That assumes that a psyche to study will be identifiable in artificially intelligent computing machinery. If we assume that, then it makes sense that psychology for these intelligences may diverge from the study of the human psyche, since the result of AI research won't necessarily produce a detailed simulation of normal human psycho-social characteristics but rather something similar.
To start this new fork of psychology, we'd need AI more sophisticated than current AI which some consider little more than pattern matching and surface fitting. THe critics of the AI hype would say, "We need a new branch of AI first. Then a new branch of psychology might be needed to promote AI mental health."
When the interaction between humans and machines enters the picture, the topic is not necessarily psychology but cybernetics. We can study the computer reaction to humans and the human reaction to computers. Neil Postman's Technopoly was one of the early works. Even the books about the psychological complications resulting from industrialization touched on the beginnings of the effects of automation.
The AI reaction to humans is the side of the question's proposal that hasn't received much attention and maybe should. Just a simple example illustrates. How does a deep network respond to a change in personnel training it, with different methodology in preparation of data and the tweaking of hyper-parameters? Will they perform poorly at first, as they adjust? What is the actual mechanism of adjustment, if any exist?
It's a little out there at this point, but not so as robotics develops further.
Will an AV get disoriented if sold to a new owner in a different location? Will any location dependent training need to be reset? Will household robotics be like cats, where they hide and react oddly when the owner moves to a new house or apartment?
If so, what questions it will address and will try to solve?