A Designing Method of the Passive Dynamic Walking Robot via Analogy with Phase Locked Loop Circuits

Recently many biped walking robots are developed, and almost all the researches about those robots adopt mass-link models to control and referring zero moment point not to fall over while walking. Here we position these conventional control methods as “model-based control”. Features of the method are that the robot moves accurate and rigid at low efficiency. So it is also important to remember that these researches also adopt other ideas to decrease their energy consumption, to absorb the impact shock of the contact, or to control the joint stiffness ...etc. For example, Honda robot “ASIMO” adopts soft material soles (Takenaka, 2001), Sony robot “SDR-4X” and Waseda university's robot controls its joint stiffness (Iribe et al, 2007) (Yamaguchi & Takanishi, 1997), and so on. So it seems important and valuable for the model-based control method to import the ideas based on the dynamics of the robots for their performance gain. On the other hand, we focus the passive dynamic walking robot which walks only by the dynamics caused by the gravity (McGeer, 1990) (Goswani et al, 1996) (Garcia et al, 1998) (Sugimoto & Osuka, 2005). Here we also position this control method which is operated by the dynamics as “dynamics-based control” method. Features of the method are that the robot moves soft and smooth at high efficiency. If the principle of the dynamics-based control is analyzed and elucidated, we will be able to apply the essence of this system to the conventional walking robot control, and also able to contribute the performance gain of walking robot control (Iribe & Osuka, 2006-2). Therefore we think that well-designed walking robots have both two above-mentioned ideas as shown in Fig.1. However, the dynamics-based control method doesn’t seems to be studied enough and does not show practical designing methods of the robot system in contrast to the model-based control method. Therefore it is important to develop robotic designing methods which are based on the ideas of the dynamics-based control. In this paper, firstly we analyze the behavior of the passive dynamic walking robot via analogy with Phase locked loop circuit which shows similar behaviors to the robot system, and ascertain the robot's gaits bifurcation and shows the chaotic behavior on the same condition which causes chaotic behaviors of Phase locked loop circuit. Secondly we ascertain that we can get initial conditions and set-up parameters which cause the desired O pe n A cc es s D at ab as e w w w .ite ch on lin e. co m