Abstract-Stability control for walking bipeds has been considered a complex task. Even two-dimensional fore-aft stability in dynamic walking appears to be difficult to achieve. In this paper we prove the contrary, starting from the basic belief that in nature stability control must be the sum of a number of very simple rules. We study the global stability of the simplest walking model by determining the basin of attraction of the Poincaré map of this model. This shows that the walker, although stable, can only handle very small disturbances. It mostly falls, either forward or backward. We show that it is impossible for any form of swing leg control to solve backward falling. For the problem of forward falling, we devise a simple but very effective rule for swing leg action: "You will never fall forward if you put your swing leg fast enough in front of your stance leg. In order to prevent falling backward the next step, the swing leg shouldn't be too far in front." The effectiveness of this rule is demonstrated with our prototype "Mike."Index Terms-Legged locomotion, passive dynamic walking, reflex, swing leg control.

This paper describes the technical principles of a high-performance force controlled robot, called the HapticMaster. It is designed as a generic platform for applications with human interaction. Therefore, it differs significantly from most industrial robots on the one hand, whereas it also differs from most haptic interfaces on the other hand due to its power. An admittance control paradigm is used, which facilitates a high joint stiffness in combination with high force sensitivity. Typical applications for the HapticMaster are found in virtual reality, haptics research, and robot rehabilitation.

Abstract-This paper describes the development of an efficient mechanical oscillator. It is capable of combining the energetic advantages of ballistic movement with cycle adjustability and active orbital control. Pneumatic artificial McKibben muscles are used as variable springs, from which the stiffness is varied in order to induce a limit cycle.

This book reports our research on pneumatic bipeds (=two-legged robots) based on the concept of passive dynamic walking. The research was done between 1998 and 2004 at Delft University of Technology, funded by the Dutch Technology Fund STW. We, Martijn Wisse and Richard van der Linde, both obtained our PhD degrees during the project under the supervision of Prof. dr. ir. H.G. Stassen and Prof. dr. F.C.T. Van der Helm. This book is a rewritten, compacted version of the combined PhD theses.The European robotics research community EURON awarded our research with the Georges Giralt PhD Award, which included an offer to publish the work as a monograph in the Springer Tracts on Advanced Robotics.This book is intended for researchers who are considering to start research on two-legged robots based on passive dynamic walking. We hope that this book will convene the key ideas behind our research. We would like you to avoid our mistakes and build on our results.This book is organized in seven chapters. The chapters 2 to 6 each present one key idea and one new robot. The background theory and computer simulations are presented where they are needed throughout the book. Some explanations may appear in more than one place so that the chapters remain mostly independent.Many people contributed to the work that we report here. Special mention goes to Arend Schwab, our teacher of multibody dynamics and stability analysis, and to Jan van Frankenhuyzen, who designed and built the robots.We much enjoyed our research work, and we hope that we can transmit some of that enthusiasm to you with this book.

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