Trajectory Tracking of a Redundant Hybrid Manipulator Using a Switching Control Method

Authors: Atilla Bayram

Abstract:

This paper presents the trajectory tracking control of a spatial redundant hybrid manipulator. This manipulator consists of two parallel manipulators which are a variable geometry truss (VGT) module. In fact, each VGT module with 3-degress of freedom (DOF) is a planar parallel manipulator and their operational planes of these VGT modules are arranged to be orthogonal to each other. Also, the manipulator contains a twist motion part attached to the top of the second VGT module to supply the missing orientation of the endeffector. These three modules constitute totally 7-DOF hybrid (parallel-parallel) redundant spatial manipulator. The forward kinematics equations of this manipulator are obtained, then, according to these equations, the inverse kinematics is solved based on an optimization with the joint limit avoidance. The dynamic equations are formed by using virtual work method. In order to test the performance of the redundant manipulator and the controllers presented, two different desired trajectories are followed by using the computed force control method and a switching control method. The switching control method is combined with the computed force control method and genetic algorithm. In the switching control method, the genetic algorithm is only used for fine tuning in the compensation of the trajectory tracking errors.

Keywords: Computed force control method, genetic algorithm, hybrid manipulator, inverse kinematics of redundant manipulators, variable geometry truss.

Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1124549

References:

[1] X. S. Gao, D. Lei, Q. Liao and G. F. Zhang, "Generalized Stewart Gough platforms and their direct kinematics," IEEE Transactions on Robotics, vol. 21, no. 2, pp 141-151, April 2005.
[2] P. C. Hughes, W. G. Sincarsin and K. A. Carroll, "Trussarm—a variable-geometry-truss manipulator," Journal of Intelligent Material Systems and Structures, 1991, 2.2: 148-160, 1991.
[3] A. Codourey, "Dynamic modeling and mass matrix evaluation of the DELTA parallel robot for axes decoupling control," Intelligent Robots and Systems' 96, IROS 96, Proceedings of the 1996 IEEE/RSJ International Conference on. Vol. 3. IEEE, 1996.
[4] K. Daniel, P. Wenger and D. Chablat, "Kinematic analysis of a serial– parallel machine tool, The VERNE machine" Mechanism and Machine Theory, 44.2 , 487-498, 2009.
[5] F. Gómez-Bravo, G. Carbone and J. C. Fortes, "Collision free trajectory planning for hybrid manipulators," Mechatronics, 22.6, 836-851, 2012.
[6] Z. Gao, and Z. Dan, "Performance analysis, mapping, and multiobjective optimization of a hybrid robotic machine tool," Industrial Electronics, IEEE Transactions on 62.1, 423-433, 2015.
[7] H. M. Do, C. Park, and J. H. Kyung, "Dual arm robot for packaging and assembling of IT products," Automation Science and Engineering (CASE), 2012 IEEE International Conference on. IEEE, p. 1067-1070, 2012.
[8] A. Atawnih, P. Dimitrios, and D. Zoe, "Kinematic control of redundant robots with guaranteed joint limit avoidance," Robotics and Autonomous Systems, 2016.
[9] Y. Zhang and W. Jun, "Obstacle avoidance for kinematically redundant manipulators using a dual neural network," Systems, Man, and Cybernetics, Part B: Cybernetics, IEEE Transactions on 34.1, 752-759, 2004.
[10] S. Chiaverini, "Singularity-robust task-priority redundancy resolution for real-time kinematic control of robot manipulators," Robotics and Automation, IEEE Transactions on 13.3, 398-410, 1997.
[11] J. Jamisola, S. Rodrigo, A. M. Anthony and G. R. Rodney, "Failuretolerant path planning for kinematically redundant manipulators anticipating locked-joint failures," Robotics, IEEE Transactions on 22.4, 603-612, 2006.
[12] R. Boudreau, and N. Scott, "Force Optimization of kinematicallyredundant planar parallel manipulators following a desired trajectory," Mechanism and Machine Theory, 56, 138-155, 2012.
[13] Y. Oh, W. Chung and Y. Youm, "Extended impedance control of redundant manipulators based on weighted decomposition of joint space. Journal of Robotic Systems, Vol. 15(5), pp. 231-258, 1998.
[14] M. Z. Ding, C. J. Ong, and A.N. Poo, "Resolution of redundant manipulator via distance optimization," Proc. of the Inst. of Mech. Eng, Journal of Mechanical Engineer Scince, Vol. 204, No: 8, 2000
[15] A. R. Cherif, V. Perdereau and M. Droin, M., "Penalty approach for a constrainted optimization to solve on-line to the inverse kinematic problem of redundant manipulators," Proceedings of the 1996 IEEE International Conference on Robotics and Automation, Minneapolis- Minnesota, April 1996
[16] A. Khoukhi, L. Baron, M. Balazinski and K. Demirli, "Hybrid neurofuzzy multi-objective trajectory planning of redundant manipulators. Journal of Control and Intelligent Systems, Vol.37, No:2, 2009.
[17] X. Luo and W. Wei, "A new immune genetic algorithm and its application in redundant manipulator path planning," Journal of Robotic Systems, Vol. 21(3), pp. 141-151, 2004.
[18] A. Müller, and T. Hufnagel, "Model-based control of redundantly actuated parallel manipulators in redundant coordinates," Robotics and Autonomous Systems, 60(4), 563-571, 2012.
[19] W. Shang and C. Shuang, "Nonlinear computed torque control for a high-speed planar parallel manipulator," Mechatronics, 19.6: 987-992, 2009.
[20] A. Jahed, F. Piltan, H. Rezaie and B. Boroomand, "Design computed torque controller with parallel fuzzy inference system compensator to control of robot manipulator," International Journal of Information Engineering & Electronic Business, 5(3), 2013.
[21] A. Elkady, G. Elkobrosy, S. Hanna and T. Sobh, "Cartesian parallel manipulator modeling, control and simulation," INTECH Open Access Publisher, 2008.
[22] N. Kumar, V. Panwar, N. Sukavanam, S .P. Sharma and J. H. Borm, "Neural network-based nonlinear tracking control of kinematically redundant robot manipulators," Mathematical and Computer Modeling, 53(9), 1889-1901, 2011.
[23] B. Daachi, T. Madani and A. Benallegue, "Adaptive neural controller for redundant robot manipulators and collision avoidance with mobile obstacles," Neurocomputing 79: 50-60, 2012.
[24] A. Ayman, O. Hidetoshi and A. A. Ahmed, "Adaptive control of a parallel robot using fuzzy inverse model," International Journal Of Control, Automation and Systems Vol. 1, No. 1, January 2012.
[25] L. Tian and C. Collins, "An effective robot trajectory planning method using a genetic algorithm," Mechatronics 14.5: 455-470, 2004.
[26] A. Bayram, and M. K. Özgören, "the conceptual design of a spatial binary hyper redundant manipulator and its forward kinematics," Proc IMechE, Part C: J. Mechanical Engineering Science, vol. 226, no. 1, p. 217–227, 2012.
[27] M. K. Özgören, "Kinematic analysis of spatial mechanical systems using exponential rotation matrices," Journal of Mechanical Design, ASME, Vol. 129, pp. 1144-1152, 2007
[28] B. Dasgupta, and T. S. Mruthyunjaya, "A Newton-Euler formulation for the inverse dynamics of the Stewart platform manipulator," Mechanism and Machine Theory, 1998, 33.8: 1135-1152.7, 1998
[29] H. Abdellatif and B. Heımann, "Computational efficient inverse dynamics of 6-DOF fully parallel manipulators by using the Lagrangian formalism," Mechanism and Machine Theory, 2009, 44.1: 192-207, 2009
[30] McPhee, J., P. Shi. and Piedbuf, J-C., (2002), Dynamics of multibody systems using virtual work and symbolic programming. Mathematical and Computer Modelling of Dynamical Systems 8.2 (2002): 137-155.
[31] M. Mitchell, "An introduction to genetic algorithms," 5th Ed., The MIT Press, 1999