The analysis on period doubling gait and chaotic gait of the compass-gait biped model

The passive dynamic walking model, which can only depend on the gravity and its own inertia, presents stable, high-efficient, natural periodic gait on a slight slope. The stable periodic gait of the robot has a delicate balance of energy conversion, which makes the gait adjust itself as the parameters of the model change. In our work, the cell mapping method is combined with Newton-Raphson iteration to obtain the limit cycle of the periodic gait in the model, the track stability of the limit cycle is analyzed, and the eigenvalues change rule of Poincaré Jacobi matrix is deduced. The influence of changing parameters on the gait is analyzed and discussed by simulations on the model with different sets of parameters. The result suggests that, the location of the center of leg mass too high or too low, foot radius increase or decrease, the slope or moment of inertia increase, will lead to the occurrence of bifurcation of the gait period and chaos; while the way the gait enters chaos from period doubling bifurcation, which results from different parameters change, obeys the law all the period doubling bifurcation share, that is, it has the same Feigenbaum constant. Furthermore, the dynamic features of the robot at the entrance of the chaos are obtained by the rule of the period doubling bifurcation of the gait; meanwhile, it can be found by the analysis of the gait features in the chaos area that there is also certain periodic law in the chaotic gait.