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3.00

- 3 - 2 - 1 0 1 2 - 3 - 2 - 1 0 1 2 3 4
(a) 0.00 s (c) 2.00 s

- 3 - 2 - 1 0 1 2 3 4 5 6 - 3 - 2 - 1 0 1 2 3 4 5 6 - 3 - 2 - 1 0 1 2 3 4
(d) 3.00 s (e) 4.00 s (f) 5.00 s
Figure 5: Process of indirect simultaneous positioning to desired lines

5 CONCLUDING REMARKS
I have applied continua, modeling of a viscoelastic object to the indirect simultaneous position-
ing and have simulated the positioning process. I have shown that a simple I-control based on
a distance-based mapping among positioned and manipulated displacements performs the posi-
tioning successfully without any physical parameter. Note that an iterative control law proposed
in this paper requires no time-derivatives of sensor signals and works well with time interval
around 0.5, which is larger than the sampling time in video frame rate. In addition, I have shown
that a redundant system, where the number of manipulated displacements exceeds the number of
positioned displacements, performs the positioning successfully.
I am going to investigate the stability of the positioning process based on the continua modeling
and its finite element approximation of viseoelastic deformation. Experimental verification is also
a future issue. I will investigate the positioning of an inelastic object including hysteresis and
rheological deformation.

References

Baumgarte, J. (1972). Stabilization of Constraints and Integrals of Motion in Dynamical Systems.
Computer Methods in Applied Mechanics and Engineering 1, 1—16.
Henrich, D. and Worn, H. eds. (2000). Robot Manipulation of Deformable Objects. Springer
Verlag.
Taylor, P. M. et al. (1990). Sensory Robotics for the Handling of Limp Materials. Springer—Verlag.

Wada, T., Hirai, S., and Kawamura, S. (1998). Indirect Simultaneous Positioning Operations
of Extensionally Deformable Objects. Proc. IEEE/RSJ Int. Conf. on Intelligent Robots and
Systems, 1333 1338.
Wada, T., Hirai, S., Kawamura, S., and Kamiji, N. (2001). Robust Manipulation of Deformable
Objects By a Simple PID Feedback. Proc. IEEE Int. Conf. on Robotics and Automation.
85-90.