Engineering limit cycle systems:adaptive frequency oscillators and applications to adaptive locomotion control of compliant robots

In this thesis, we present a dynamical systems approach to adaptive controllers for locomotion control. The approach is based on a rigorous mathematical framework using nonlinear dynamical systems and is inspired by theories of self-organization. Nonlinear dynamical systems such as coupled oscillators are an interesting approach for the on-line generation of trajectories for robots with many degrees of freedom (e.g. legged locomotion). However, designing a nonlinear dynamical system to satisfy a given specification and goal is not an easy task, and, hitherto no methodology exists to approach this problem in a unified way. Nature presents us with satisfactory solutions for the coordination of many degrees of freedom. One central feature observed in biological subjects is the ability of the neural systems to exploit natural dynamics of the body to achieve efficient locomotion. In order to be able to exploit the body properties, adaptive mechanisms must be at work. Recent work has pointed out the importance of the mechanical system for efficient locomotion. Even more interestingly, such well suited mechanical systems do not need complicated control. Yet, in robotics, in most approaches, adaptive mechanisms are either missing or they are not based on a rigorous framework, i.e. they are based on heuristics and ad-hoc approaches. Over the last three decades there has been enormous progress in describing movement coordination with the help of Synergetic approaches. This has led to the formulation of a theoretical framework: the theory of dynamic patterns. This framework is mathematically rigorous and at the same time fully operational. However, it does not provide any guidelines for synthetic approaches as needed for the engineering of robots with many degrees of freedom, nor does it directly help to explain adaptive systems. We will show how we can extend the theoretical framework to build adaptive systems. For this purpose, we propose the use of multi-scale dynamical systems. The basic idea behind multi-scale dynamical systems is that a given dynamical system gets extended by additional slow dynamics of its parameters, i.e. some of the parameters become state variables. The advantages of the framework of multi-scale dynamical systems for adaptive controllers are 1) fully dynamic description, 2) no separation of learning algorithm and learning substrate, 3) no separation of learning trials or time windows, 4) mathematically rigorous, 5) low dimensional systems. However, in order to fully exploit the framework important questions have to be solved. Most importantly, methodologies for designing the feedback loops have to be found and important theoretical questions about stability and convergence properties of the devised systems have to be answered. In order to tackle this challenge, we first introduce an engineering view on designing nonlinear dynamical systems and especially oscillators. We will highlight the important differences and freedom that this engineering view introduces as opposed to a modeling one. We then apply this approach by first proposing a very simple adaptive toy-system, consisting of a dynamical system coupled to a spring-mass system. Due to its spring-mass dynamics, this system contains clear natural dynamics in the form of resonant frequencies. We propose a prototype adaptive multi-scale system, the adaptive frequency oscillator, which is able to adapt its intrinsic frequency to the resonant frequency of the body dynamics. After a small sidetrack to show that we can use adaptive frequency oscillators also for other applications than for adaptive controllers, namely for frequency analysis, we then come back to further investigation of the adaptive controller. We apply the same controller concept to a simple spring-mass hopper system. The spring-mass system consists of a body with two legs attached by rotational joints. The legs contain spring-damper elements. Finally, we present results of the implementation of the controller on a real robot, the experimental robot PUPPY II. This robot is a under-actuated robot with spring dynamics in the knee joints. It will be shown, that due to the appropriate simplification and concentration on relevant features in the toy-system the controller concepts works without a fundamental change on all systems from the toy system up to the real robot

In silico case studies of compliant robots: AMARSI deliverable 3.3

In the deliverable 3.2 we presented how the morphological computing ap- proach can significantly facilitate the control strategy in several scenarios, e.g. quadruped locomotion, bipedal locomotion and reaching. In particular, the Kitty experimental platform is an example of the use of morphological computation to allow quadruped locomotion. In this deliverable we continue with the simulation studies on the application of the different morphological computation strategies to control a robotic system

The Future of Humanoid Robots

This book provides state of the art scientific and engineering research findings and developments in the field of humanoid robotics and its applications. It is expected that humanoids will change the way we interact with machines, and will have the ability to blend perfectly into an environment already designed for humans. The book contains chapters that aim to discover the future abilities of humanoid robots by presenting a variety of integrated research in various scientific and engineering fields, such as locomotion, perception, adaptive behavior, human-robot interaction, neuroscience and machine learning. The book is designed to be accessible and practical, with an emphasis on useful information to those working in the fields of robotics, cognitive science, artificial intelligence, computational methods and other fields of science directly or indirectly related to the development and usage of future humanoid robots. The editor of the book has extensive R&D experience, patents, and publications in the area of humanoid robotics, and his experience is reflected in editing the content of the book