Application of hybrid van der Pol-Rayleigh oscillators for modeling of a bipedal robot

A large number of degrees of freedom is involved in human locomotion and well-coordinated movements of these degrees of freedom is essential. The main part of this coordination occurs in the central nervous system, which generates signals according to the desired gait. Nervous networks in the spinal marrow, known as central pattern generators (CPGs), are capable to produce rhythmic movements. A set of nonlinear oscillators can be used in control systems of locomotion as pattern generator, providing approximate trajectories for the legs. The objective of this work is the application of a coupled hybrid van der Pol-Rayleigh oscillators system for modeling of a bipedal robot. We analyzed a 2D model, with the three most important determinants of gait, that performs movements in the sagittal plane. Using oscillators with integer relation of frequency, we determined the response as a function of time and the stable limit cycles of the network formed by three oscillators, showing the behavior of knee and hip angles. From plotted graphics, the system provided excellent results when compared to experimental analysis, and we concluded that the use of coupled hybrid van der Pol-Rayleigh oscillators can represent an excellent method to signal generation, allowing their application for feedback control of a walking machine, presenting optimized functioning in relation to the systems that use only van der Pol or Rayleigh oscillators.