  Planning accurate manipulation for deformable objects requires prediction of
their state. The prediction is often complicated by a loss of stability that
may result in collapse of the deformable object. In this work, stability of a
fabric strip folding performed by a robot is studied. We show that there is a
static instability in the folding process. This instability is detected in a
physics-based simulation and the position of the instability is verified
experimentally by real robotic manipulation. Three state-of-the-art methods for
folding are assessed in the presence of static instability. It is shown that
one of the existing folding paths is suitable for folding of materials with
internal friction such as fabrics. Another folding path that utilizes dynamic
motion exists for ideal elastic materials without internal friction. Our
results show that instability needs to be considered in planning to obtain
accurate manipulation of deformable objects.
