A Limited Interval Gradient Projection Algorithm for Inverse Kinematics

Abstract:

The Jacobian inverse(JI) method is a well-known algorithms used for inverse kinematics solutions in motion generation. JI algorithm can be easily implemented, but it can generate singularity problems and it is not straight forward to implement constraints in the JI method. This paper presents a novel gradient projection algorithm that can convert the inverse kinematics problem to a constraint nonlinear programming problem. Meanwhile, by changing the programming time of each frame, local linearization of the nonlinear function and limited interval computing can be achieved simultaneously. Experimental results are presented to show the performance benefits of the proposed algorithm over JI methods.

• Periodical: Advanced Materials Research (Volumes 490-495)
• Pages: 7-12
• DOI: https://doi.org/10.4028/www.scientific.net/AMR.490-495.7
• Online since: March 2012
• Authors: Wei Song, Guang Hu
• Keywords: Gradient, Inverse Kinematic, JI, Limited Interval

References

[1] K. C. Gupta and K. Kazerounian, Improved numerical solutions of inverse kinematics of robots, in Proceedings of the 1985 IEEE International Conference on Robotics and Automation, vol. 2, March 1985, p.743–748.

DOI: 10.1109/robot.1985.1087237

[2] A. Goldenberg, B. Benhabib, and R. Fenton, A complete generalized solution to the inverse kinematics of robots, IEEE Journal of Robotics and Automation, vol. 1, March 1985 , p.14–20.

DOI: 10.1109/jra.1985.1086995

[3] V. J. Lumelsky, Iterative coordinate transformationprocedure for one class of robots, IEEE Transactions on Systems Man and Cybernetics, vol. 14, Jun. 1984, p.500–505.

DOI: 10.1109/tsmc.1984.6313247

[4] V. D. Tourassis and J. Ang, M.H., A modular architecture for inverse robot kinematics, IEEE Transactions on Robotics and Automation, vol. 5, October 1989, p.555–568.

DOI: 10.1109/70.88076

[5] M. Fedor, Application of inverse kinematics for skeleton manipulation in real-time, " in SCCG , 03: Proceedings of the 19th spring conference on Computer graphics. New York, NY, USA: ACM Press, 2003 , p.203–212.

DOI: 10.1145/984952.984986

[6] Jianmin Zhao, Norman I. Badler, Inverse kinematics positioning using nonlinear programming for highly articulated figures, ACM Transactions on Graphics, Volume 13 Issue 4, Oct. (1994).

DOI: 10.1145/195826.195827

[7] Fletcher, R., and Powell, M. J. D. A rapidly convergent descent method for minimization. Computer J. 6 (1963), pp.163-168.

DOI: 10.1093/comjnl/6.2.163

[8] Fletcher, R. A new approach to variable metric algorithms. Computer J. 13 (1970), pp.317-322.

[9] Goldfarb, D. Extension of Davidon's variable metric method to maximization under linear inequality and equality constraints. SIAM J. Appl. Math. 17 (1969), pp.739-764.

DOI: 10.1137/0117067

[10] Goldfarb, D. A family of variable metric methods derived by variational means. Math. Computation 24 (1970), pp.23-26.

DOI: 10.1090/s0025-5718-1970-0258249-6