Complex walking behaviours, chaos and bifurcations of a simple passive compass-gait biped model suffering from leg length asymmetry. (2018)

• Record Type: Journal Article
• Authors: Gritli, Hassène; Khraief, Nahla; Belghith, Safya
• Is Part Of: International journal of simulation and process modelling. Volume 13:Number 5(2018)
• Page Start: 446
• Page End: 462
• Publication Date: 2018
• Subjects: compass-gait model -- leg length asymmetry -- chaos -- bifurcations -- hysteresis phenomenon -- Neimark-Sacker-2 bifurcation -- cyclic-fold bifurcation -- CFB -- boundary crisis; Management -- Computer simulation -- Periodicals; Mathematical models -- Periodicals; Operations research -- Periodicals; Simulation methods -- Periodicals; 003.05
• Languages: English
• ISSNs: 1740-2123

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 Poincaré map.