automation, vol. 2 ,pp. 1608- 1613, May 1994.
[10] John T. Wen and Steve H. Murphy, "PID control for robot manipulators", Rensselaer Polytechnic Institute, CIRSSE Document #54, May 1990.
[11] R.Kelly, V.santibanez A.Loria, Control of Robot Manipulators in joint space, Springer Advanced Textbooks in Control and Signal Processing, series 2005
[12] David A.Coley, Introduction to Genetic Algorithm for scientist and engineer, World scientific Publishing 1999
[13] D.P.KWOK, Fang Sheng "Genetic algorithm and simulated annealing for optimal robot am PID control," IEEE conference on evolutionary computing, vol. 2, pp. 707 - 713, June 1994.
[14] S. Kirkpatrick, C. D. Gelatt, Jr., M. P. Vecchi, "Optimization by simulated annealing," Science, vol. 220, no. 459813, May 1983.
[15] R.A.Rutenber," Simulated Annealing Algorithms: An Overview," IEEE Circuits and Devices, pp. 19-26,Jan. 1989.
[16] Robert Hooke, T. A. Jeeves, "Direct Search Solution of Numerical and Statistical Problems," Journal of the ACM, vol. 8, issue 2 pp: 212 - 229, April 1961.
[17] Robert Michael Lewis and Virginia Torczon, "Pattern Search Methods For Linearly Constrained Minimization," Institute for Computer Applications in Science and Engineering, Report no.98-3, 1998.
[18] LiYing Liu, XueSheng Zhang "Generalized pattern search methods for linearly equality constrained optimization problems," Applied Mathematics and Computation, vol. 181, Issue 1, pp 527-535, Oct. 2006.
[19] T.J.Tarn, A.K.Bejczy, G.T.Marth, A.K.Ramadorai "Performance Comparison of Four Manipulator Servo Schemes" IEEE control system magazine, vol. 3 issue 1, Feb 1993.
[20] P. Corke, "A robotics toolbox for MATLAB," IEEE Robotics and Automation Magazine, vol. 3, pp. 24-32, Mar 1996.
[21] Naganna G.E and Surendra Kumar," Conventional and intelligent controllers for robotic manipulator," IEEE International conference on industrial technology, pp. 424-428, Dec 2006.