ANZIAM J.
47 (2006), 541554

Computational models satisfying relative angle constraints for 2dimensional segmented bodies

S. Munzir
School of Mathematics and Statistics
The University of Western Australia
35 Stirling Hwy
Crawley WA 6009
Australia
msaid@maths.uwa.edu.au


L. S. Jennings
School of Mathematics and Statistics
The University of Western Australia
35 Stirling Hwy
Crawley WA 6009
Australia



M. T. Koh
Physical Education and Sports Science Group
National Institute of Education
1 Nanyang Walk
Singapore



Abstract

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: alltime angle constraints, a
restoring torque in the state equations and an
exponential penalty model. The models are applied
to a 2D threesegment 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 halfcircle. The
result shows the behaviour of each model in
maintaining the angle constraints. The alltime
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.

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