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.
Bibliographical noteReference text:  T. Yoshikawa, Foundation of Robotics, Analysis and Control, Prentice Hall of
India, New Delhi, 2001.
 P. Martin, J.R. Millan, Robot arm reaching through neural inversions
and reinforcement learning, Robotics and Autonomous Systems 31 (2000)
 M. Kuperstein, Neural model of adaptive hand-eye coordination for single
postures, Science 239 (1988) 1308-1311.
 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)
 G. Sun, B. Scassellati, A fast and efficient model for learning to reach,
International Journal of Humanoid Robotics 2 (4) (2005) 391-413.
 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,
 S. Vijayakumar, A. D'Souza, T. Shibata, J. Conradt, S. Schaal, Statistical learning
for humanoid robots, Autonomous Robots 12 (2002) 55-69.
 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.
 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.
 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.
 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.
 Z. Mao, T.C. Hsia, Obstacle avoidance inverse kinematics solution of redundant
robots by neural networks, Robotica 15 (1997) 3-10.
 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.
 J. Peters, S. Schaal, Learning to control in operational space, International
Journal of Robotics Research 27 (2) (2008) 197-212.
 M.I. Jordan, D.E. Rumelhart, Forward models: Supervised learning with a distal
teacher, Cognitive Science 16 (1992) 307-354.
 J. Wang, Q. Hu, D. Jiang, A lagrangian network for kinematic control of
redundant robot manipulators, IEEE Transactions on Neural Networks 10 (5)
 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)
 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.
 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.
 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)
 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.
 T. Kohonen, Self Organization and Associative Memory, Springer-Verlag,
 S. Kumar, P. Premkumar, A. Dutta, L. Behera, Visual motor control of a 7
DOF robot manipulator using KSOM-based redundancy preserving network,
 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.
 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.
 T.C. Hsia, Z.Y. Guo, New inverse kinematic algorithms for redundant robots,
Journal of Robotics Systems 8 (1) (1991) 117-132.
 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.
 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.
 N. Mansard, F. Chaumette, Visual servoing sequencing able to avoid obstacles,
in: Proc. of Int. Conf. on Robotics and Automation, IEEE, Barcelona, Spain, 2005,
 O. Khatib, Real-time obstacle avoidance for manipulators and mobile robots,
International Journal of Robotics Research 5 (1) (1986) 90-98.
 Y.K. Hwang, N. Ahuja, A potential field approach to path planning, IEEE
Transactions on Robotics and Automation 8 (1) (1992) 23-32.
 J. Kim, P.K. Khosla, Real-time obstacle avoidance using harmonic potential
functions, IEEE Transactions on Robotics and Automation 8 (3) (1992)
 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.
 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.
 Powercube manipulators, SCHUNKGmbH& Co. KG, 2009. http://www.schunk.
 J.J. Craig, Introduction to Robotics, Pearson Education, Inc., 1989.
 G. Tevatia, S. Schaal, Inverse kinematics of humanoid robots, in: Proc. of
IEEE Int. Conf. on Robotics and Automation, San Francisco, CA, 2000, pp.
- Redundant manipulator
- Inverse kinematic solution
- Kohonen Self-Organizing Map (KSOM)
- Network inversion
- Radial Basis Function Network (RBFN)
- KSOM-SC architecture
- Redundancy resolution