Abstract
An indicator of a passive biped walker’s global stability is its domain of attraction, which is usually estimated by the simple cell mapping method. It needs to calculate a large number of cells’ Poincare mapping result in the estimating process. However, the Poincare mapping is usually computationally expensive and time-consuming due to the complex dynamical equation of the passive biped walker. How to estimate the domain of attraction efficiently and reliably is a problem to be solved. Based on the simple cell mapping method, an improved method is proposed to solve it. The proposed method uses the multiple iteration algorithm to calculate a stable domain of attraction and effectively decreases the total number of Poincare mappings. Through the simulation of the simplest passive biped walker, the improved method can obtain the same domain of attraction as that calculated using the simple cell mapping method and reduce calculation time significantly. Furthermore, this improved method not only proposes a way of rapid estimating the domain of attraction, but also provides a feasible tool for selecting the domain of interest and its discretization level.
Highlights
Due to the energy-efficient of passive dynamic walking, the study of the passive biped walker is a popular area of scientific research [1, 2]
The domain covered by all failure cells is called Domain Of Failure (DOF) and the domain covered by all candidate cells is called Domain Of Candidate (DOC)
For showing the boundaries of DOF and DOC clearly, the candidate cells are not shown in cell deletion procedure and the failure cells are not shown in cell refinement procedure
Summary
Due to the energy-efficient of passive dynamic walking, the study of the passive biped walker is a popular area of scientific research [1, 2]. The stable gait is usually a periodic or cyclic gait, which is shown as a manifold in the state space or a limit cycle in the two-dimension phase diagram [3]. These passive biped walkers will lose their stability when they are moving from a wrong initial state or encountering a very small disturbance [4]. The detailed structure of DOA is an important aspect of studying the nonlinear properties of the passive biped walker [8, 9]
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