  Robotic manipulation of deformable objects remains a challenging task. One
such task is folding a garment autonomously. Given start and end folding
positions, what is an optimal trajectory to move the robotic arm to fold a
garment? Certain trajectories will cause the garment to move, creating
wrinkles, and gaps, other trajectories will fail altogether. We present a novel
solution to find an optimal trajectory that avoids such problematic scenarios.
The trajectory is optimized by minimizing a quadratic objective function in an
off-line simulator, which includes material properties of the garment and
frictional force on the table. The function measures the dissimilarity between
a user folded shape and the folded garment in simulation, which is then used as
an error measurement to create an optimal trajectory. We demonstrate that our
two-arm robot can follow the optimized trajectories, achieving accurate and
efficient manipulations of deformable objects.
