A Multi-rhythmic Oscillator Model that Can Integrate Motion Stabilization with Motion Exploration

Abstract

Central pattern generators (CPGs) have been increasingly attracting roboticists in the hope that they enable robots to realize truly supple and agile locomotion under real world constraints. Thus far, various CPG models have been proposed, particularly in terms of motion stabilization against external perturbations, i.e., limit cycle behavior. On the other hand, biological CPGs have another crucial aspect that cannot be neglected, i.e., motion exploration. Here, note that motion stabilization and motion exploration should be performed in different time-scales. Now the following questions arise: how can different time-scales be embedded into a single CPG effectively?; and what is a good mathematical tool for describing the coexistence of different time-scales? To overcome these problems, this paper introduces a novel oscillator model in which the two functions of motion stabilization and motion exploration can be seamlessly integrated by exploiting the concept of multi-rhythmicity, without relying on any hierarchical structure, which in turn enables that learning is an integral part of the motor control system. We applied this model to the learning of hopping motion as a practical example. Simulation results indicate that the robot can successfully perform online learning without the need for a separation between learning and performance phases.