I am trying to find a book I read recently (in the past year) about the main character being hired by an AI to take its robot along with him and travel the parallel dimensions to find the limit of the travel (or something along these lines). I also remember the story had something about the traveller not being able to carry more then a certain amount of material with them. In the story there is a massive social impact of the parallel travelling too cause some people could not travel and had to be left behind.
Thanks!