{"title":"Complex walking behaviours, chaos and bifurcations of a simple passive compass-gait biped model suffering from leg length asymmetry","authors":"H. Gritli, N. K. Haddad, S. Belghith","doi":"10.1504/IJSPM.2018.094735","DOIUrl":null,"url":null,"abstract":"This paper is concerned with the analysis of the displayed nonlinear phenomena, chaos and bifurcations, in the planar passive dynamic walking of the planar compass-gait biped model under a leg length asymmetry as it goes down an inclined surface. The passive dynamic walking of the compass-gait model is modelled with an impulsive hybrid nonlinear dynamics. In this work, we present a normalised dynamics expressed in terms of dimensionless ratios. Our analysis and simulation of the passive bipedal gaits is realised mainly through bifurcation diagrams where a normalised leg length discrepancy is adopted as the bifurcation parameter. We report the exhibition of complex behaviours, namely the period-doubling bifurcation (PDB), the cyclic-fold bifurcation (CFB), the period-doubling route to chaos, the period-remerging scheme, the boundary crisis (BC), etc. We demonstrate also the exhibition of the Neimark-Sacker-2 bifurcation by investigating the tendency of the characteristic multipliers of the Jacobian matrix of the Poincare map.","PeriodicalId":266151,"journal":{"name":"Int. J. Simul. Process. Model.","volume":"19 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2018-09-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"8","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Int. J. Simul. Process. Model.","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1504/IJSPM.2018.094735","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 8
Abstract
This paper is concerned with the analysis of the displayed nonlinear phenomena, chaos and bifurcations, in the planar passive dynamic walking of the planar compass-gait biped model under a leg length asymmetry as it goes down an inclined surface. The passive dynamic walking of the compass-gait model is modelled with an impulsive hybrid nonlinear dynamics. In this work, we present a normalised dynamics expressed in terms of dimensionless ratios. Our analysis and simulation of the passive bipedal gaits is realised mainly through bifurcation diagrams where a normalised leg length discrepancy is adopted as the bifurcation parameter. We report the exhibition of complex behaviours, namely the period-doubling bifurcation (PDB), the cyclic-fold bifurcation (CFB), the period-doubling route to chaos, the period-remerging scheme, the boundary crisis (BC), etc. We demonstrate also the exhibition of the Neimark-Sacker-2 bifurcation by investigating the tendency of the characteristic multipliers of the Jacobian matrix of the Poincare map.