Hostname: page-component-848d4c4894-4rdrl Total loading time: 0 Render date: 2024-06-20T01:52:05.214Z Has data issue: false hasContentIssue false
  • English
  • Français

Inverse Kinematics of Redundant Manipulators Formulated as Quadratic Programming Optimization Problem Solved Using Recurrent Neural Networks: A Review

Published online by Cambridge University Press:  25 November 2019

Ahmed A. Hassan Open the ORCID record for Ahmed A. Hassan [Opens in a new window] ,
Mohamed El-Habrouk  and
Samir Deghedie
Ahmed A. Hassan*
Affiliation:
Department of Electrical Engineering, Faculty of Engineering, Alexandria University, Alexandria, Egypt
Mohamed El-Habrouk
Affiliation:
Department of Electrical Engineering, Faculty of Engineering, Alexandria University, Alexandria, Egypt
Samir Deghedie
Affiliation:
Department of Electrical Engineering, Faculty of Engineering, Alexandria University, Alexandria, Egypt
*
*Corresponding author. E-mail: a.hassan0305@gmail.com
Rights & Permissions [Opens in a new window]

Summary

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

The Inverse Kinematics (IK) problem of manipulators can be divided into two distinct steps: (1) Problem formulation, where the problem is developed into a form which can then be solved using various methods. (2) Problem solution, where the IK problem is actually solved by producing the values of different joint space variables (joint angles, joint velocities or joint accelerations). The main focus of this paper is concentrated on the discussion of the IK problem of redundant manipulators, formulated as a quadratic programming optimization problem solved by different kinds of recurrent neural networks.

Keywords

Inverse kinematicsRedundant manipulatorsQuadratic programmingRecurrent neural networksBi-criteria kinematic control
Type
Articles
Information
Robotica , Volume 38 , Issue 8 , August 2020 , pp. 1495 - 1512
Copyright
© Cambridge University Press 2019

References

Gardner, J. F., Brandt, A. and Luecke, G., “Applications of neural networks for coordinate transformations in robotics,” J. Intell. Rob. Syst. 8(3), 361–373 (1993).CrossRefGoogle Scholar
Bingul, Z., Ertunc, H. M. and Oysu, C., “Applying Neural Network to Inverse Kinematic Problem for 6R Robot Manipulator with Offset Wrist,” In: Adaptive and Natural Computing Algorithms (Ribeiro, B., Albrecht, R. F., Dobnikar, A., Pearson, D. W. and Steele, N. C., eds.) (Springer, Vienna, 2005).Google Scholar
Hasan, A. T., Al-Assadi, H. M. A. A. and Isa, A. A. M., “Neural Networks’ Based Inverse Kinematics Solution for Serial Robot Manipulators Passing Through Singularities,” In: Artificial Neural Networks - Industrial and Control Engineering Applications (IntechOpen, London, 2011) pp. 459–478.Google Scholar
Oltean, S., Şoaita, D., Dulau, M. and Jovrea, T., “Aspects of Interdisciplinarity in the MRIP 02 System Design,” International Conference “Optimization of the Robots and Manipulators” (OPTIROB) (Bren Publishing House, 2007) pp. 121–125.Google Scholar
Secarã, C. and Vlãdãreanu, L., “Iterative Genetic Algorithm Based Strategy for Obstacles Avoidance of a Redundant Manipulator,” Proceedings of the 2010 American Conference on Applied Mathematics, Cambridge, USA (2010) pp. 361–366.Google Scholar
Featherstone, R., “Position and velocity transformations between robot end-effector coordinates and joint angles,” Int. J. Rob. Res. 2(2), 33–45 (1983).CrossRefGoogle Scholar
Lee, G. C. S., “Robot arm kinematics, dynamics, and control,” IEE Comput. 15(12), 62–79 (1982).CrossRefGoogle Scholar
Lee, C. S. G. and Ziegler, M., “Geometric approach in solving inverse kinematics of PUMA robots,” IEEE Trans. Aero. Electron. Syst. (6), 695–706 (1984).CrossRefGoogle Scholar
Tokarz, K. and Kieltyka, S., “Geometric approach to inverse kinematics for arm manipulator,” ICS’10 Proceedings of the 14th WSEAS International Conference on Systems: Part of the 14th WSEAS CSCC Multi-conference, Corfu Island, Greece (2010) pp. 682–687.Google Scholar
Rodriguez, G., Jain, A. and Kreutz-Delgado, K., “A spatial operator algebra for manipulator modelling and control,” Int. J. Rob. Res. 10(4), 371–381 (1991).CrossRefGoogle Scholar
Wang, X. and Verriest, J.-P., “A geometric algorithm to predict the arm reach posture of computer-aided ergonomic evaluation,” J. Visual Comput. Animat. 9(1), 33–47 (1998).3.0.CO;2-Q>CrossRefGoogle Scholar
Duffy, J., Analysis of Mechanism and Robot Manipulators (John Wiley & Sons, Inc., New York, NY, 1980). ISBN: 0470270020.Google Scholar
Manocha, D. and Canny, J. F., “Efficient inverse kinematics for general 6R manipulators,” IEEE Trans. Rob. Autom. 10(5), 648–657 (1994).CrossRefGoogle Scholar
Paul, R. P., Shimano, B. and Mayer, G. E., “Differential kinematic control equations for simple manipulators,” IEEE Trans. Syst. Man Cybern. 1(1), 66–72 (1981).Google Scholar
Fu, K. S., Gonzalez, R. C. and Lee, C. S. G., Robotics: Control, Sensing, Vision and Intelligence (McGraw-Hill, Inc., New York, NY, 1987). ISBN: 0070226253.Google Scholar
Manocha, D. and Zhu, Y., “A fast Algorithm and System for the Inverse Kinematics of General Serial Manipulators,” Proceedings of the 1994 IEEE International Conference on Robotics and Automation, San Diego, CA, USA, vol. 4 (1994) pp. 3348–3353.Google Scholar
Paul, R. P., Robot Manipulators: Mathematics, Programming and Control (MIT Press, Cambridge, MA, 1982). ISBN: 026216082X.Google Scholar
Stiffer, S., “Algebraic methods for computing inverse kinematics,” J. Intell. Rob. Syst. 11(1–2), 79–89 (1994).CrossRefGoogle Scholar
Buchberger, B., “Gröbner Bases: An Algorithmic Method in Polynomial Ideal Theory,” In: Multidimensional Systems Theory (Bose, N. K., ed.) (Springer, Dordrecht, 1985) pp. 184–232.CrossRefGoogle Scholar
Manocha, D., Algebraic and Numeric Techniques in Modeling and Robotics (University of California at Berkeley, Berkeley, CA, 1992).Google Scholar
Snyder, W. E., Industrial Robots: Computer Interfacing and Control (Prentice-Hall Industrial Robots Series, Prentice-Hall, Englewood Cliffs, NJ, 1985). ISBN: 9780134631592.Google Scholar
Craig, J. J., Introduction to Robotics - Mechanics & Control, 3rd edition (Pearson, Prentice Hall, Upper Saddle River, NJ, 2005). ISBN: 0201543613.Google Scholar
Korein, J. U. and Balder, N. I., “Techniques for generating the goal-directed motion of articulated structures,” IEEE Comput. Graphics Appl. 2(9), 71–81 (1982).CrossRefGoogle Scholar
Wang, L.-C. T. and Chen, C. C., “A combined optimization method for solving the inverse kinematics problems of mechanical manipulators,” IEEE Trans. Rob. Autom. 7(4), 489–499 (1991).CrossRefGoogle Scholar
Grudić, G. Z. and Lawrence, P. D., “Iterative inverse kinematics with manipulator configuration control,” IEEE Trans. Rob. Autom. 9(4), 476–483 (1993).CrossRefGoogle Scholar
Karlik, B. and Aydin, S., “An improved approach to the solution of inverse kinematics problems for robot manipulators,” Eng. Appl. Artif. Intell. 13(2), 159–164 (2000).CrossRefGoogle Scholar
Köker, R., “Reliability-based approach to the inverse kinematics solution of robots using Elman’s networks,” Eng. Appl. Artif. Intell. 18(6), 685–693 (2005).CrossRefGoogle Scholar
Grudic, Z. G. and Lawrange, P. D., “Iterative inverse kinematics with manipulator configuration control,” IEEE Trans. Rob. Autom. 9(4), 476–483 (1993).CrossRefGoogle Scholar
Yahya, S., Moghavvemia, M. and Mohamed, H. A. F., “Geometrical approach of planar hyper-redundant manipulators: Inverse kinematics, path planning and workspace,” Simul. Modell. Pract. Theory 19(1), 406–422 (2011).CrossRefGoogle Scholar
Chiddarwar, S. S. and Babu, N. R., “Comparison of RBF and MLP neural networks to solve inverse kinematic problem for 6R serial robot by a fusion approach,” Eng. Appl. Artif. Intell. 23(7), 1083–1092 (2010).CrossRefGoogle Scholar
Daunicht, W. J., “Approximation of the Inverse Kinematics of an Industrial Robot by DEFAnet,” Proceedings of the 1991 IEEE International Joint Conference on Neural Networks, Singapore, vol. 3 (1991) pp. 1995–2000.Google Scholar
Hakala, J., Fahner, G. and Eckmiller, R., “Rapid Learning of Inverse Robot Kinematics Based on Connection Assignment and Topographical Encoding (CATE),” Proceedings of the 1991 IEEE International Joint Conference on Neural Networks, Singapore, vol. 2 (1991) pp. 1536–1541.CrossRefGoogle Scholar
Hasan, A. T., Hamouda, A. M. S., Ismail, N. and Al-Assadi, H. M. A. A., “An adaptive-learning algorithm to solve the inverse kinematics problem of a 6 D.O.F serial robot manipulator,” Adv. Eng. Software 37(7), 432–438 (2006).CrossRefGoogle Scholar
Hasan, A. T., Ismail, N., Hamouda, A. M. S., Aris, I., Marhaban, M. H. and Al-Assadi, H. M. A. A., “Artificial neural network-based kinematics Jacobian solution for serial manipulator passing through singular configurations,” Adv. Eng. Software 41(2), 359–367 (2010).CrossRefGoogle Scholar
Köker, R., Öz, C., Çakar, T. and Ekiz, H., “A study of neural network based inverse kinematics solution for a three-joint robot,” Rob. Auton. Syst. 49(3–4), 227–234 (2004).CrossRefGoogle Scholar
de Lope, J. and Santos, M., “A method to learn the inverse kinematics of multi-link robots by evolving neuro-controllers,” Neurocomputing 72(13–15), 2806–2814 (2009).Google Scholar
Martinetz, T. M., Ritter, H. J. and Schulten, K. J., “Three-dimensional neural net for learning visuomotor coordination of a robot arm,” IEEE Trans. Neural Networks 1(1), 131–136 (1990).CrossRefGoogle ScholarPubMed
Mayorga, R. V. and Sanongboon, P., “Inverse kinematics and geometrically bounded singularities prevention of redundant manipulators: An Artificial Neural Network approach,” Rob. Auton. Syst. 53(3–4), 164–176 (2005).CrossRefGoogle Scholar
Oyama, E., Chong, N. Y., Agah, A., Maeda, T. and Tachi, S., “Inverse Kinematics Learning by Modular Architecture Neural Networks with Performance Prediction Networks,”Proceedings 2001 ICRA. IEEE International Conference on Robotics & Automation, Seoul, South Korea, vol. 1 (2001) pp. 1006–1012.Google Scholar
Tejomurtula, S. and Kak, S., “Inverse kinematics in robotics using neural networks,” Inf. Sci. 116(2–4), 147–164 (1999).CrossRefGoogle Scholar
Chen, P. C. Y., Mills, J. K. and Smith, K. C., “Performance improvement of robot continuous-path operation through iterative learning using neural networks,” Mach. Learn. J. 23(2–3), 191–220 (1996).CrossRefGoogle Scholar
Köker, R., Oz, C. and Ferikoglu, A., “Development of a Vision Based Object Classification System for an Industrial Robotic Manipulator,” ICECS 2001. 8th IEEE International Conference on Electronics, Circuits and Systems, Malta, vol. 3 (2001) pp. 1281–1284.Google Scholar
Lu, B.-L. and Ito, K., “Regularization of Inverse Kinematics for Redundant Manipulators Using Neural Network Inversions,” Proceedings of ICNN’95 - International Conference on Neural Networks, Perth, WA, Australia, vol. 5 (1995) pp. 2726–2731.Google Scholar
Nagata, F., Kishimoto, S., Kurita, S., Otsuka, A. and Watanabe, K., “Neural Network-Based Inverse Kinematics for an Industrial Robot and its Learning Method,”Proceedings of the 4th IIAE International Conference on Industrial Application Engineering, Beppu, Oita, Japan (2016).Google Scholar
Almusawi, A. R. J., Dülger, L. C. and Kapucu, S., “A New Artificial Neural Network Approach in Solving Inverse Kinematics of Robotic Arm (Denso VP 6242),” Comput. Intell. Neurosci. 2016, 5720163 (2016).Google Scholar
Zhang, Z., Zheng, L., Yu, J., Li, Y. and Yu, Z., “Three recurrent neural networks and three numerical methods for solving a repetitive motion planning scheme of redundant robot manipulators,” IEEE/ASME Trans. Mech. 22(3), 1423–1434 (2017).CrossRefGoogle Scholar
Li, S., Zhou, M. and Luo, X., “Modified primal-dual neural networks for motion control of redundant manipulators with dynamic rejection of harmonic noises,” IEEE Trans. Neural Networks Learn. Syst. 29(10), 4791–4801 (2018).CrossRefGoogle Scholar
Guez, A. and Ahmad, Z., “Solution to the Inverse Problem in Robotics by Neural Networks,” IEEE 1988 International Conference on Neural Networks, 1988, San Diego, CA, USA, vol. 2 (1988) pp. 617–624.Google Scholar
Josin, G., Charney, D. and White, D., “Robot Control Using Neural Networks,” IEEE 1988 International Conference on Neural Networks, 1988, San Diego, CA, USA, vol. 2 (1988) pp. 625–631.Google Scholar
Guo, J. and Cherkassky, V., “A Solution to the Inverse Kinematics Problem in Robotics Using Neural Network Processing,” International 1989 Joint Conference on Neural Networks, 1989, Washington, DC, USA, vol. 2 (1989) pp. 299–304.Google Scholar
Guez, A. and Ahmad, Z., “Accelerated Convergence in the Inverse Kinematics via Multilayer Feedforward Networks,” International 1989 Joint Conference on Neural Networks, 1989, Washington, DC, USA, vol. 2 (1989) pp. 341–344.Google Scholar
Arteaga-Bravo, F. J., “Multilayer Back-Propagation Network for Learning the Forward and Inverse Kinematics Equations,” Proceedings of the International Conference on Neural Networks, Washington, DC, USA (1990) pp. 319–322.Google Scholar
Lee, S. and Kil, R. M., “Robot Kinematic Control Based on Bidirectional Mapping Neural Network,” 1990 IJCNN International Joint Conference on Neural Networks, San Diego, CA, USA, vol. 3 (1990) pp. 327–335.Google Scholar
Ding, H. and Wang, J., “Recurrent neural networks for minimum infinity-norm kinematic control of redundant manipulators,” IEEE Trans. Syst. Man Cybern. Part A Syst. Humans 29(3), 269–276 (1999).CrossRefGoogle Scholar
Wang, J., Hu, Q. and Jiang, D., “A Lagrangian network for kinematic control of redundant robot manipulators,” IEEE Trans. Neural Networks 10(5), 1123–1132 (1999).CrossRefGoogle ScholarPubMed
Bekey, G. A., “Robotics and Neural Networks,” In: Neural Networks for Signal Processing (Prentice-Hall, Englewood, 1992) pp. 161–185.Google Scholar
Li, Y. and Zeng, N., “A Neural Network Based Inverse Kinematics Solution in Robotics,” In: Neural Networks in Robotics (Springer, Boston, MA, 1993).Google Scholar
Lee, S. and Kil, R. M., “Redundant arm Kinematic Control with Recurrent Loop,” Proceedings of 32nd IEEE Conference on Decision and Control, San Antonio, TX, USA, vol. 2 (1993) pp. 1109–1115.Google Scholar
Mao, Z. and Hsia, T. C., “Obstacle avoidance inverse kinematics solution of redundant robots by neural networks,” Robotica 15(1), 3–10 (1997).CrossRefGoogle Scholar
de Angulo, V. R. and Torras, C., “Learning inverse kinematics: Reduced sampling through decomposition into virtual robots,” IEEE Trans. Syst. Man Cybern. Part B Cybern. 38(6), 1571–1577 (2008).CrossRefGoogle ScholarPubMed
Clark, C. M. and Mills, J. K., “Robotic system sensitivity to neural network learning rate: Theory, simulation, and experiments,” Int. J. Rob. Res. 19(10), 955–968 (2000).CrossRefGoogle Scholar
Alavandar, S. and Nigam, M. J., “Neuro-Fuzzy based approach for inverse kinematics solution of industrial robot manipulators,” Int. J. Comput. Commun. Contr. 3(3), 224–234 (2008).CrossRefGoogle Scholar
Husty, M. L., Pfurner, M. and Schrocker, H. P., “A new and efficient algorithm for the inverse kinematics of a general serial 6R manipulator,” Mech. Mach. Theory 42(1), 66–81 (2007).CrossRefGoogle Scholar
Sciavicco, L. and Siciliano, B., Modeling and Control of Robot Manipulators (Springer-Verlag, London, UK, 2000). ISBN: 978-1-4471-0449-0.CrossRefGoogle Scholar
Zhang, Y., Analysis and Design of Recurrent Neural Networks and their Applications to Control and Robotic Systems PhD dissertation (Chinese University of Hong Kong, 2003). ISBN: 0-493-98186-1.Google Scholar
Chen, J. and Lau, H. Y. K., “A Reinforcement Motion Planning Strategy for Redundant Robot Arms Based on Hierarchical Clustering and K-Nearest-Neighbors,” 2015 IEEE International Conference on Robotics and Biomimetics (ROBIO), Zhuhai (2015) pp. 727–732.Google Scholar
Zhang, Y., Lv, X., Li, Z., Yang, Z. and Chen, K., “Repetitive motion planning of PA10 robot arm subject to joint physical limits and using LVI-based primal–dual neural network,” Mechatron. 18(9), 475–485 (2008).CrossRefGoogle Scholar
Conkur, E., “Path following algorithm for highly redundant manipulator,” Rob. Auton. Syst. 45(1), 1–22 (2003).CrossRefGoogle Scholar
Zhang, Y., Wang, J. and Xia, Y., “A dual neural network for redundancy resolution of kinematically redundant manipulators subject to joint limits and joint velocity limits,” IEEE Trans. Neural Networks 14(3), 658–667 (2003).CrossRefGoogle ScholarPubMed
Hock, O. and Šedo, J., “Forward and inverse kinematics using pseudoinverse and transposition method for robotic arm DOBOT,” IntechOpen (2017).CrossRefGoogle Scholar
Ulrey, R. R., Maciejewski, A. A. and Siegel, H. J., “Parallel Algorithms for Singular Value Decomposition,” Proceedings of 8th IEEE International Conference of Parallel Processing Symposium, Cancun, Mexico (1994) pp. 524–533.Google Scholar
Liegeois, A., “Automatic supervisory control of the configuration and behavior of multibody mechanisms,” IEEE Trans. Syst. Man Cybern. 7(12), 868–871 (1977).Google Scholar
Goel, M., Maciejewski, A. A., Balakrishnan, V. and Proctor, R. W., “Failure tolerant teleoperation of a kinematically redundant manipulator: An experimental study,” IEEE Trans. Syst. Man Cybern. Part B Syst. Humans 33(6), 758–765 (2003).CrossRefGoogle Scholar
Khatib, O. and Bowling, A., “Optimization of the Inertial and Acceleration Characteristics of Manipulators,” Proceedings of IEEE International Conference on Robotics and Automation, Minneapolis, MN, USA, vol. 4 (1996) pp. 2883–2889.Google Scholar
De Luca, A., Lanari, L. and Oriolo, G., “Control of Redundant Robots on Cyclic Trajectories,” Proceedings 1992 IEEE International Conference on Robotics and Automation, Nice, France, vol. 1 (1992) pp. 500–506.Google Scholar
English, J. D. and Maciejewski, A. A., “On the implementation of velocity control for kinematically redundant manipulators,” IEEE Trans. Syst. Man Cybern. Part A Syst. Humans 30(3), 233–237 (2000).CrossRefGoogle Scholar
Maciejemski, A. A. and Klein, C. A., “Obstacle avoidance for kinematically redundant manipulators in dynamically varying environments,” Int. J. Rob. Res. 4(3), 109–117 (1985).CrossRefGoogle Scholar
Pourazady, M. and Ho, L., “Collision avoidance control of redundant manipulators,” Mech. Mach. Theory 26(6), 603–611 (1991).CrossRefGoogle Scholar
Wang, X., Yang, C., Chen, J., Ma, H. and Liu, F., “Obstacle avoidance for kinematically redundant robot,” IFAC-PapersOnLine 48(28), 490–495 (2015).CrossRefGoogle Scholar
Chembuly, V. V. M. J. S., “An Optimization Based Inverse Kinematics of Redundant Robots Avoiding Obstacles and Singularities,” AIR ’17 Proceedings of the Advances in Robotics, New Delhi, India (2017).Google Scholar
Blanchini, F., Fenu, G., Giordano, G. and Pellegrino, F. A., “A convex programming approach to the inverse kinematics problem for manipulators under constraints,” Eur. J. Contr. 33, 11–23 (2017).CrossRefGoogle Scholar
Kelemen, M., Virgala, I., Lipták, T., Miková, L., Filakovský, F. and Bulej, V., “A novel approach for a inverse kinematics solution of a redundant manipulator,” Appl. Sci. 8(11), 2229 (2018).CrossRefGoogle Scholar
Assal, S. F. M., Watanabe, K. and Izumi, K., “Neural network-based kinematic inversion of industrial redundant robots using cooperative fuzzy hint for the joint limits avoidance,” IEEE/ASME Trans. Mechatron. 11(5), 593–603 (2006).CrossRefGoogle Scholar
Allotta, B., Colla, V. and Bioli, G., “Kinematic control of robots with joint constraints,” ASME J. Dyn. Syst. Meas. Contr. 121(3), 433–442 (1999).CrossRefGoogle Scholar
Wan, J., Wu, H. T., Ma, R. and Zhang, L., “A study on avoiding joint limits for inverse kinematics of redundant manipulators using improved clamping weighted least-norm method,” J. Mech. Sci. Technol. 32(3), 1367–1378 (2018).CrossRefGoogle Scholar
Miyata, S., Miyahara, S. and Nenchev, D., “Analytical formula for the pseudoinverse and its application for singular path tracking with a class of redundant robotic limbs,” Adv. Rob. 31(10), 509–518 (2017).CrossRefGoogle Scholar
Zhou, H. and Ting, K.-L., “Path generation with singularity avoidance for five-bar slider-crank parallel manipulators,” Mech. Mach. Theory 40(3), 371–384 (2005).CrossRefGoogle Scholar
Jin, L., Liao, B., Liu, M., Xiao, L., Guo, D. and Yan, X., “Different-level simultaneous minimization scheme for fault tolerance of redundant manipulator aided with discrete-time recurrent neural network,” Frontiers in Neurorobotics 11 (2017).CrossRefGoogle Scholar
Hassan, M. and Notash, L., “Optimizing fault tolerance to joint jam in the design of parallel robot manipulators,” Mech. Mach. Theory 42(10), 1401–1417 (2007).CrossRefGoogle Scholar
Oen, K.-T. and Wang, L.-C. T., “Optimal dynamic trajectory planning for linearly actuated platform type parallel manipulators having task space redundant degree of freedom,” Mech. Mach. Theory 42(6), 727–750 (2007).CrossRefGoogle Scholar
Klein, C. A. and Huang, C. H., “Review of pseudoinverse control for use with kinematically redundant manipulators,” IEEE Trans. Syst. Man Cybern. (2), 245–250 (1983).CrossRefGoogle Scholar
Cheng, F.-T., Sheu, R.-J., Chen, T.-H. and Kung, F.-C., “The Improved Compact QP Method for Resolving Manipulator Redundancy,” Proceedings of IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS’94), Munich, Germany, vol. 2 (1994) pp. 1368–1375.Google Scholar
Deo, A. S. and Walker, I. D., “Minimum effort inverse kinematics for redundant manipulators”, IEEE Trans. Rob. Autom. 13(5), 767–775 (1997).CrossRefGoogle Scholar
Tang, W. S. and Wang, J., “Two recurrent neural networks for local joint torque optimization of kinematically redundant manipulators,” IEEE Trans. Syst. Man Cybern. Part B Cybern. 30(1), 120–128 (2000).CrossRefGoogle ScholarPubMed
Nedungadi, A. and Kazerounian, K., “A local solution with global characteristics for joint torque optimization of a redundant manipulator,” J. Rob. Syst. 6(5), 631–654 (1989).CrossRefGoogle Scholar
Ma, S., “A new formulation technique for local torque optimization of redundant manipulators,” IEEE Trans. Ind. Electron. 43(4), 462–468 (1996).Google Scholar
Liao, B. and Liu, W., “Pseudoinverse-type bi-criteria minimization scheme for redundancy resolution of robot manipulators,” Robotica 33(10), 2100–2113 (2015).CrossRefGoogle Scholar
Cheng, F., Chen, T. and Sun, Y., “Resolving manipulator redundancy under inequality constraints,” IEEE Trans. Rob. Autom. 10(1), 65–71 (1994).CrossRefGoogle Scholar
Zhang, Y., Lv, X., Li, Z. and Yang, Z., “Repetitive Motion Planning of Redundant Robots Based on LVI-based Primal-dual Neural Network and PUMA560 Example,” In: Life System Modeling and Simulation. LSMS 2007. Lecture Notes in Computer Science (Springer, Berlin, Heidelberg, 2007) pp. 536–545.CrossRefGoogle Scholar
Zhang, Y., Tan, Z., Chen, K., Yang, Z. and Lv, X., “Repetitive motion of redundant robots planned by three kinds of recurrent neural networks and illustrated with a four-link planar manipulator’s straight-line example,” Rob. Auton. Syst. 57(6–7), 645–651 (2009).CrossRefGoogle Scholar
Shamir, T. and Yomdin, Y., “Repeatability of redundant manipulators: Mathematical solution of the problem,” IEEE Trans. Autom. Contr. 33(11), 1004–1009 (1988).CrossRefGoogle Scholar
Shamir, T., “The singularities of redundant robot arms,” Int. J. Rob. Res. 9(1), 113–121 (1990).CrossRefGoogle Scholar
Roberts, R. G. and Maciejewski, A. A., “Nearest optimal repeatable control strategies for kinematically redundant manipulators,” IEEE Trans. Rob. Autom. 8(3), 327–337 (1992).CrossRefGoogle Scholar
Baillieul, J., “Avoiding Obstacles and Resolving Kinematic Redundancy,” Proceedings 1986 IEEE International Conference on Robotics and Automation, San Francisco, CA, USA (1986) pp. 1698–1704.Google Scholar
Klein, C. A., Chu-Jenq, C. and Ahmed, S., “A new formulation of the extended Jacobian method and its use in mapping algorithmic singularities for kinematically redundant manipulators,” IEEE Trans. Rob. Autom. 11(1), 50–55 (1995).CrossRefGoogle Scholar
Klein, C. A., Chu-Jenq, C. and Ahmed, S., “Use of an Extended Jacobian Method to Map Algorithmic Singularities,” Proceedings of the IEEE International Conference on Robotics and Automation, Atlanta, GA, USA, vol. 3 (1993) pp. 632–637.Google Scholar
Zhang, Y., Ge, S. S. and Lee, T. H., “A unified quadratic-programming-based dynamical system approach to joint torque optimization of physically constrained redundant manipulators,” IEEE Trans. Syst. Man Cybern. Part B Cybern. 34(5), 2126–2132 (2004).CrossRefGoogle ScholarPubMed
Hou, Z., Cheng, L. and Tan, M., “Multicriteria optimization for coordination of redundant robots using a dual neural network,” IEEE Trans. Syst. Man Cybern. Part B Cybern. 40(4), 1075–1087 (2010).Google ScholarPubMed
Zhang, Y., “Towards Piecewise-linear Primal Neural Networks for Optimization and Redundant Robotic,” 2006 IEEE International Conference on Networking, Sensing and Control, Ft. Lauderdale, FL (2006) pp. 374–379.CrossRefGoogle Scholar
Zhang, Y., Wu, H., Zhang, Z., Xiao, L. and Guo, D., “Acceleration-level repetitive motion planning of redundant planar robots solved by a simplified LVI-based primal-dual neural network,” Rob. Comput. Integr. Manuf. 29(2), 328–343 (2013).CrossRefGoogle Scholar
Zhang, Y., Wua, H., Guo, D., Xiao, L. and Zhu, H., “The link and comparison between velocity-level and acceleration-level repetitive motion planning schemes verified via PA10 robot arm,” Mech. Mach. Theory 69, 245–262 (2013).CrossRefGoogle Scholar
Hopfield, J. and Tank, D., “ “Neural” computation of decision in optimization problems,” Biol. Cybern. 52(3), 141–52 (1985).Google ScholarPubMed
Xia, Y. and Wang, J., “A dual neural network for kinematic control of redundant robot manipulators,” IEEE Trans. Syst. Man Cybern. Part B Cybern. 31(1), 147–154 (2001).Google ScholarPubMed
Zhang, Y. and Wang, J., “A dual neural network for constrained joint torque optimization of kinematically redundant manipulators,” IEEE Trans. Syst. Man Cybern. Part B Cybern. 32(5), 654–662 (2002).CrossRefGoogle ScholarPubMed
Owen, W. S., Croft, E. A. and Benhabib, B., “A multi-arm robotic system for optimal sculpting,” Rob. Comput. Integr. Manuf. 24(1), 92–104 (2008).CrossRefGoogle Scholar
Klein, C. A. and Ahmed, S., “Repeatable pseudoinverse control for planar kinematically redundant manipulators,” IEEE Trans. Syst. Man Cybern. 25(12), 1657–1662 (1995).CrossRefGoogle Scholar
Huang, L., “An Extended form of Damped Pseudoinverse Control of Kinematically Redundant Manipulators,” 1997 IEEE International Conference on Systems, Man, and Cybernetics Computational Cybernetics and Simulation, Orlando, FL, USA, vol. 4 (1997) pp. 3791–3796.CrossRefGoogle Scholar
Klein, C. A. and Kee, K.-B., “The nature of drift in pseudoinverse control of kinematically redundant manipulators,” IEEE Trans. Rob. Autom. 5(2), 231–234 (1989).CrossRefGoogle Scholar
Gravagne, I. A. and Walker, I. D., “On the structure of minimum effort solutions with application to kinematic redundancy resolution,” IEEE Trans. Rob. Autom. 16(6), 855–862 (2000).CrossRefGoogle Scholar
Lee, J., “A structured algorithm for minimum |∞-norm solutions and its application to a robot velocity workspace analysis,” Robotica 19(3), 343–352 (2001).CrossRefGoogle Scholar
Tang, W. S. and Wang, J., “A recurrent neural network for minimum infinity-norm kinematic control of redundant manipulators with an improved problem formulation and reduced architecture complexity,” IEEE Trans. Syst. Man Cybern. Part B Cybern. 31(1), 98–105 (2001).CrossRefGoogle ScholarPubMed
Zhang, Y., Wang, J. and Xu, Y., “A dual neural network for Bi-Criteria Kinematic control of redundant manipulators,” IEEE Trans. Rob. Autom. 18(6), 923–931 (2002).CrossRefGoogle Scholar
Zhang, Y. and Wang, J., “A dual neural network for convex quadratic programming subject to linear equality and inequality constraints,” Phys. Lett. A 298(4), 271–278 (2002).CrossRefGoogle Scholar
Zhang, Y., Tan, Z., Yang, Z., Lv, X. and Chen, K., “A Simplified LVI-based Primal-dual Neural Network for Repetitive Motion Planning of PA10 Robot Manipulator Starting from Different Initial States,” 2008 IEEE International Joint Conference on Neural Networks International Joint Conference on Neural Networks (IEEE World Congress on Computational Intelligence), Hong Kong (2008) pp. 19–24.Google Scholar
Pennock, G. R. and Squires, C. C., “Velocity analysis of two 3-R robots manipulating a disk,” Mech. Mach. Theory 33(1–2), 71–86 (1998).CrossRefGoogle Scholar
Yang, M., Zhang, Y., Huang, H., Chen, D. and Li, J., “Jerk-level Cyclic Motion Planning and Control for Constrained Redundant Robot Manipulators using Zhang Dynamics: Theoretics,” 2018 Chinese Control and Decision Conference (CCDC), Shenyang (2018) pp. 450–455.Google Scholar
Amaei, S., “An algorithm for solving indefinite quadratic programming problems,” J. Appl. Comput. Math. 7(1), (2018).CrossRefGoogle Scholar
Optimization Toolbox for Use with MATLAB (Version 2.3, The MathWorks Inc., 2003).Google Scholar
Li, W. and Swetits, J., “A new algorithm for solving strictly convex quadratic programs,” SIAM J. Optim. 7(3), 595–619 (1997).CrossRefGoogle Scholar
Bazaraa, M. S., Sherali, H. D. and Shetty, C. M., Nonlinear Programming—Theory and Algorithms (Wiley, New York, 1993).Google Scholar
Dang, T. V., Tran, T. and Ling, K. V., “Numerical Algorithms for Quadratic Programming in Model Predictive Control - An Overview,” ISSAT MCSE’15, Danang, Vietnam (2015).Google Scholar
Xiao, L., Zhang, Y., Liao, B., Zhang, Z., Ding, L. and Jin, L., “A velocity-level Bi-Criteria optimization scheme for coordinated path tracking of dual robot manipulators using recurrent neural network,” Front. Neurorobo. 11 (2017).CrossRefGoogle Scholar
Xia, Y., “A new neural network for solving linear programming problems and its application,” IEEE Trans. Neural Networks 7(2), 525–529 (1996).Google ScholarPubMed
Wang, J. and Zhang, Y., “Recurrent neural networks for real-time computation of inverse kinematics of redundant manipulators,” In: Machine Intelligence (Quo Vadis, World Scientific, Singapore, 2004).Google Scholar
Mead, C., Analog VLSI and Neural Systems, 1st edition (Addison-Wesley VLSI Systems Series, Addison-Wesley, January 1989). ISBN: 978-0201059922.Google Scholar
Zhang, Y., Li, Z., Tan, H. and Fan, Z., “On the Simplified LVI-based Primal-dual Neural Network for Solving LP and QP Problems,” 2007 IEEE International Conference on Control and Automation, Guangzhou (2007) pp. 3129–3134.Google Scholar
Wang, J., “Recurrent neural networks for computing pseudoinverses of rank-deficient matrices,” SIAM J. Sci. Comput. 18(5), 1479–1493 (1997).CrossRefGoogle Scholar
Pyne, I. B., “Linear programming on an electronic analogue computer,” Trans. Am. Inst. Electr. Eng. Part I Commun. Electro. 75(2), 139–143 (1956).Google Scholar
Tank, D. W. and Hopfield, J. J., “Simple ‘neural’ optimization networks: an A/D converter, signal decision circuit, and a linear programming circuit,” IEEE Trans. Circuits Syst. 33(5), 533–541 (1986).CrossRefGoogle Scholar
Ge, S. S., Lee, T. H. and Harris, C. J., Adaptive Neural Network Control of Robotic Manipulators, World Scientific Series in Robotics and Intelligent Systems (World Scientific, Singapore, 1998).Google Scholar
Diorio, C. and Rao, R. P. N., “Neural circuits in silicon,” Nature 405, 891–892 (2000).CrossRefGoogle ScholarPubMed
Wu, S., He, L., Zou, M., Li, J. and Zhang, Y., “Time-varying Linear Programming via LVI-PDNN with Numerical Examples,” 2016 IEEE 13th International Conference on Signal Processing (ICSP), Chengdu, China (2016).Google Scholar
Ding, H. and Tso, S. K., “A fully neural-network-based planning scheme for torque minimization of redundant manipulators,” IEEE Trans. Ind. Electron. 46(1), 199–206 (1999).CrossRefGoogle Scholar
Liu, J., Wang, Y., Ma, S. and Li, B., “Shape Control of Hyper-redundant Modularized Manipulator Using Variable Structure Regular Polygon,” 2004 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS), Sendai, vol. 4 (2004) pp. 3924–3929.Google Scholar
Zhang, S. and Constantinides, A., “Lagrange programming neural networks,” IEEE Trans. Circuits Syst. II Analog Digital Signal Process. 39(7), 441–452 (1992).CrossRefGoogle Scholar
Tang, W. and Wang, J., “A Primal-dual Neural Network for Kinematic Control of Redundant Manipulators Subject to Joint Velocity Constraints,” ICONIP’99. ANZIIS’99 & ANNES’99 & ACNN’99. 6th International Conference on Neural Information Processing, Perth, WA, Australia, vol. 2 (1999) pp. 801–806.Google Scholar
Zhang, Y., Yin, J. and Cai, B., “Infinity-norm acceleration minimization of robotic redundant manipulators using the LVI-based primal-dual neural network,” Rob. Comput. Integr. Manuf. 25(2), 358–365 (2009).CrossRefGoogle Scholar
Zhang, Z., Zhou, Q. and Fan, W., “Neural-dynamic based synchronous-optimization scheme of dual redundant robot manipulators,” Front. Neurorob. 12 (2018).CrossRefGoogle Scholar
Zhang, Y. and Wang, J., “Obstacle avoidance of kinematically redundant manipulators using a dual neural network,” IEEE Trans. Syst. Man Cybern. Part B Cybern. 34(1), 752–759 (2004).CrossRefGoogle ScholarPubMed
Zhang, Y., “Inverse-free computation for infinity-norm torque minimization of robot manipulators,” Mechatron. 16(3–4), 177–184 (2006).CrossRefGoogle Scholar
He, B. and Yang, H., “A neural network model for monotone linear asymmetric variational inequalities,” IEEE Trans. Neural Networks 11(1), 3–16 (2000).Google ScholarPubMed
Ferris, M. C. and Pang, J. S., “Complementarity and Variational Problems: State of the Art,” Proceedings in Applied Mathematics. Society for Industrial & Applied, March 1997. ISBN: 978-0898713916.Google Scholar
Zhang, Y., “On the LVI-based Primal–dual Neural Network for Solving Online Linear and Quadratic Programming Problems,” Proceedings of the 2005 American Control Conference, Portland, OR, USA, vol. 2 (2005) pp. 1351–1356.Google Scholar
Xia, Y. and Wang, J., “A recurrent neural network for solving linear projection equations,” Neural Netw. 13(3), 337–350 (2000).CrossRefGoogle ScholarPubMed
Kinderlehrer, D. and Stampacchia, G., An Introduction to Variational Inequalities and their Applications, vol. 88, 1st edition (SIAM, Philadelphia, 1980). ISBN: 9780080874043.Google Scholar
Zhang, Y., Yi, C. and Ma, W., “Simulation and verification of Zhang neural network for online time-varying matrix inversion,” Simul. Modell. Pract. Theory 17(10), 1603–1617 (2009).CrossRefGoogle Scholar