From 1978 to 1998, Robertson occupied various positions in the Institution for Social and Policy Studies and the Department of Epidemiology and Public Health at Yale University.
He was also Senior Behavioral Scientist in the Insurance Institute for Highway Safety (1970–78).
Robertson contributed 11 books and 150 articles and chapters to scientific literature.
He was a member of the National Research Council/Institute of Medicine Committee on Trauma Research that produced the report Injury in America: A Continuing Public Health Problem and was vice-chair of the NRC committee that reviewed the injury control program of the Centers for Disease Control.
The American Public Health Association' injury prevention section gave Robertson the Distinguished Career Award.