Aroudi, A., Debbat, M. and Martinez-Salamero, L. (2007) Poincaré Maps Modeling and Local Orbital Stability Analysis of Discontinuous Piecewise Affine Periodically Driven Systems. Nonlinear Dynamics, 50, 431-445.
http://dx.doi.org/10.1007/s11071-006-9190-1

has been cited by the following article:

• TITLE: Influence of Slope Angle on the Walking of Passive Dynamic Biped Robot

  AUTHORS: Nita H. Shah, Mahesh A. Yeolekar

  KEYWORDS: Biped Robot, Limit Cycle Walking, Passive Dynamic Walking, Poincare Map, Orbital Stability, Bifurcation

  JOURNAL NAME: Applied Mathematics, Vol.6 No.3, March 5, 2015

  ABSTRACT: In this paper, we modeled a simple planer passive dynamic biped robot without knee with point feet. This model has a stable, efficient and natural periodic gait which depends on the values of parameters like slope angle of inclined ramp, mass ratio and length ratio. The described model actually is an impulse differential equation. Its corresponding poincare map is discrete case. With the analysis of the bifurcation properties of poincare map, we can effectively understand some feature of impulse model. The ideas and methods to cope with this impulse model are common. But, the process of analysis is rigorous. Numerical simulations are reliable.