Looks like creeping phlox, but apparently is Trailing Rosemary? One pinner said: Trailing Rosemary produces beautiful blue foliage. It requires little water, and has a moderate growth rate. It has no allergens, but yet is very fragrant.
Foot-Traffic-Friendly Groundcovers Compete well w/weeds & Stay relatively short w/o Mowing include: Mat-forming Creeping Thyme, Grasslike Blue Sedge (Carex Glauca), & Mounding Moss Phlox (a good choice on hillsides where mowing is difficult).
Isotoma fluviatilis - Fast growing ground cover good in in sun to part shade. Tolerates being walked on. I think the flowers close up when stepped on and reopen after a few seconds. Great for around flagstone.
Less-is-more landscape approach - with a gravel mulch you have an attractive background while the (undisturbed) plants have room to spread. Helichotrichon, sedum, thyme, with pebbles, large and small rocks. This is very well done.