Dynamical Analysis of a Biped Locomotion CPG Modelled by Means of Oscillators

The study of mechanisms like mechanical members intends not only to build autonomous robots, but also to help in the rehabilitation of human being. The study of locomotion to take part in this context, and has been intensively studied since the second half of 20th century. An ample vision of the state of the technique up to 1990 can be found in works as Raibert (1986) and Vukobratovic et al. (1990). Year after year, from technological advances, based on theoretical and experimental researches, the man tries to copy or to imitate some systems of the human body. It is the case, for example, of the central pattern generator (CPG), responsible for the production of rhythmic movements. Modelling of this CPG can be made by means of coupled oscillators, and this system generates patterns similar to human CPG, becoming possible the human gait simulation. There are some significant works about the locomotion of vertebrates controlled by central pattern generators: Grillner (1985), and Pearson (1993). From a model of two-dimensional locomotor, oscillators with integer relation of frequency can be used for simulating the behaviour of the hip angle and of the knees angles. Each oscillator has its own parameters and the link to the other oscillators is made through coupling terms. We intend to evaluate a system with coupled van der Pol oscillators. Some previous works about CPGs using nonlinear oscillators, applied in the human gait simulation, can be seen in Bay & Hemami (1987), Zielinska (1996), Dutra et al. (2003), Pina Filho (2005), and Pina Filho (2008). The objective of this work is to analyze the dynamics of this coupled oscillators system by means of bifurcation diagrams and Poincaré maps. From the analysis and graphs generated in MATLAB, it was possible to evaluate some characteristics of the system, such as: sensitivity to the initial conditions, presence of strange attractors and other phenomena of the chaos.