An Enhanced Poincaré Map Expression for the Passive Dynamic Walking of the Compass-Gait Biped Robot

摘要

This paper presents a continuous work of designing a classical analytical expression of the Poincaré map to improve our research related to the passive dynamic walking (PDW) of the planar compass-gait biped robot. The demonstration illustrated in this paper provides the steps and simulation results allowing to consistently modeling the expression of the Poincaré map. The design method we followed is based on the linearization of the flow of the impulsive hybrid nonlinear dynamics of the passive biped robot around a desired one-periodic hybrid limit cycle. Thus, via the second-order Taylor approximation, we design an explicit expression of the Poincaré map. We develop also an equation providing the step period of the biped locomotion. In the end, we present some numerical and graphical simulation results to compare between the features exhibited with the impulsive hybrid nonlinear dynamics and the developed Poincaré map and also the previously designed Poincaré map using the first-order Taylor approximation. These results show the efficiency and the validity of the designed Poincaré map in the analysis of the PDW of the compass-gait biped robot.