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 de...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.展开更多
In this paper, we modeled a simple planer passive dynamic biped robot without knee with point feet. This model has a stable, efficient and natural periodic gait which depends on the values of parameters like slope ang...In this paper, we modeled a simple planer passive dynamic biped robot without knee with point feet. This model has a stable, efficient and natural periodic gait which depends on the values of parameters like slope angle of inclined ramp, mass ratio and length ratio. The described model actually is an impulse differential equation. Its corresponding poincare map is discrete case. With the analysis of the bifurcation properties of poincare map, we can effectively understand some feature of impulse model. The ideas and methods to cope with this impulse model are common. But, the process of analysis is rigorous. Numerical simulations are reliable.展开更多
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)
文摘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.
文摘In this paper, we modeled a simple planer passive dynamic biped robot without knee with point feet. This model has a stable, efficient and natural periodic gait which depends on the values of parameters like slope angle of inclined ramp, mass ratio and length ratio. The described model actually is an impulse differential equation. Its corresponding poincare map is discrete case. With the analysis of the bifurcation properties of poincare map, we can effectively understand some feature of impulse model. The ideas and methods to cope with this impulse model are common. But, the process of analysis is rigorous. Numerical simulations are reliable.
