In Pennsylvania Genealogies there is mention of the Family of Robinson. It gives the genealogy of Thomas Robinson who came to America before 1730. This is not the line of Annie Robinson's family. She was born in Manchester, England, and although her parents did move to Pittsburgh, it was in the 1880s, not the 1700s.
Source: Family of ROBINSON. [Descendants of Thomas of Derry, Pa., about 1730] Egle's Pennsylvania Genealogies, chiefly Scotch-Irish and German (1896), p. 611-626.