  Shape control of deformable objects is a challenging and important robotic
problem. This paper proposes a model-free controller using novel 3D global
deformation features based on modal analysis. Unlike most existing controllers
using geometric features, our controller employs a physically-based deformation
feature by decoupling 3D global deformation into low-frequency mode shapes.
Although modal analysis is widely adopted in computer vision and simulation, it
has not been used in robotic deformation control. We develop a new model-free
framework for modal-based deformation control under robot manipulation.
Physical interpretation of mode shapes enables us to formulate an analytical
deformation Jacobian matrix mapping the robot manipulation onto changes of the
modal features. In the Jacobian matrix, unknown geometry and physical
properties of the object are treated as low-dimensional modal parameters which
can be used to linearly parameterize the closed-loop system. Thus, an adaptive
controller with proven stability can be designed to deform the object while
online estimating the modal parameters. Simulations and experiments are
conducted using linear, planar, and solid objects under different settings. The
results not only confirm the superior performance of our controller but also
demonstrate its advantages over the baseline method.
