Interesting question. They are called by a specialised technical name " inch-long caterpillar thingies ".
Being an amateur biologist, you may have discovered a new species. It is most unusual for caterpillars to form nests, as birds often do that sort of thing and with my eagle eye, they often do in the Spring, for some strange reason.
Anyway back to the " thingies". I would collect a sample and put them in an old Robertson's jam-jar. They feel at home in these jars and are not actually fussed if they had contained strawberry, rasberry or blackcurrant jam.
Make sure to put in some of the flora where you discovered them and tag each one with a small name-plate. I have a habit of naming my caterpillars after My Little Pony Horses.
And lo and behold they will pupate and a lovely moth will emerge. I would then promptly kill them with insect spray as they will only fly off and eat peoples coats and things.
Hope this helps.