In this paper we regard legged locomotion (e.g., running) as adaptive vibration, which is capable of adapting to changes in internal parameters and in the external environment. We propose control concepts for such adaptive running in general, and present a theoretical study of the bounding locomotion of a quadruped robot according to the proposed control concepts. In our control method, a forced vibratory system with a synchronization function is constructed by using a rhythm generator and a torque generator. The states of both generators are modified by delayed feedback control (DFC) using a stance phase period measured by contact sensors. Such sensory feedback to both generators makes the system adaptive to changes in the physical parameters and also adaptive to changes in terrain. The effectiveness of the proposed method was confirmed by simulations using a quadruped robot with an active hip joint and a passive knee joint in each leg. MPEG footage of these simulations can be seen at: http://www.kimura.is.uec.ac.jp/running.
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