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Ch18-I044963.fm Page 81 Tuesday, August 1, 2006 2:59 PM
1, 2006
Tuesday, August
Page 81
2:59 PM
Ch18-I044963.fm
81 81
INDIRECT SIMULTANEOUS POSITIONING
OF DEFORMABLE OBJECTS WITHOUT
PHYSICAL PARAMETERS OR TIME-DERIVATIVES

Shinichi Hirai
Dept. Robotics, Ritsumeikan Univ.
Kusatsu, Shiga 525-8577, Japan

ABSTRACT
This paper describes the control of indirect simultaneous positioning of a viscoelastic 2D ob-
ject without any physical parameter of the manipulated object. Applying continua modeling of
isotropic viscoelastic deformation, I first show that the positioning can be performed successfully
by a simple integral control among positioned and manipulated displacements without physical pa-
rameters. Then, I show that a redundant system, where the number of manipulated displacements
exceeds the number of positioned displacements, performs the positioning successfully.

KEYWORDS
deformation, positioning, feedback control, continua, manipulation

1 INTRODUCTION

Many manipulative operations that deal with deformable objects result in a positioning of multiple
points on a deformable object [Taylor et al. 1990, Henrich and Worn 2000]. In this positioning,
multiple points on a deformable object should be guided to their desired locations simultaneously.
Moreover, it is often impossible to manipulate the positioned points directly. For example, one
operation called linking is popular in garment manufacturing. In linking of fabrics, loops at the
end of a fabric must be matched to loops of another fabric so that the two fabrics can be sewed
seamlessly. These points cannot be manipulated directly since a sewing needle is guided along
the matched loops. Mating of a flexible part in electric industry also results in the positioning
of mated points on the object. These points cannot be manipulated directly since the points in
a mating part contact with a mated part. Consequently, we find that a positioning of multiple
points on a deformable object is one of fundamental operations in the manipulation of deformable
objects. Since the positioned points cannot be manipulated directly, the guidance of positioned
points must be performed by controlling some points except the positioned points, as illustrated in