Their fabric handling is reasonable, but not a breakthrough. They're laying flat pieces of fabric on top of other flat pieces.[1] A human flattens out the pieces and feeds them in. This has been done before with vacuum pickers.[2] There's also an approach where the fabric is starched first to make it stiff for robot handling. After assembly, the garment is washed to remove the starch.[3]

Dealing with fabric that isn't flat is a popular robotics research topic, but results are not very good.[4] Willow Robotics used to have a demo of towel folding with a robot, but it was extremely slow.

[1] https://grabitinc.com/ [2] https://www.youtube.com/watch?v=zI7u9V5aYt4 [3] http://money.cnn.com/2016/10/11/technology/robots-garment-ma... [4] http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.689...