Analysis of period doubling bifurcation and chaos mirror of biped passive dynamic robot gait |
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Authors: | Jie Zhao XiaoGuang Wu XiZhe Zang and JiHong Yan |
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Institution: | State Key Laboratory of Robotics and System, Harbin Institute of Technology, Harbin 150080, China |
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Abstract: | With a reasonable parameter configuration, the passive dynamic walking model has a stable, efficient, natural periodic gait,
which depends only on gravity and inertia when walking down a slight slope. In fact, there is a delicate balance in the energy
conversion in the stable periodic gait, making the gait adjustable by changing the model parameters. Poincaré mapping is combined
with Newton-Raphson iteration to obtain the numerical solution of the final state of the passive dynamic walking model. In
addition, a simulation on the walking gait of the model is performed by increasing the slope step by step, thereby fixing
the model’s parameters synchronously. Then, the gait features obtained in the different slope stages are analyzed and discussed,
the intrinsic laws are revealed in depth. The results indicate that the gait can present features of a single period, doubling
period, the entrance of chaos, merging of sub-bands, and so on, because of the high sensitivity of the passive dynamic walking
to the slope. From a global viewpoint, the gait becomes chaotic by way of period doubling bifurcation, with a self-similar
Feigenbaum fractal structure in the process. At the entrance of chaos, the gait sequence comprises a Cantor set, and during
the chaotic stage, sub-bands in the final-state diagram of the robot system present as a mirror of the period doubling bifurcation. |
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Keywords: | period doubling bifurcation chaos fractals passive dynamic walking final-state diagram Feigenbaum constant |
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