A Dynamical Systems Approach to Learning: A Frequency-Adaptive Hopper Robot

We present an example of the dynamical systems approach to learning and adaptation. Our goal is to explore how both control and learning can be embedded into a single dynamical system, rather than having a separation between controller and learning algorithm. First, we present our adaptive frequency Hopf oscillator, and illustrate how it can learn the frequencies of complex rhythmic input signals. Then, we present a controller based on these adaptive oscillators applied to the control of a simulated 4-degrees-of-freedom spring-mass hopper. By the appropriate design of the couplings between the adaptive oscillators and the mechanical system, the controller adapts to the mechanical properties of the hopper, in particular its resonant frequency. As a result, hopping is initiated and locomotion similar to the bound emerges. Interestingly, efficient locomotion is achieved without explicit inter-limb coupling, i.e. the only effective inter-limb coupling is established via the mechanical system and the environment. Furthermore, the self-organization process leads to forward locomotion which is optimal with respect to the velocity/power ratio.