A Simple, Adaptive Locomotion Toy-System

In order to make the transfer of biological principles to engineering problems successful, it is important to study the fundamental properties of biological systems. The goal is to arrive with useful abstractions that are (1) implementable, (2) testable by experiments and sample implementations, (3) retain the, for the engineering problems, essential good properties and features of the biological systems. At BIRG, we are interested in the fundamentals of locomotion control and their possible applications to robotics. In this contribution, we present a simple, adaptive locomotion toy system that is of oscillatory nature. It is composed of two parts: an adaptive controller based on a nonlinear oscillator, and a mechanical system made of two blocks attached by an active and a passive spring. The controller is designed to be robust against perturbations, and to adapt its locomotion control to changing body kinematics or added external load. The tools to develop such a toy-system are a 2-scale nonlinear dynamical system -- a Hopf oscillator with adaptive frequency -- and a understanding of synchronization behavior of oscillators. A further central ingredient that will be discussed is the concept of asymmetric friction forces. We show that the system possess es several critical parameters. It is illustrated that the bifurcations connected with some of these parameters can be identified as non-smooth phase transitions and power law behavior. Links to biology and possible applications to robotic s are discussed.