Adaptive Dynamical Systems – A promising tool for embodied artificial intelligence

Introduction Nonlinear Dynamical Systems (NDS) are an interesting tool to devise locomotion controllers for mDOF robots, e.g. CPGs for quadrupeds [1]. Furthermore, this approach has a strong foundation based on the investigation of biological coordination tasks [7]. One of the difficulties that limits the usability of this approach to robots is the problem of how to design a suitable NDS to control a given robot and, if the NDS can be found, how to tune its parameters. Furthermore, one would like to have a certain flexibility and adaptivity in the controllers in order for them to adapt to changing body properties and non stationary, complex environments. In a " proof of principle " implementation in a simulation [2] we showed that we can extend a simple dynamical system (i.e. an oscillator) with an additional state variable and the corresponding evolution law (i.e. differential equation) in order to make it adaptive to a mechanical structure. The mechanical structure (body) and the adaptive frequency oscil-lator (controller) make up a simple adaptive locomotion system. This locomotion system is capable of adapting to changing body properties or an addition of external load. In this contribution we show that we can successfully implement these concepts in the real world. As briefly discussed in [2] we consider the therein presented system as an example of a much broader class of systems. Namely, we propose that the extension of dynamical systems by state variables with different time scales could be a useful tool for many applications in robotics, machine learning and other areas were dynamic adaptive behavior is desirable. We call such dynamical systems which are extended with additional state variables , which evolve on different (normally slower) time scales than the rest of the state variables, Multiscale Dynamical Systems. In contrast to conventional adaptive control, this systems and the feedback loops are usually strongly non-linear. This allows for interesting pattern formation capabilities. Adaptive Dynamical Systems We implement an adaptive dynamical system by using a plastic NDS, as described in the following. The controller is described by the dynamical system which has four additive contributions, i.e. the Effective flow F (q, t) is the sum of all the parts described in the following and is the effective dynamics: (1) The Intrinsic flow: F 0 (q) describes the