International Journal of Engineering and Manufacturing (IJEM)
IJEM Vol. 5, No. 2, 8 Aug. 2015
Cover page and Table of Contents: PDF (size: 462KB)
Inverse Kinematics of Redundant Manipulator using Interval Newton Method
Full Text (PDF, 462KB), PP.19-29
Views: 0 Downloads: 0
Author(s)
Virendra Kumar
1,*
Soumen Sen
1
S.S. Roy
2
S.K Das
1
S.N.Shome
1
Index Terms
Interval Newton Method, Redundant Manipulator, Inverse Kinematics, Manipulability
Abstract
The paper presents an application of Interval Newton method to solve the inverse kinematics and redundancy resolution of a serial redundant manipulator. Such inverse problems are often encountered when the manipulator link lengths, joint angles and end-effector uncertainty bounds are given, which occurs due to because of inaccuracies in joint angle measurements, manufacturing tolerances, link geometries approximations, etc. The inverse kinematics of three degree of freedom planar redundant positioning manipulator without end-effector has been evaluated using the manipulability of Jacobian matrix as performance metric. To solve the nonlinear equation of inverse kinematics, the multidimensional Newton method is used. The inverse kinematics is intended to produce solutions for joint variables in interval of tolerances for specified end effector accuracy range. As exemplar problem solving, a planar 3-degrees-of-freedom serial link redundant manipulators is considered.
Cite This Paper
Virendra Kumar, Soumen Sen, S.S. Roy, S.K Das, S.N.Shome,"Inverse Kinematics of Redundant Manipulator using Interval Newton Method", IJEM, vol.5, no.2, pp.19-29, 2015. DOI: 10.5815/ijem.2015.02.03
Reference
[1]Yoshikawa, T. "Manipulability of robotic mechanisms", The International Journal of Robotics Research, vol. 4, no. 2, pp. 3–9, 1985.
[2]Chirikjian, G. and Burdick, J. "Kinematically optimal hyper-redundant manipulator configurations", IEEE Transactions on Robotics and Automation, vol. 11, pp. 794-806, Dec 1995.
[3]Salisbury, J.K. and Craig, J.J. "Articulated hands: force control and kinematic issues", The International Journal of Robotics Research, Vol. 1, No. 1, pp. 4-17, 1982.
[4]Klein,C. and Blaho, B. "Dexterity measures for the design and control of kinematically redundant manipulators", The International Journal of Robotics Research, Vol. 6, No. 2,72-83, Summer 1987.
[5]Angeles,J. "The design of isotropic manipulator architectures in the presence of redundancies", The International Journal of Robotics Research, Vol. 11, No. 3, 196-201, June 1992.
[6]Rao R.S, Asaithambi A., and Agrawal S.K. "Inverse kinematic solution of robot manipulators using interval analysis", J. of Mechanical Design, 120(1):147-150, 1998.
[7]Castellet, A. and Thomas, F. "Towards an Efficient Interval Method for Solving Inverse Kinematic Problems", International Conference on Robotics and Automation, IEEE, Albuquerque, New Mexico, pp 3615-3620, - April 1997.
[8]Pac M., Rakotondrabe M., Khadraoui S., Popa D., Lutz P. "Guaranteed Manipulator Precision via Interval Analysis of Inverse Kinematics", In IDETC/CIE 2013 August 4-7, 2013, Portland, Oregon, USA.
[9]Klein, C.A. and Huang, C.H. "Review of the Pseudoinverse for control of kinematically redundant manipulators", IEEE Transactions on systems, Man and Cybernetics, VOL. SMC-13, NO. 3, pp 245-250, March, 1983.
[10]Mahato, S. K. and Bhunia, A. K. "Interval-Arithmetic-Oriented Interval Computing Technique for Global Optimization", AMRX Applied Mathematics Research express, Volume 2006, Article ID 69642, Pages 1–19
[11]Hansen, E. R. and Walster, G. W. "Global Optimization Using Interval Analysis", Marcel Dekker, New York, NY, 2004.
[12]Hansen, E.R. and Sengupta, S. "Global constrained optimization using interval analysis", in Nickel (1980), pp. 25-47.
[13]Moore, R. E., "Interval Analysis", Prentice Hall, Englewood Cliffs, NJ, 1966.
[14]Rump, S. M., 1999. "Intlab interval laboratory", In Developments in Realiable Computing, T. Csendes, edito, Kluwer Academic Publishers, Dordrecht, pp. 77–104.