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u
operation UOiv as shown in Fig.5(d). Action 2 is to release segment \L and to grasp segment iL\ as
u
shown in Fig.5(e) for operation UOi or for operation UOi V. Action 3 is to grasp segment L i keeping
segment \L grasped for operation UOi as shown in Fig.5(f). Anyway, we have to change grasping
points for the last transition from state S5 to state Si i. Consequently, in the above plans to perform
sequence SQj, N c=\ and it is minimum. We can also derive the minimum N c for sequence SQ2 and
sequence SQ3. The former is N c=2 and the latter is N c=\. This implies that sequence SQ2 should be
eliminated from adequate manipulation plans. Thus, we can narrow down candidates of manipulation
plans by considering N t and N c. After that, quantitative analysis (Wakamatsu 2004) should be
performed in order to check whether a selected manipulation can be realized practically or not
considering physical properties of a linear object such as rigidity. Thus, we conclude that our proposed
method is useful for planning of knotting/unknotting manipulation of deformable linear objects.

CONCLUSIONS

A planning method for knotting/unknotting manipulation of deformable linear objects was proposed.
First, knotting/unknotting processes of a linear object were represented as a sequence of finite crossing
state transitions. Next, grasping points and their moving direction to perform each state transition were
defined. Then, possible qualitative manipulation plans can be generated by a computer system when
the initial state and the objective state of a linear object are given. Finally, criteria for evaluation of
generated manipulation plans were introduced. By considering them, we can narrow down candidates
of manipulation plans.

REFERENCES
Hopcroft J.E., Kearney J.K., and Krafft D.B. (1991). A Case Study of Flexible Object Manipulation.
Int. J. of Robotics Research, 10:1, 41-50.

Inoue H. and Inaba M. (1984). Hand-eye Coordination in Rope Handling, Robotics Research: The
First International Symposium, MIT Press, 163—174.

Matsuno T., Fukuda T., and Arai F. (2001). Flexible Rope Manipulation by Dual Manipulator System
Using Vision Sensor, Proc. of International Conference on Advanced Intelligent Mechatronics, 677—
682.

Morita T., Takamatsu J., Ogawara K., Kimura H., and Tkeuchi K. (2003). Knot Planning from
Observation, Proc. of IEEE Int. Conf. Robotics and Automation, 3887-3892.

Wakamatsu H., and Hirai S. (2004). Static Modeling of Linear Object Deformation based on
Differential Geometry, Int. J. of Robotics Research, 23:3, 293—311.