Design, implementation and analysis of an alternation-based Central Pattern Generator for multidimensional trajectory generation

In this paper, we introduce a multidimensional Central Pattern Generator (CPG) model with an explicit and defined basin of attraction for generating any arbitrary continuous periodic signal. Having a defined basin of attraction is highly desired, especially in robotic applications, as it provides tracking stability in addition to robustness against disturbances. The CPG model is composed of a set of phase-locked coordinated one-dimensional models; called ζζ-models. The idea behind the ζζ-model is generating any one-dimensional periodic signal by altering the behavior of an existing oscillator through two nonlinear maps. The mappings are designed in such a way that the Poincaré–Bendixson theorem is satisfied and, consequently, the desired basin of attraction is shaped. The proposed CPG model is extensively tested for generating multidimensional signals; including DC, triangular, and smooth wavy ones. The results show that the CPG model has a low tracking error in addition to being robust against disturbances within the designed basin of attraction. Finally, the proposed CPG model is successfully employed to generate the dancing motion of a situated robotic marionette.

► Central Pattern Generator (CPG) with defined and explicit basin of attraction.
► Incorporating the Poincaré–Bendixson theorem into the learning process to enforce shaping of the limit cycle behavior.
► CPG with the ability to encode any arbitrary signal of any type: smooth, DC, sharp, etc.
► Median phase based coupling for multidimensional trajectory encoding.
► Applying CPG on robotic marionette for periodic motions.