Ah, la recherche! Du temps perdu. (source)
This is a summary of my general research interests, along with some highlights of recent activity.
General problem domains
My main interest lies in robotics, which, from my point of view, includes all interactions of an intelligent agent with the real world. I believe that in my lifetime robotics will lead to some form of strong AI, and I hope to retire as a robopsychologist. While I'm waiting for that to happen, I'm particularly interested in perception problems.
I am fascinated by cybernetics, in its original meaning of comparative study of artificial and neural information processing: nature's solutions are often much more robust than the current state of the art.
Approach / philosophy
Simple is better than complicated. In robotics applications, this means staying close to the measurement space.
Formal is better than informal. Also, "formal" usually implies "simple", because you usually can prove something only if it is simple enough.
Data before models, as long as formal results can still be proved.
Open is better than closed. Reproducible research is a worthy goal. I predict that, in 15 years, it will be unthinkable to publish in engineering research or computational sciences without publishing the full source code and data.
Favorite theories and methods
My first love is estimation and filtering. At Caltech I was infected with people's enthusiasm on differential geometry.
When you apply geometry to estimation you get information geometry (Wikipedia summary, serious introduction).
When you apply estimation to geometry you get intrinsic estimation (see for example the theory of shape spaces, and my favorite paper).
I'm interested in both combinations (and both will provide a lifetime learning experience).