These two poems are from Li Bai's Sleepwalking in the Heavenly Mother:
...
I wear pegged boots which were first used by Xie, up a ladder of blue cloud.
sunny ocean half-way, holy cock-crow in space.
...
It's a wooden shoe. Xie Gong means Xie Lingyun.
So, Xie Gongqi refers to a kind of wooden shoes that Xie Lingyun wears when climbing mountains. There are two wooden teeth on the sole. Go up the mountain to remove the front teeth and go down the mountain to remove the rear teeth, which is convenient for walking on the mountain road.
This is the invention of Xie Lingyun, which naturally first appeared in Xie Gongsuo's time, and there may have been similar ones before, but it must be Xie Lingyun's name and stereotype.
Xie Lingyun (385-433) was a minister, Buddhist scholar, traveler and the originator of landscape poetry school from Eastern Jin Dynasty to Liu Song Dynasty.
Xie Gongqi first appeared in the Eastern Jin Dynasty to Liu Song Dynasty.