Robinson, an African American, started his college education at LeMoyne-Owen College and graduated from Memphis State University now the University of Memphis, in 1979 with summa cum laude honors and a B.S. degree in chemistry. He received a Ph.D. in nuclear chemistry from Washington University in St. Louis in 1984. In that same year, he joined the research staff of Oak Ridge National Laboratory (ORNL), where he was a research scientist and served as a group leader, of the neutron activation analysis facility. He accepted a position as a visiting professor at FAMU in January 1995, and left ORNL two years later to accept a permanent faculty position at FAMU.
At FAMU, Robinson became director of the universitys Environmental Sciences Institute. In addition to conducting research on environmental chemistry of coastal ecosystems, he had a leadership role in establishing new B.S. and Ph.D. degree programs. In 2003, he became FAMU provost and vice president for academic affairs, serving until 2005. In 2007 he became the universitys chief operating officer and vice president for research, and served for several weeks as the school's interim president. In May 2010, he left that position to become Assistant Secretary for Conservation and Management in the National Oceanic and Atmospheric Administration. In November 2011 he returned to FAMU as a professor and special assistant, and in March 2012 he was named provost and vice president for academic affairs.
In July 2012, the FAMU Board of Trustees appointed Robinson to serve as the university's interim president, replacing James H. Ammons. On September 15, 2016, he was named to a third stint as interim university president following the approval of a separation agreement with the 11th president, Elmira Mangum. On November 30, 2017, Robinson was named the 12th President of Florida A&M University.