Analysis of period doubling bifurcation and chaos mirror of biped passive dynamic robot gait  

作　　者：ZHAO Jie WU XiaoGuang ZANG XiZhe YAN JiHong 

机构地区：[1]State Key Laboratory of Robotics and System, Harbin Institute of Technology, Harbin 150080, China

出　　处：《Chinese Science Bulletin》2012年第14期1743-1750,共8页

基　　金：supported by the National Natural Science Foundation of China (60905049);the self-managed Project of State Key Laboratory of Robotic Technology and System in Harbin Institute of Technology(200804C)

摘　　要：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.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. Poincar6 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 parame- ters 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 fi- nal-state diagram of the robot system present as a mirror of the period doubling bifurcation.

关 键 词：倍周期分岔 步态分析 机器人系统 CANTOR集 模型参数 混沌 动态行走 参数配置 

分 类 号：TP242[自动化与计算机技术—检测技术与自动化装置] O415.5[自动化与计算机技术—控制科学与工程]