I don't have any ideas but all my girls have done this between 14 months and 2 years for some reason. For some time we thought it was a developmental thing, and my DD1's legs were sore because she was learning to walk, so we used to massage her before she went to bed. Of course that didn't really help, but at least we were doing something.

DH used to camp out next to her bed and get as much sleep as he could while she was playing.

Now DD3 is going through it, and we just lay down and try to doze while she plays around us. Not the best solution but it stops me getting angry at her. Occasionally, I will lie her down and tell her its sleep time, sometimes it works, mostly not, so we just make the best out of a bad situation.