I understand anthrobotics as the study of human-robot intermixing.
As far as I can tell, the term anthrobotics was originally coined by Mark Rosheim in a paper entitled “Design of An Omnidirectional Arm”, in 1990. Rosheim says he derived the term from ‘anthropomorphic and robotics to distinguish the new generation of dexterous robots from its simple industrial robot forbears.’ The word gained wider recognition as a result of its use in the title of Rosheim’s subsequent book Robot Evolution: The Development of Anthrobotics.
A wider definition of the term anthrobotics has been proposed, in which the meaning is derived from anthropology rather than anthropomorphic. This site understands anthrobotics as a cross-disciplinary reflection on the 21st century merging of humans and robots.