Kinematic control of a redundant manipulator using inverse-forward adaptive scheme with a KSOM based hint generator

Swagat Kumar, Laxmidhar Behera, Martin McGinnity

    Research output: Contribution to journalArticle

    26 Citations (Scopus)

    Abstract

    This paper proposes an online inverse-forward adaptive scheme with a KSOM based hint generator forsolving the inverse kinematic problem of a redundant manipulator. In this approach, a feed-forwardnetwork such as a radial basis function (RBF) network is used to learn the forward kinematic map ofthe redundant manipulator. This network is inverted using an inverse-forward adaptive scheme until thenetwork inversion solution guides the manipulator end-effector to reach a given target position witha specified accuracy. The positioning accuracy, attainable by a conventional network inversion scheme,depends on the approximation error present in the forward model. But, an accurate forward map wouldrequire a very large size of training data as well as network architecture. The proposed inverse-forwardadaptive scheme effectively approximates the forward map around the joint angle vector provided by ahint generator. Thus the inverse kinematic solution obtained using the network inversion approach cantake the end-effector to the target position within any arbitrary accuracy.In order to satisfy the joint angle constraints, it is necessary to provide the network inversion algorithmwith an initial hint for the joint angle vector. Since a redundant manipulator can reach a given target end-effector position through several joint angle vectors, it is desirable that the hint generator is capable ofproviding multiple hints. This problem has been addressed by using a Kohonen self organizing map basedsub-clustering (KSOM-SC) network architecture. The redundancy resolution process involves selecting asuitable joint angle configuration based on different task related criteria.The simulations and experiments are carried out on a 7 DOF PowerCubeTM manipulator. It is shownthat one can obtain a positioning accuracy of 1 mm without violating joint angle constraints even whenthe forward approximation error is as large as 4 cm. An obstacle avoidance problem has also been solvedto demonstrate the redundancy resolution process with the proposed scheme.
    LanguageEnglish
    Pages622-633
    JournalRobotics and Autonomous Systems
    Volume58
    Issue number5
    DOIs
    Publication statusPublished - 2010

    Fingerprint

    Redundant Manipulator
    Redundant manipulators
    End effectors
    Kinematics
    Inverse kinematics
    Generator
    Network architecture
    Angle
    Manipulators
    Redundancy
    Inversion
    Inverse Kinematics
    Radial basis function networks
    Self organizing maps
    Approximation Error
    Collision avoidance
    Network Architecture
    Manipulator
    Positioning
    Target

    Keywords

    • Redundant manipulator
    • Inverse kinematic solution
    • Kohonen Self-Organizing Map (KSOM)
    • Network inversion
    • Radial Basis Function Network (RBFN)
    • KSOM-SC architecture
    • Redundancy resolution

    Cite this

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    title = "Kinematic control of a redundant manipulator using inverse-forward adaptive scheme with a KSOM based hint generator",
    abstract = "This paper proposes an online inverse-forward adaptive scheme with a KSOM based hint generator forsolving the inverse kinematic problem of a redundant manipulator. In this approach, a feed-forwardnetwork such as a radial basis function (RBF) network is used to learn the forward kinematic map ofthe redundant manipulator. This network is inverted using an inverse-forward adaptive scheme until thenetwork inversion solution guides the manipulator end-effector to reach a given target position witha specified accuracy. The positioning accuracy, attainable by a conventional network inversion scheme,depends on the approximation error present in the forward model. But, an accurate forward map wouldrequire a very large size of training data as well as network architecture. The proposed inverse-forwardadaptive scheme effectively approximates the forward map around the joint angle vector provided by ahint generator. Thus the inverse kinematic solution obtained using the network inversion approach cantake the end-effector to the target position within any arbitrary accuracy.In order to satisfy the joint angle constraints, it is necessary to provide the network inversion algorithmwith an initial hint for the joint angle vector. Since a redundant manipulator can reach a given target end-effector position through several joint angle vectors, it is desirable that the hint generator is capable ofproviding multiple hints. This problem has been addressed by using a Kohonen self organizing map basedsub-clustering (KSOM-SC) network architecture. The redundancy resolution process involves selecting asuitable joint angle configuration based on different task related criteria.The simulations and experiments are carried out on a 7 DOF PowerCubeTM manipulator. It is shownthat one can obtain a positioning accuracy of 1 mm without violating joint angle constraints even whenthe forward approximation error is as large as 4 cm. An obstacle avoidance problem has also been solvedto demonstrate the redundancy resolution process with the proposed scheme.",
    keywords = "Redundant manipulator, Inverse kinematic solution, Kohonen Self-Organizing Map (KSOM), Network inversion, Radial Basis Function Network (RBFN), KSOM-SC architecture, Redundancy resolution",
    author = "Swagat Kumar and Laxmidhar Behera and Martin McGinnity",
    note = "Reference text: [2] T. Yoshikawa, Foundation of Robotics, Analysis and Control, Prentice Hall of India, New Delhi, 2001. [3] P. Martin, J.R. Millan, Robot arm reaching through neural inversions and reinforcement learning, Robotics and Autonomous Systems 31 (2000) 227-246. [4] M. Kuperstein, Neural model of adaptive hand-eye coordination for single postures, Science 239 (1988) 1308-1311. [5] W.T. Miller III, Sensor-based control of robotic manipulators using a general learning algorithm, IEEE Journal of Robotics and Automation RA-3 (2) (1987) 157-165. [6] G. Sun, B. Scassellati, A fast and efficient model for learning to reach, International Journal of Humanoid Robotics 2 (4) (2005) 391-413. [7] R.V. Mayorga, P. Sanongboon, A radial basis function network approach for inverse kinematics and singularities prevention of redundant manipulators, in: Proc. of Int. Conf. on Robotics and Automation, ICRA, IEEE, 2002, pp. 1955-1960. [8] S. Vijayakumar, A. D'Souza, T. Shibata, J. Conradt, S. Schaal, Statistical learning for humanoid robots, Autonomous Robots 12 (2002) 55-69. [9] A. D'Souza, S. Vijayakumar, S. Schaal, Learning inverse kinematics, in: Interna- tional Conference on Intelligent Robots and Systems, IROS, IEEE, Maui, Hawai, USA, 2001, pp. 298-303. [10] G.G. Lendaris, K. Mathia, R. Saeks, Linear hopfield networks and constrained optimization, IEEE Transactions on System, Man and CyberneticsPart B: Cybernetics 29 (1) (1999) 114-118. [11] T.M. Martinetz, H.J. Ritter, K.J. Schulten, Three-dimensional neural net for learning visual motor coordination of a robot arm, IEEE Transactions on Neural Networks 1 (1) (1990) 131-136. [12] J.A. Walter, K.J. Schulten, Implementation of self-organizing neural networks for visual-motor control of an industrial robot, IEEE Transactions on Neural Networks 4 (1) (1993) 86195. [13] Z. Mao, T.C. Hsia, Obstacle avoidance inverse kinematics solution of redundant robots by neural networks, Robotica 15 (1997) 3-10. [14] D. DeMers, K. Kreutz-Delgado, Canonical parameterization of excess motor degrees of freedom with self organizing maps, IEEE Transactions on Neural Networks 7 (1) (1996) 43-55. [15] J. Peters, S. Schaal, Learning to control in operational space, International Journal of Robotics Research 27 (2) (2008) 197-212. [16] M.I. Jordan, D.E. Rumelhart, Forward models: Supervised learning with a distal teacher, Cognitive Science 16 (1992) 307-354. [17] J. Wang, Q. Hu, D. Jiang, A lagrangian network for kinematic control of redundant robot manipulators, IEEE Transactions on Neural Networks 10 (5) (1999) 1123-1132. [18] W.S. Tang, J. Wang, A recurrent neural network for minimum infinity- norm kinematic control of redundant manipulators with an improved problem formulation and reduced architecture complexity, IEEE Transactions on Systems, Man and Cybernetics-Part B: Cybernetics 31 (1) (2001) 98-105. [19] J. Peters, D. Nguyen-Tuong, Real-time learning of resolved velocity control on a Mitsubishi PA-10, in: International Conference on Robotics and Automation, ICRA, IEEE, Prasadena, CA, USA, 2008, pp. 2872-2877. [20] L. Bao-Liang, K. Ito, Regularization of inverse kinematics for redundant manipulator using neural network inversions, in: International Conference on Neural Networks, ICNN, IEEE, Perth, Australia, 1995, pp. 2726-2731. [21] S.F.M. Assal, K. Watanabe, K. Izumi, Neural network-based kinematic inversion of industrial redundant robots using cooperative fuzzy hint for the joint limits avoidance, IEEE Transactions on Mechatronics 11 (5) (2006) 593-603. [22] 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) 17-33. [23] T. Kohonen, Self Organization and Associative Memory, Springer-Verlag, 1984. [24] S. Kumar, P. Premkumar, A. Dutta, L. Behera, Visual motor control of a 7 DOF robot manipulator using KSOM-based redundancy preserving network, Robotica (2009). [25] H. Zha, T. Onitsuka, T. Nagata, A self-organization learning algorithm for visuo- motor coordination in unstructured environment, Artificial Life and Robotics 1 (3) (1997) 131-136. [26] M. Han, N. Okada, E. Kondo, Collision avoidance for a visuo-motor system using multiple self-organizing maps, in: Memoirs of the Faculty of Engineering, Kyushu University, 65 (4), 2005 pp. 129-142. [27] T.C. Hsia, Z.Y. Guo, New inverse kinematic algorithms for redundant robots, Journal of Robotics Systems 8 (1) (1991) 117-132. [28] Y. Mezouar, F. Chaumette, Path planning in image space for robust visual servoing, in: Proc. of IEEE Int. Conf. on Robotics and Automation, San Francisco, CA, 2000, pp. 2759-2763. [29] M. Han, N. Okada, E. Kondo, Coordination of an uncalibrated 3-d visuo-motor system based on multiple self-organizing maps, JSME International Journal Series C 49 (1) (2006) 230-239. [30] N. Mansard, F. Chaumette, Visual servoing sequencing able to avoid obstacles, in: Proc. of Int. Conf. on Robotics and Automation, IEEE, Barcelona, Spain, 2005, pp. 3143-3148. [31] O. Khatib, Real-time obstacle avoidance for manipulators and mobile robots, International Journal of Robotics Research 5 (1) (1986) 90-98. [32] Y.K. Hwang, N. Ahuja, A potential field approach to path planning, IEEE Transactions on Robotics and Automation 8 (1) (1992) 23-32. [33] J. Kim, P.K. Khosla, Real-time obstacle avoidance using harmonic potential functions, IEEE Transactions on Robotics and Automation 8 (3) (1992) 338-349. [34] W. Cho, D. Kwon, A sensor-based obstacle avoidance for a redundant ma- nipulator using a velocity potential field, in: IEEE International Work- shop on Robots and Human Communication, Tsukuba, Japan, 1996, pp. 306-310. [35] Y. Zhang, J. Wang, Obstacle avoidance for kinematically redundant manipula- tors using a dual neural network, IEEE Transactions on System, Man and Cy- bernetics, Part B 34 (1) (2004) 752-759. [36] Powercube manipulators, SCHUNKGmbH& Co. KG, 2009. http://www.schunk. com/. [37] J.J. Craig, Introduction to Robotics, Pearson Education, Inc., 1989. [38] 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.",
    year = "2010",
    doi = "10.1016/j.robot.2009.12.002",
    language = "English",
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    pages = "622--633",
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    }

    Kinematic control of a redundant manipulator using inverse-forward adaptive scheme with a KSOM based hint generator. / Kumar, Swagat; Behera, Laxmidhar; McGinnity, Martin.

    In: Robotics and Autonomous Systems, Vol. 58, No. 5, 2010, p. 622-633.

    Research output: Contribution to journalArticle

    TY - JOUR

    T1 - Kinematic control of a redundant manipulator using inverse-forward adaptive scheme with a KSOM based hint generator

    AU - Kumar, Swagat

    AU - Behera, Laxmidhar

    AU - McGinnity, Martin

    N1 - Reference text: [2] T. Yoshikawa, Foundation of Robotics, Analysis and Control, Prentice Hall of India, New Delhi, 2001. [3] P. Martin, J.R. Millan, Robot arm reaching through neural inversions and reinforcement learning, Robotics and Autonomous Systems 31 (2000) 227-246. [4] M. Kuperstein, Neural model of adaptive hand-eye coordination for single postures, Science 239 (1988) 1308-1311. [5] W.T. Miller III, Sensor-based control of robotic manipulators using a general learning algorithm, IEEE Journal of Robotics and Automation RA-3 (2) (1987) 157-165. [6] G. Sun, B. Scassellati, A fast and efficient model for learning to reach, International Journal of Humanoid Robotics 2 (4) (2005) 391-413. [7] R.V. Mayorga, P. Sanongboon, A radial basis function network approach for inverse kinematics and singularities prevention of redundant manipulators, in: Proc. of Int. Conf. on Robotics and Automation, ICRA, IEEE, 2002, pp. 1955-1960. [8] S. Vijayakumar, A. D'Souza, T. Shibata, J. Conradt, S. Schaal, Statistical learning for humanoid robots, Autonomous Robots 12 (2002) 55-69. [9] A. D'Souza, S. Vijayakumar, S. Schaal, Learning inverse kinematics, in: Interna- tional Conference on Intelligent Robots and Systems, IROS, IEEE, Maui, Hawai, USA, 2001, pp. 298-303. [10] G.G. Lendaris, K. Mathia, R. Saeks, Linear hopfield networks and constrained optimization, IEEE Transactions on System, Man and CyberneticsPart B: Cybernetics 29 (1) (1999) 114-118. [11] T.M. Martinetz, H.J. Ritter, K.J. Schulten, Three-dimensional neural net for learning visual motor coordination of a robot arm, IEEE Transactions on Neural Networks 1 (1) (1990) 131-136. [12] J.A. Walter, K.J. Schulten, Implementation of self-organizing neural networks for visual-motor control of an industrial robot, IEEE Transactions on Neural Networks 4 (1) (1993) 86195. [13] Z. Mao, T.C. Hsia, Obstacle avoidance inverse kinematics solution of redundant robots by neural networks, Robotica 15 (1997) 3-10. [14] D. DeMers, K. Kreutz-Delgado, Canonical parameterization of excess motor degrees of freedom with self organizing maps, IEEE Transactions on Neural Networks 7 (1) (1996) 43-55. [15] J. Peters, S. Schaal, Learning to control in operational space, International Journal of Robotics Research 27 (2) (2008) 197-212. [16] M.I. Jordan, D.E. Rumelhart, Forward models: Supervised learning with a distal teacher, Cognitive Science 16 (1992) 307-354. [17] J. Wang, Q. Hu, D. Jiang, A lagrangian network for kinematic control of redundant robot manipulators, IEEE Transactions on Neural Networks 10 (5) (1999) 1123-1132. [18] W.S. Tang, J. Wang, A recurrent neural network for minimum infinity- norm kinematic control of redundant manipulators with an improved problem formulation and reduced architecture complexity, IEEE Transactions on Systems, Man and Cybernetics-Part B: Cybernetics 31 (1) (2001) 98-105. [19] J. Peters, D. Nguyen-Tuong, Real-time learning of resolved velocity control on a Mitsubishi PA-10, in: International Conference on Robotics and Automation, ICRA, IEEE, Prasadena, CA, USA, 2008, pp. 2872-2877. [20] L. Bao-Liang, K. Ito, Regularization of inverse kinematics for redundant manipulator using neural network inversions, in: International Conference on Neural Networks, ICNN, IEEE, Perth, Australia, 1995, pp. 2726-2731. [21] S.F.M. Assal, K. Watanabe, K. Izumi, Neural network-based kinematic inversion of industrial redundant robots using cooperative fuzzy hint for the joint limits avoidance, IEEE Transactions on Mechatronics 11 (5) (2006) 593-603. [22] 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) 17-33. [23] T. Kohonen, Self Organization and Associative Memory, Springer-Verlag, 1984. [24] S. Kumar, P. Premkumar, A. Dutta, L. Behera, Visual motor control of a 7 DOF robot manipulator using KSOM-based redundancy preserving network, Robotica (2009). [25] H. Zha, T. Onitsuka, T. Nagata, A self-organization learning algorithm for visuo- motor coordination in unstructured environment, Artificial Life and Robotics 1 (3) (1997) 131-136. [26] M. Han, N. Okada, E. Kondo, Collision avoidance for a visuo-motor system using multiple self-organizing maps, in: Memoirs of the Faculty of Engineering, Kyushu University, 65 (4), 2005 pp. 129-142. [27] T.C. Hsia, Z.Y. Guo, New inverse kinematic algorithms for redundant robots, Journal of Robotics Systems 8 (1) (1991) 117-132. [28] Y. Mezouar, F. Chaumette, Path planning in image space for robust visual servoing, in: Proc. of IEEE Int. Conf. on Robotics and Automation, San Francisco, CA, 2000, pp. 2759-2763. [29] M. Han, N. Okada, E. Kondo, Coordination of an uncalibrated 3-d visuo-motor system based on multiple self-organizing maps, JSME International Journal Series C 49 (1) (2006) 230-239. [30] N. Mansard, F. Chaumette, Visual servoing sequencing able to avoid obstacles, in: Proc. of Int. Conf. on Robotics and Automation, IEEE, Barcelona, Spain, 2005, pp. 3143-3148. [31] O. Khatib, Real-time obstacle avoidance for manipulators and mobile robots, International Journal of Robotics Research 5 (1) (1986) 90-98. [32] Y.K. Hwang, N. Ahuja, A potential field approach to path planning, IEEE Transactions on Robotics and Automation 8 (1) (1992) 23-32. [33] J. Kim, P.K. Khosla, Real-time obstacle avoidance using harmonic potential functions, IEEE Transactions on Robotics and Automation 8 (3) (1992) 338-349. [34] W. Cho, D. Kwon, A sensor-based obstacle avoidance for a redundant ma- nipulator using a velocity potential field, in: IEEE International Work- shop on Robots and Human Communication, Tsukuba, Japan, 1996, pp. 306-310. [35] Y. Zhang, J. Wang, Obstacle avoidance for kinematically redundant manipula- tors using a dual neural network, IEEE Transactions on System, Man and Cy- bernetics, Part B 34 (1) (2004) 752-759. [36] Powercube manipulators, SCHUNKGmbH& Co. KG, 2009. http://www.schunk. com/. [37] J.J. Craig, Introduction to Robotics, Pearson Education, Inc., 1989. [38] 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.

    PY - 2010

    Y1 - 2010

    N2 - This paper proposes an online inverse-forward adaptive scheme with a KSOM based hint generator forsolving the inverse kinematic problem of a redundant manipulator. In this approach, a feed-forwardnetwork such as a radial basis function (RBF) network is used to learn the forward kinematic map ofthe redundant manipulator. This network is inverted using an inverse-forward adaptive scheme until thenetwork inversion solution guides the manipulator end-effector to reach a given target position witha specified accuracy. The positioning accuracy, attainable by a conventional network inversion scheme,depends on the approximation error present in the forward model. But, an accurate forward map wouldrequire a very large size of training data as well as network architecture. The proposed inverse-forwardadaptive scheme effectively approximates the forward map around the joint angle vector provided by ahint generator. Thus the inverse kinematic solution obtained using the network inversion approach cantake the end-effector to the target position within any arbitrary accuracy.In order to satisfy the joint angle constraints, it is necessary to provide the network inversion algorithmwith an initial hint for the joint angle vector. Since a redundant manipulator can reach a given target end-effector position through several joint angle vectors, it is desirable that the hint generator is capable ofproviding multiple hints. This problem has been addressed by using a Kohonen self organizing map basedsub-clustering (KSOM-SC) network architecture. The redundancy resolution process involves selecting asuitable joint angle configuration based on different task related criteria.The simulations and experiments are carried out on a 7 DOF PowerCubeTM manipulator. It is shownthat one can obtain a positioning accuracy of 1 mm without violating joint angle constraints even whenthe forward approximation error is as large as 4 cm. An obstacle avoidance problem has also been solvedto demonstrate the redundancy resolution process with the proposed scheme.

    AB - This paper proposes an online inverse-forward adaptive scheme with a KSOM based hint generator forsolving the inverse kinematic problem of a redundant manipulator. In this approach, a feed-forwardnetwork such as a radial basis function (RBF) network is used to learn the forward kinematic map ofthe redundant manipulator. This network is inverted using an inverse-forward adaptive scheme until thenetwork inversion solution guides the manipulator end-effector to reach a given target position witha specified accuracy. The positioning accuracy, attainable by a conventional network inversion scheme,depends on the approximation error present in the forward model. But, an accurate forward map wouldrequire a very large size of training data as well as network architecture. The proposed inverse-forwardadaptive scheme effectively approximates the forward map around the joint angle vector provided by ahint generator. Thus the inverse kinematic solution obtained using the network inversion approach cantake the end-effector to the target position within any arbitrary accuracy.In order to satisfy the joint angle constraints, it is necessary to provide the network inversion algorithmwith an initial hint for the joint angle vector. Since a redundant manipulator can reach a given target end-effector position through several joint angle vectors, it is desirable that the hint generator is capable ofproviding multiple hints. This problem has been addressed by using a Kohonen self organizing map basedsub-clustering (KSOM-SC) network architecture. The redundancy resolution process involves selecting asuitable joint angle configuration based on different task related criteria.The simulations and experiments are carried out on a 7 DOF PowerCubeTM manipulator. It is shownthat one can obtain a positioning accuracy of 1 mm without violating joint angle constraints even whenthe forward approximation error is as large as 4 cm. An obstacle avoidance problem has also been solvedto demonstrate the redundancy resolution process with the proposed scheme.

    KW - Redundant manipulator

    KW - Inverse kinematic solution

    KW - Kohonen Self-Organizing Map (KSOM)

    KW - Network inversion

    KW - Radial Basis Function Network (RBFN)

    KW - KSOM-SC architecture

    KW - Redundancy resolution

    U2 - 10.1016/j.robot.2009.12.002

    DO - 10.1016/j.robot.2009.12.002

    M3 - Article

    VL - 58

    SP - 622

    EP - 633

    JO - Robotics and Autonomous Systems

    T2 - Robotics and Autonomous Systems

    JF - Robotics and Autonomous Systems

    SN - 0921-8890

    IS - 5

    ER -