The Edgehog, invented by John Driver, is a Queen that can move only to or from the edge cells of the board. The 'or' can be inclusive (I-type) where moves from edge to edge are permitted, or exclusive (E-type) where they are prohibited. Applied to Grasshoppers the same principle produces Edgehoppers.
See also the Retroanalysis section for an Edge Chess composition.

G. P. Jelliss, 10905
The British Chess Magazine
December 1975 (p.560)
Edgehoppers (E-type).
Helpmate in 9.

Solution: 1.Ke2 Kg2 2.Eh1 Ee8 3-6.Ka6 Kc6 7.Eb7 Kc7 8.Ka7 Kc8 9.Ka8 Ec6 (BCM Jun 1976 p.269)

G. P. Jelliss
The British Chess Magazine Dec 1976 p.576 #11112
(solution May 1977 p.237)
Edgehoppers (E-type).
Mate in 2

Solution: 1.Ra6 Exc5/Exc4/Eg5/Ef7 2.Bxc5/Rxc4/Ea3/Ea2 mate.