Hostname: page-component-586b7cd67f-tf8b9 Total loading time: 0 Render date: 2024-11-22T07:53:02.587Z Has data issue: false hasContentIssue false
  • English
  • Français

Computational models satisfying relative angle constraints for 2-dimensional segmented bodies

Published online by Cambridge University Press:  17 February 2009

S. Munzir ,
L. S. Jennings  and
M. T. Koh
S. Munzir
Affiliation:
School of Mathematics and Statistics, The University of Western Australia, 35 Stirling Hwy. Crawley, WA 6009, Australia; e-mail: [email protected].
L. S. Jennings
Affiliation:
School of Mathematics and Statistics, The University of Western Australia, 35 Stirling Hwy, Crawley, WA 6009, Australia.
M. T. Koh
Affiliation:
Physical Education and Sports Science Group, National Institute of Education, 1 Nanyang Walk, Singapore.
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

Planar hinged segmented bodies have been used to represent models of biomechanical systems. One characteristic of a segmented body moving under gravitational acceleration and torques between segments is the possibility that the body's segments spin through more than a revolution or past a natural limit, and a computational mechanism to stop such behaviour should be provided. This could be done by introducing angle constraints between segments, and computational models utilising optimal control are studied here. Three models to maintain angle constraints between segments are proposed and compared. These models are: all-time angle constraints, a restoring torque in the state equations and an exponential penalty model. The models are applied to a 2-D three-segment body to test the behaviour of each model when optimising torques to minimise an objective. The optimisation is run to find torques so that the end effector of the body follows the trajectory of a half-circle. The result shows the behaviour of each model in maintaining the angle constraints. The all-time constraints case exhibits a behaviour of not allowing torques (at a solution) which makes segments move past the constraints, while the other two show a flexibility in handling the angle constraints which is more similar to what occurs in a real biomechanical system.

Keywords

biomechanicsoptimal controlall-time constraints.
Type
Research Article
Information
The ANZIAM Journal , Volume 47 , Issue 4 , April 2006 , pp. 541 - 554
Copyright
Copyright © Australian Mathematical Society 2006

References

[1]Agrawal, S. K., “Inertia matrix singularity of planar series-chain manipulators”, in Proceedings of the 1991 IEEE conference on robotics and automation, Sacramento, California, Vol. 1 (IEEE Computer Society, Los Alamos, CA, 1991), Pp. 102–107.CrossRefGoogle Scholar
[2]Alonge, F., D'Ippolito, F. and Raimondi, F. M., “An adaptive control law for robotic manipulator without velocity feedback”, Control Eng. Prac. 11 (2003) 999–1005.CrossRefGoogle Scholar
[3]Azevedo, C., Andreff, N. and Arias, S. “Bipedal walking: from gait design to experimental analysis”, Mechatronics 14 (2004) 639–665.CrossRefGoogle Scholar
[4]Jennings, L. S., Fisher, M. E., Teo, K. L. and Goh, C. J., MISER3: Optimal Control Software, Theory and User Manual, Version 3 (http://www.maths.uwa.edu.au/u/les, 2004).Google Scholar
[5]Koh, M. T. and Jennings, L. S., “Dynamic optimization: A solution to the inverse dynamic problem of biomechanics using MISER3”, Dyn. Contin. Discrete Impulsv. Syst. Ser. B Appl. Algorithms 9B (2002) 369–386.Google Scholar
[6]Koh, M. T. and Jennings, L. S., “Dynamic optimization: inverse analysis for the Yurchenko layout vault in women's artistic gymnastics”, J. Biomech. 36 (2003)1177–1183.CrossRefGoogle ScholarPubMed
[7]Koh, M. T., Jennings, L. S. and Elliott, B. “Role of joint torques generated in an optimized Yurchenko layout vault”, Sports Biomech. 2 (2003) 177–190.CrossRefGoogle Scholar
[8]Koh, M. T., Jennings, L. S., Elliott, B. and Lloyd, D. “A predicted optimal performance of the Yurchenko layout vault in women's artistic gymnastics”, J. Appl. Biomech. 19 (2003) 187–204.CrossRefGoogle Scholar
[9]Lee, H. W. J., Teo, K. L. and Jennings, L. S., “An optimal control of multi-link vertical planar robot arms systems moving under the effect of gravity”, J. Austral. Math. Soc. Ser B 39 (1997) 195–213.CrossRefGoogle Scholar
[10]Menegaldo, L. L., Fleury, A. D. T. and Weber, H. I., “Biomechanical modeling and optimal control of human posture”, J. Biomech. 36 (2003) 1701–1712.CrossRefGoogle ScholarPubMed
[11]Teo, K. L., Gob, C. J. and Wong, K. H., A Unified Computational Approach to Optimal Control Problems (Longman Scientific and Technical, New York, 1991).Google Scholar
[12]Teo, K. L. and Jennings, L. S., “Nonlinear optimal control problems with continuous state inequality constraints”, J. Optim. Theory Appl. 63 (2003) 1–22.CrossRefGoogle Scholar
[13]Tian, L. and Gilbertson, L. G., “The study of control methods for the robotic testing system for human musculoskeletal joints”. Computer Meth. Prog. Bio. 74(2004) 211–220.CrossRefGoogle Scholar