An oscillator model that enables motion stabilization and motion exploration by exploiting multi-rhythmicity

Central pattern generators (CPGs) have been increasingly attracting the attention of roboticists in the hope that they will 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 (e.g., Higher Center), which in turn enables that learning is the time evolution of a dynamical system (motor control system) that integrates motion exploration with motion stabilization. We applied this model to the learning of hopping motion as a practical example. Simulation and experimental results indicate that the robot can successfully perform online learning without the need for a separation between learning and performance phases.