How active is the current research scene on the application of algebraic and differential topology to robotics? I have spent a decent portion of time researching and reading introductory papers, but have struggled to determine if this field is very active or not. I've come to understand that algebraic topology as a field has slown down in recent times and given way to algebraic geometry, but I've also read that more computational applications of the former (Topological Data Analysis, for instance) are enjoying considerable attention.
I suppose a side question is also: to all the researchers on this site, how important is it to factor in how active a field of research is before planning to enter it? Should I follow my heart etc. etc., or is a pragmatic approach best?
For context: I'm a recent graduate of a Mathematics/Electrical Engineering double bachelor's degree, currently working at a robotics and automation firm, and I'm intensely interested in algebraic topology. I'm strongly considering pursuing postgrad studies in mathematics and then possibly onto academia, and this is the research avenue I'm currently most interested in, but I want to have some perspective about the state of the field.