Anthony M. Robeson followed an apprenticeship at the Scranton Steelworks, Pennsylvania. Subsequently he was appointed as mechanic by the El Callao Gold Mining Company in eastern Venezuela and later became mechanical engineer at the Austin Gold Mining Company in that country, and then at El Callao. From 1890 he studied mechanical and electrical engineering at the Massachusetts Institute of Technology, but did not graduate. In 1893 he came to South Africa and on 10 February the next year married an American lady, Grace Perry.
Robeson succeeded Louis I. Seymor* as mechanical engineer and electrician at De Beers Consolidated Mines, Kimberley, until his appointment as assistant general manager of De Beers in 1897. During the next two years he was an examiner in mining for the second mining examination of the University of the Cape of Good Hope. In 1898 he went to New York and took a course in mining engineering at Columbia University, but again did not graduate. On leaving the university he went to Alaska as general manager of the Alaska-Mexican Gold Mining Company. Following Seymor's death in 1900 Robeson moved to Johannesburg and succeeded him as consulting mechanical engineer to H. Eckstein and Co.
Robeson was an early member of the South African Association for the Advancement of Science and in 1903/4 served as a member of the committee of Section C of the association, which included engineering. At the joint meeting of the British and South African Associations for the Advancement of Science, held in South Africa in 1905, he read a paper on "Some experiments in dust-fuel firing". His innovative experiments, using powdered coal and air as boiler fuel, were conducted with ten differently designed furnaces and proved fairly successful. A summary of the paper was published in the British Association's Report for 1905 and the complete paper was included in the Addresses and papers... published after the meeting (Vol. 2, pp. 242-260). The next year he was joint author, with E.J. Lashinger* and H.C. Behr*, of a paper read before the South African Association of Engineers on "Steam consumption tests on a twin tandem compound condensing winder at No. 1 shaft, Village Deep, Ltd." The paper was published in the Association's Proceedings for 1906 and reprinted as a pamphlet.
In 1902 Robeson became a member of the Chemical, Metallurgical and Mining Society of South Africa. The next year he served on the Technical Education Commission, appointed by the governor of the Transvaal Colony to make recommendations on the development of technical and higher education in the colony. He was a member of the (British) Institution of Mining and Metallurgy (MIMM) and played a significant role in the founding of the Victoria Falls and Transvaal Power Company in 1906. During 1907-1908 he was honorary president of the Transvaal Institute of Mechanical Engineers (while W.M. Epton* was president) and contributed "Notes of a proposed new method of constructing stamp mills" to its Journal (1907/8, Vol. 6). He retired in 1911, living in France and England, but died in South Africa.