Abstract
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 ζ -models. The idea behind the ζ -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.
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