A Single Network Adaptive Critic based Redundancy Resolution Scheme for Robot Manipulators

Prem Kumar Patchaikani, Laxmidhar Behera, Girijesh Prasad

    Research output: Contribution to journalArticle

    Abstract

    This paper proposes an adaptive critic based realtime redundancy resolution scheme for kinematic control of a redundant manipulator. The kinematic control of the redundant manipulator is formulated as a discrete-time input affine system and then an optimal real-time redundancy resolution scheme is proposed. The optimal control law is derived in real-time using adaptive critic framework. The proposed single network adaptive critic based methodology defines the additional task in terms of integral cost function which results in global optimal solution. With adaptive critic based optimal control scheme, the optimal redundancy resolution is achieved in real-time without the computation of inverse which makes the method computationally efficient. The problem formulation as proposed in this paper is first of its kinds. Further the real-time optimal redundancy resolution using an integral cost function has been comprehensively solved which is also a novel contribution. The proposed scheme is tested in both simulation and experiment on a 7 degree of freedom (7DOF) PowerCubeTM manipulator from Amtec Robotics.
    LanguageEnglish
    Pages3241-3253
    JournalIEEE Transactions on Industrial Electronics
    Volume59
    Issue number8
    DOIs
    Publication statusPublished - Aug 2012

    Fingerprint

    Manipulators
    Redundancy
    Robots
    Redundant manipulators
    Cost functions
    Kinematics
    Robotics
    Experiments

    Keywords

    • Adaptive Critic
    • Approximate Dynamic Programming
    • Inverse Kinematic Control
    • Redundancy Resolution
    • Redundant Manipulator

    Cite this

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    title = "A Single Network Adaptive Critic based Redundancy Resolution Scheme for Robot Manipulators",
    abstract = "This paper proposes an adaptive critic based realtime redundancy resolution scheme for kinematic control of a redundant manipulator. The kinematic control of the redundant manipulator is formulated as a discrete-time input affine system and then an optimal real-time redundancy resolution scheme is proposed. The optimal control law is derived in real-time using adaptive critic framework. The proposed single network adaptive critic based methodology defines the additional task in terms of integral cost function which results in global optimal solution. With adaptive critic based optimal control scheme, the optimal redundancy resolution is achieved in real-time without the computation of inverse which makes the method computationally efficient. The problem formulation as proposed in this paper is first of its kinds. Further the real-time optimal redundancy resolution using an integral cost function has been comprehensively solved which is also a novel contribution. The proposed scheme is tested in both simulation and experiment on a 7 degree of freedom (7DOF) PowerCubeTM manipulator from Amtec Robotics.",
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    note = "Reference text: [1] Yunong Zhang and Jun Wang, “Obstacle avoidance for kinematic control redundant manipulators using a dual neural network,” IEEE Trans. System, Man and Cybernetics - Part B:Cybernetics, vol. 34, no. 1, pp. 752–759, February 2004. [2] T. F. Chan and R. V. Dubey, “A weighted least-norm based solution scheme for avoiding joint limits for redundant joint manipulators,” IEEE Trans. Robotics and Automation, vol. 11, no. 2, pp. 286–292, April 1995. [3] Yunong Zhang, Shuzhi Sam Ge, and Tong Heng Lee, “A unified quadratic programming-based dynamical system approach to torque minimization of physically constrained redundant manipulators,” IEEE Trans. Systems, Man, and Cybernetics - Part B: Cybernetics, vol. 34, no. 5, pp. 2126–2132, October 2004. [4] A. Ryberg, M. Ericsson, A. K. Christiansson, K. Eriksson, J. Nilsson, and M. Larsson, “Stereo vision for path correction in off-line programmed robot welding,” in 2010 IEEE International Conference on Industrial Technology (ICIT). IEEE, March 2010, pp. 1700–1705. [5] Wook Choi, Minoo Akbarian, Vladimir Rubstov, and Chang-Jin ”CJ” Kim, “Microhand with internal visual system,” IEEE Trans. Industrial Electronics, vol. 56, no. 4, pp. 1005–1011, April 2009. [6] Yuichi Motai and Akio Kosaka, “Hand-eye calibration applied to viewpoint selection for robotic vision,” IEEE Trans. Industrial Electronics, vol. 55, no. 10, pp. 3731–3831, October 2008. [7] F. Chaumette, “Image moments: A general and useful set of features for visual servoing,” IEEE Trans. Robotics and Automation, vol. 20, no. 4, pp. 713–723, August 2004. [8] W. Wilson, C. Hulls, and G. Bell, “Relative end-effector control using cartesian position based servoing,” IEEE Trans. Robotics and Automation, vol. 12, no. 5, pp. 684–696, October 1996. [9] Lingfeng Deng, Janabi-Sharifi, and William J. Wilson, “Hybrid motion control and planning strategies for visual servoing,” IEEE Trans. Industrial Electronics, vol. 54, no. 4, pp. 1024–1040, August 2005. [10] F. Chaumette and S. Hutchinson, “Visual servo control Part I: Basic approaches,” IEEE Robotics and Automation Magazine, vol. 13, no. 4, pp. 82–90, December 2006. [11] F. Chaumette and S. Hutchinson, “Visual servo control Part II: Advanced approaches (tutorial),” IEEE Robotics and Automation Magazine, vol. 14, no. 1, pp. 109–118, March 2007. [12] F. Chaumette and E. Marchand, “A redundancy-based iterative approach for avoiding joint limits: Application to visual servoing,” IEEE Trans. Robotics and Automation, vol. 17, no. 5, pp. 719–730, October 2001. [13] Bruno Siciliano, “Kinematic control of redundant robot manipulators: A tutorial,” Journal of Intelligent and Robotic systems, vol. 4, no. 4, pp. 201–212, August 1990. [14] D.P. Martin, John Baillieul, and J. M. Hollerbach, “Resolution of kinematic redundancy using optimization,” IEEE Trans. Robotics and Automation, vol. 5, no. 4, pp. 529–533, 1989. [15] Sung-Woo Kim, Kang-Bark Park, and Ju-Jang Lee, “Redundancy resolution of robot manipulators using optimal kinematic control,” in IEEE International Conference on Robotics and Automation, 1994, vol. 1, pp. 683–688. [16] P. J. Werbos, Approximate dynamic programming for real-time control and neural modeling, In D. A. White, and D. A Sofge (Eds.), Handbook of Intelligent control, Multiscience Press, 1992. [17] D. V. Prokhorov an D. C. Wunsch II, “Adaptive critic designs,” IEEE Trans. Neural Networks, vol. 8, no. 5, pp. 997–1007, September 1997. [18] S. Ferrari and R. F. Stengel, Model based adaptive critic designs., In Jennie Si, A. G. Barto, W. B. Powell, and D.Wunsch II (Eds.), Handbook of learning and Approximate Dynamic Programming, IEEE Press, 2004. [19] X. Liu and S. N. Balakrishnan, “Convergence analysis of adaptive critic based optimal control,” in Proceedings of the American Control Conference, Chicago, USA, 2000, pp. 1929–1933. [20] Asma Al-Tamimi, Frank L. Lewis, and Murad Abu-Khalaf, “Discretetime nonlinear HJB solution using approximate dynamic programming: Convergence proof,” IEEE Trans. System, Man and Cybernetics-Part B:Cybernetics, vol. 38, no. 4, pp. 943–949, August 2008. [21] Tao Cheng, Frank L. Lewis, and Murad Abu-Khalaf, “Fixed-final-timeconstrained optimal control of nonlinear systems using neural network HJB approach,” IEEE Trans. Neural Networks, vol. 18, no. 6, pp. 1725– 1737, November 2007. [22] Salman Mohagheghi, Yamille del Valle, Ganesh Kumar Venayagamoorthy, and Ronald G. Harley, “A proportional-integrator type adaptive critic design-based neurocontroller for a static compensator in a multimachine power system,” IEEE Trans. Industrial Electronics, vol. 54, no. 1, pp. 86–96, February 2007. [23] Radhakant Padhi, Nishant Unnikrishnan, Xiaohua Wang, and S.N. Balakrishnan, “A single network adaptic critic (SNAC) architecture for optimal control,” Neural Networks, vol. 19, pp. 1648–1660, 2006. [24] Prem Kumar P., Laxmidhar Behera, and Girijesh Prasad, “Adaptive critic based redundancy resolution scheme for robot manipulators,” in IEEE International Conference on System, Man and Cybernetics, 2009, vol. 1, pp. 683–688. [25] “Amtec robotics,” www.amtec-robotics.com. [26] Mark W. Spong, Seth Hutchinson, and M. Vidyasagar, Robot Modeling and Control, John Wiley & sons Inc., 2005. [27] Prem Kumar P. and Laxmidhar Behera, “Visual servoing of redundant manipulator with Jacobian estimation using self-organizing map,” Robotics and Autonomous Systems, vol. 58, no. 8, pp. 978–990, August 2010. [28] H. Zghal, R. V. Dubey, and J. A. Euler, “Efficient gradient projection optimization for manipulators with multiple degrees of redundancy,” in Proceedings of IEEE International Conference on Robotics and Automation, 1990, vol. 2, pp. 1006–1011. [29] G. H. Golub and C. Reinsch, “Singular value decomposition and least square solutions,” Numerische Mathematik, vol. 14, no. 5, pp. 403–420, 1970. [30] “Unibrain,” http://www.unibrain.com/.",
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    }

    A Single Network Adaptive Critic based Redundancy Resolution Scheme for Robot Manipulators. / Patchaikani, Prem Kumar; Behera, Laxmidhar; Prasad, Girijesh.

    In: IEEE Transactions on Industrial Electronics, Vol. 59, No. 8, 08.2012, p. 3241-3253.

    Research output: Contribution to journalArticle

    TY - JOUR

    T1 - A Single Network Adaptive Critic based Redundancy Resolution Scheme for Robot Manipulators

    AU - Patchaikani, Prem Kumar

    AU - Behera, Laxmidhar

    AU - Prasad, Girijesh

    N1 - Reference text: [1] Yunong Zhang and Jun Wang, “Obstacle avoidance for kinematic control redundant manipulators using a dual neural network,” IEEE Trans. System, Man and Cybernetics - Part B:Cybernetics, vol. 34, no. 1, pp. 752–759, February 2004. [2] T. F. Chan and R. V. Dubey, “A weighted least-norm based solution scheme for avoiding joint limits for redundant joint manipulators,” IEEE Trans. Robotics and Automation, vol. 11, no. 2, pp. 286–292, April 1995. [3] Yunong Zhang, Shuzhi Sam Ge, and Tong Heng Lee, “A unified quadratic programming-based dynamical system approach to torque minimization of physically constrained redundant manipulators,” IEEE Trans. Systems, Man, and Cybernetics - Part B: Cybernetics, vol. 34, no. 5, pp. 2126–2132, October 2004. [4] A. Ryberg, M. Ericsson, A. K. Christiansson, K. Eriksson, J. Nilsson, and M. Larsson, “Stereo vision for path correction in off-line programmed robot welding,” in 2010 IEEE International Conference on Industrial Technology (ICIT). IEEE, March 2010, pp. 1700–1705. [5] Wook Choi, Minoo Akbarian, Vladimir Rubstov, and Chang-Jin ”CJ” Kim, “Microhand with internal visual system,” IEEE Trans. Industrial Electronics, vol. 56, no. 4, pp. 1005–1011, April 2009. [6] Yuichi Motai and Akio Kosaka, “Hand-eye calibration applied to viewpoint selection for robotic vision,” IEEE Trans. Industrial Electronics, vol. 55, no. 10, pp. 3731–3831, October 2008. [7] F. Chaumette, “Image moments: A general and useful set of features for visual servoing,” IEEE Trans. Robotics and Automation, vol. 20, no. 4, pp. 713–723, August 2004. [8] W. Wilson, C. Hulls, and G. Bell, “Relative end-effector control using cartesian position based servoing,” IEEE Trans. Robotics and Automation, vol. 12, no. 5, pp. 684–696, October 1996. [9] Lingfeng Deng, Janabi-Sharifi, and William J. Wilson, “Hybrid motion control and planning strategies for visual servoing,” IEEE Trans. Industrial Electronics, vol. 54, no. 4, pp. 1024–1040, August 2005. [10] F. Chaumette and S. Hutchinson, “Visual servo control Part I: Basic approaches,” IEEE Robotics and Automation Magazine, vol. 13, no. 4, pp. 82–90, December 2006. [11] F. Chaumette and S. Hutchinson, “Visual servo control Part II: Advanced approaches (tutorial),” IEEE Robotics and Automation Magazine, vol. 14, no. 1, pp. 109–118, March 2007. [12] F. Chaumette and E. Marchand, “A redundancy-based iterative approach for avoiding joint limits: Application to visual servoing,” IEEE Trans. Robotics and Automation, vol. 17, no. 5, pp. 719–730, October 2001. [13] Bruno Siciliano, “Kinematic control of redundant robot manipulators: A tutorial,” Journal of Intelligent and Robotic systems, vol. 4, no. 4, pp. 201–212, August 1990. [14] D.P. Martin, John Baillieul, and J. M. Hollerbach, “Resolution of kinematic redundancy using optimization,” IEEE Trans. Robotics and Automation, vol. 5, no. 4, pp. 529–533, 1989. [15] Sung-Woo Kim, Kang-Bark Park, and Ju-Jang Lee, “Redundancy resolution of robot manipulators using optimal kinematic control,” in IEEE International Conference on Robotics and Automation, 1994, vol. 1, pp. 683–688. [16] P. J. Werbos, Approximate dynamic programming for real-time control and neural modeling, In D. A. White, and D. A Sofge (Eds.), Handbook of Intelligent control, Multiscience Press, 1992. [17] D. V. Prokhorov an D. C. Wunsch II, “Adaptive critic designs,” IEEE Trans. Neural Networks, vol. 8, no. 5, pp. 997–1007, September 1997. [18] S. Ferrari and R. F. Stengel, Model based adaptive critic designs., In Jennie Si, A. G. Barto, W. B. Powell, and D.Wunsch II (Eds.), Handbook of learning and Approximate Dynamic Programming, IEEE Press, 2004. [19] X. Liu and S. N. Balakrishnan, “Convergence analysis of adaptive critic based optimal control,” in Proceedings of the American Control Conference, Chicago, USA, 2000, pp. 1929–1933. [20] Asma Al-Tamimi, Frank L. Lewis, and Murad Abu-Khalaf, “Discretetime nonlinear HJB solution using approximate dynamic programming: Convergence proof,” IEEE Trans. System, Man and Cybernetics-Part B:Cybernetics, vol. 38, no. 4, pp. 943–949, August 2008. [21] Tao Cheng, Frank L. Lewis, and Murad Abu-Khalaf, “Fixed-final-timeconstrained optimal control of nonlinear systems using neural network HJB approach,” IEEE Trans. Neural Networks, vol. 18, no. 6, pp. 1725– 1737, November 2007. [22] Salman Mohagheghi, Yamille del Valle, Ganesh Kumar Venayagamoorthy, and Ronald G. Harley, “A proportional-integrator type adaptive critic design-based neurocontroller for a static compensator in a multimachine power system,” IEEE Trans. Industrial Electronics, vol. 54, no. 1, pp. 86–96, February 2007. [23] Radhakant Padhi, Nishant Unnikrishnan, Xiaohua Wang, and S.N. Balakrishnan, “A single network adaptic critic (SNAC) architecture for optimal control,” Neural Networks, vol. 19, pp. 1648–1660, 2006. [24] Prem Kumar P., Laxmidhar Behera, and Girijesh Prasad, “Adaptive critic based redundancy resolution scheme for robot manipulators,” in IEEE International Conference on System, Man and Cybernetics, 2009, vol. 1, pp. 683–688. [25] “Amtec robotics,” www.amtec-robotics.com. [26] Mark W. Spong, Seth Hutchinson, and M. Vidyasagar, Robot Modeling and Control, John Wiley & sons Inc., 2005. [27] Prem Kumar P. and Laxmidhar Behera, “Visual servoing of redundant manipulator with Jacobian estimation using self-organizing map,” Robotics and Autonomous Systems, vol. 58, no. 8, pp. 978–990, August 2010. [28] H. Zghal, R. V. Dubey, and J. A. Euler, “Efficient gradient projection optimization for manipulators with multiple degrees of redundancy,” in Proceedings of IEEE International Conference on Robotics and Automation, 1990, vol. 2, pp. 1006–1011. [29] G. H. Golub and C. Reinsch, “Singular value decomposition and least square solutions,” Numerische Mathematik, vol. 14, no. 5, pp. 403–420, 1970. [30] “Unibrain,” http://www.unibrain.com/.

    PY - 2012/8

    Y1 - 2012/8

    N2 - This paper proposes an adaptive critic based realtime redundancy resolution scheme for kinematic control of a redundant manipulator. The kinematic control of the redundant manipulator is formulated as a discrete-time input affine system and then an optimal real-time redundancy resolution scheme is proposed. The optimal control law is derived in real-time using adaptive critic framework. The proposed single network adaptive critic based methodology defines the additional task in terms of integral cost function which results in global optimal solution. With adaptive critic based optimal control scheme, the optimal redundancy resolution is achieved in real-time without the computation of inverse which makes the method computationally efficient. The problem formulation as proposed in this paper is first of its kinds. Further the real-time optimal redundancy resolution using an integral cost function has been comprehensively solved which is also a novel contribution. The proposed scheme is tested in both simulation and experiment on a 7 degree of freedom (7DOF) PowerCubeTM manipulator from Amtec Robotics.

    AB - This paper proposes an adaptive critic based realtime redundancy resolution scheme for kinematic control of a redundant manipulator. The kinematic control of the redundant manipulator is formulated as a discrete-time input affine system and then an optimal real-time redundancy resolution scheme is proposed. The optimal control law is derived in real-time using adaptive critic framework. The proposed single network adaptive critic based methodology defines the additional task in terms of integral cost function which results in global optimal solution. With adaptive critic based optimal control scheme, the optimal redundancy resolution is achieved in real-time without the computation of inverse which makes the method computationally efficient. The problem formulation as proposed in this paper is first of its kinds. Further the real-time optimal redundancy resolution using an integral cost function has been comprehensively solved which is also a novel contribution. The proposed scheme is tested in both simulation and experiment on a 7 degree of freedom (7DOF) PowerCubeTM manipulator from Amtec Robotics.

    KW - Adaptive Critic

    KW - Approximate Dynamic Programming

    KW - Inverse Kinematic Control

    KW - Redundancy Resolution

    KW - Redundant Manipulator

    U2 - 10.1109/TIE.2011.2143372

    DO - 10.1109/TIE.2011.2143372

    M3 - Article

    VL - 59

    SP - 3241

    EP - 3253

    JO - IEEE Transactions on Industrial Electronics

    T2 - IEEE Transactions on Industrial Electronics

    JF - IEEE Transactions on Industrial Electronics

    SN - 0278-0046

    IS - 8

    ER -