I also have a Robert Aikins in my family, about whom i know rather little. Believe he was born about 1800, possibly in Belmont County, OH, son of Robert and Mary Aikins of PA.
Married an Elizabeth Nash in Washinton County, OH 10 Dec 1818.
In the 1850 federal census for Vinton County, Ohio, the first entry for Richland Township is a Robert and Elizabeth Aikins and family: Robert Aikins, 50, m, farmer, 7,000, PA Elizabeth, 45, f, PA Sarah, 18, f, OH, school Cyntha, 15, f, OH, school Barnet, 13, m, OH, school Izabel, 10, f, OH, school Martha, 8, f, OH, school Armuide?, 1, f, OH
"Barnet" would seem to indicate that this is your family, but I do not know if they are mine.