Design of an explicit expression of the Poincaré map for the passive dynamic walking of the compass-gait biped model

Wafa Znegui, Hassène Gritli and Safya Belghith

Chaos, Solitons & Fractals, 2020, vol. 130, issue C

Abstract: This paper presents a design method of an explicit analytical classical expression of the Poincaré map for the passive dynamic walking (PDW) of the planar compass-gait biped model. Our methodology is based chiefly on a time-piecewise linearization of the impulsive hybrid nonlinear dynamics of the PDW around a desired one-periodic hybrid limit cycle. We start by linearizing the continuous dynamics of the swing phase and also the discrete dynamics of the impact phase. Thus, we obtain a simplified impulsive hybrid linear dynamics. By means of the first-order Taylor approximation, we design an explicit expression of the Poincaré map. Moreover, we provide a simplified expression of the Poincaré map with a reduced dimension. The expression of the Jacobian matrix of this reduced Poincaré map is also developed. Finally, some numerical results and graphical simulations are presented in order to compare between the impulsive hybrid nonlinear dynamics and the developed Poincaré map. These results show the similarity between the two models and then the efficiency and the validity of the designed Poincaré map in the analysis of the PDW of the compass-gait biped robot.

Keywords: Compass-gait biped model; Impulsive hybrid nonlinear dynamics; Hybrid limit cycle; Poincaré map; Jacobian matrix; Comparison and similarity (search for similar items in EconPapers)
Date: 2020
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (3)

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0960077919303820
Full text for ScienceDirect subscribers only

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:130:y:2020:i:c:s0960077919303820

DOI: 10.1016/j.chaos.2019.109436

Access Statistics for this article

Chaos, Solitons & Fractals is currently edited by Stefano Boccaletti and Stelios Bekiros

More articles in Chaos, Solitons & Fractals from Elsevier
Bibliographic data for series maintained by Thayer, Thomas R. ().