This may give you a lead to pursue. The 1850 US Federal Census lists Smith Robbins as the father of an Edwin B Robbins born about 1835:
Household members:
Smith Robbins Age 49
Emily Robbins Age 43
Arthur K Robbins Age 17
Edwin B Robbins Age 15
Charles M Robins Age 11
Lydia M Robbins Age 6
Lydia M Doane Age 17