Robert III, King of the Scots was born John Stewart. He took the name Robert upon becoming king in deference to popular feeling.
John Stewart was born in 1337. He was baptized as John Stewart. He died on 04 April 1406 at Dundonald Castle. He was 68 at the time of his death. He was buried three days later on 7 April 1406 at the Paisley Abbey, Paisley, Renfrewshire, Scotland.
22 Jun 1368: Received the title of Earl of Carrick
17 Oct 1379: Received the title Earl of Atholl
19 April 1390 - 04 Apr 1406: Robert III, King of Scots 19 Apr 1390. He was crowned on Scone Abbey 
Robert married Annabella Drummond, daughter of Sir John Drummond of Stobhall and Lady Mary Montifex, daughter of Sir William Montifex on 13 March 1365 in Kyle, Ayrshire, Scotland They had 7 seven children:
David, Duke of Rothesay (b. 24 Oct 1378- d. 26 Mar 1402), he was once betrothed to Elizabeth Dunbar but married Marjory Douglas, daughter of Archibald Douglas, 3rd Earl of Douglas and Jean Moray (or Joanna Moravia) of Strathearn.
↑ 1.01.11.2The Scots Peerage, Founded on Wood's Edition of Sir Robert Douglas's Peerage of Scotland, containing an Historical and Genealogical Account of the Nobility of that Kingdom, Edited by Sir James Balfour Paul, Lord Lyon King of Arms with Armorial Illustrations, Published 1904 by D. Douglas in Edinburgh, Vol. 1, p.17., http://archive.org/stream/scotspeeragefoun01pauluoft#page/17/mode/1up
↑ Dispensation. Record for Annabella Drummond Stewart of Scotland; Robert III Stewart "King of Scotland".
Royal Ancestry by Douglas Richardson Vol. I p. 615
Royal Ancestry by Douglas Richardson Vol. I p. 647
It may be possible to confirm family relationships with Robert III by comparing test results with other carriers of his Y-chromosome or his mother's mitochondrial DNA.
Y-chromosome DNA test-takers in his direct paternal line on WikiTree:
No, Margaret (Graham) Stewart was married to Robert, Duke of Albany and brother to King Robert III.The Duke was regent but not King. King Robert III married Annabelle Drummond and they had seven children and he fathered a couple of natural children besides. Therer are 16 children listed under him here - some are likely his brother's children with Margaret Graham. Perhaps someone could have a look.