Robert Barnes is the son of mass murderer on retrial Leland Barnes and brother of spree hitman Harlan Barnes on Leland's directive. He mourned the loss of his mother Kelly at Leland's hands most out of his family and dreaded his father's violence. When Harlan started trying to kill witnesses so Leland's retrial would be successful, Robert helped tracked him down.
When Leland still unfortunately got off on all charges and was walking out of the courthouse, Robert pulled a handgun on the steps and shot Leland dead. He then surrendered and was immediately arrested for murder. Jack McCoy, who originally prosecuted Leland and failed to keep him in jail at the retrial, lamented in his shock he thought Robert was aiming at him instead of Leland.
Afterwards, Robert was presumably convicted of premeditated murder and imprisoned. (L&O: "Criminal Law")