That's what I put on DD right now (she just started walking a week or so ago). They have a slightly thicker sole than Robeez, but otherwise seem pretty similar. I didn't think about slipping - so far she doesn't do much walking in shoes on slick surfaces. She goes barefoot at home and when we're inside for the most part.
Re: Pediped ? (PIP)
DD tried on a pair of those and slipped, banged her knee and refused to get up till they were off her feet.
I like see kai run shoes.