Title: Complex walking behaviours, chaos and bifurcations of a simple passive compass-gait biped model suffering from leg length asymmetry

Authors: Hassène Gritli; Nahla Khraief; Safya Belghith

Addresses: Institut Supérieur des Technologies de l'Information et de la Communication, Université de Carthage, Borj Cedria, 1164 Tunis, Tunisia; Laboratoire Robotique, Informatique et Systèmes Complexes (RISC LR16ES07), Ecole Nationale d'Ingénieurs de Tunis, Université de Tunis El Manar, BP. 37, Le Belvédère, 1002 Tunis, Tunisia ' Laboratoire Robotique, Informatique et Systèmes Complexes (RISC LR16ES07), Ecole Nationale d'Ingénieurs de Tunis, Université de Tunis El Manar, BP. 37, Le Belvédère, 1002 Tunis, Tunisia ' Laboratoire Robotique, Informatique et Systèmes Complexes (RISC LR16ES07), Ecole Nationale d'Ingénieurs de Tunis, Université de Tunis El Manar, BP. 37, Le Belvédère, 1002 Tunis, Tunisia

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.

Keywords: compass-gait model; leg length asymmetry; chaos; bifurcations; hysteresis phenomenon; Neimark-Sacker-2 bifurcation; cyclic-fold bifurcation; CFB; boundary crisis.

DOI: 10.1504/IJSPM.2018.094735

International Journal of Simulation and Process Modelling, 2018 Vol.13 No.5, pp.446 - 462

Received: 02 Jan 2018
Accepted: 27 Mar 2018
Published online: 14 Sep 2018 *

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