Bernd Porr, Florentin Wörgötter
We develop a systems theoretical treatment of a behavioural system that interacts with its environment in a closed loop situation such that its mo- tor actions inﬂuence its sensor inputs. The simplest form of a feedback is a reﬂex. Reﬂexes occur always “too late”; i.e., only after a (unpleas- ant, painful, dangerous) reﬂex-eliciting sensor event has occurred. This deﬁnes an objective problem which can be solved if another sensor input exists which can predict the primary reﬂex and can generate an earlier reaction. In contrast to previous approaches, our linear learning algo- rithm allows for an analytical proof that this system learns to apply feed- forward control with the result that slow feedback loops are replaced by their equivalent feed-forward controller creating a forward model. In other words, learning turns the reactive system into a pro-active system. By means of a robot implementation we demonstrate the applicability of the theoretical results which can be used in a variety of different areas in physics and engineering.