It has been suggested that Richard Warren was the son of Anthony Warren, but this is only speculative. Other possibilities for Richard's father are discussed at this website. He could be a grandson of Sir Laurence Warren. NOTE: Apparently, this website has disappeared.
Note: see this website at Ancestry of Tipperary Wallers which includes the discussion.
So far, there is no evidence that his name was "Robert." That has been deleted.
Richard Waller was probably from Long Stowe originally, probably born about 1501, and later lived in Bassingbourn, Cambridgeshire, England.
According to TAG 58:166ff, Richard Waller/Warren wrote a will 28 mar 1557 in Bassingbourn, Cambridgeshire, England, in which he named wife Alice and children. Wife Alice is almost certainly Alice Jenaway. From this and from the wills of his named children, it can be surmised that Richard and Alice had the following children:
Richard passed away in before 1557. 
Richard Waller's will was proved on 2 May 1557.
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Richard is 18 degrees from John James Audubon, 23 degrees from Jacques-Yves Cousteau, 29 degrees from Gerald Durrell, 18 degrees from Dian Fossey, 20 degrees from Steve Irwin, 30 degrees from Ernest Just, 22 degrees from Ian Player, 17 degrees from Peter Scott, 30 degrees from Antoon van Hooff and 18 degrees from Marta Johnson on our single family tree. Login to find your connection.