A new Poincaré map for investigating the complex walking behavior of the compass-gait biped robot

The planar compass-gait biped robot is recognized by its simple passive morphological structure and by a complex dynamic walking system modeled by an impulsive hybrid nonlinear dynamics. Such complexity inhibits investigating the biped locomotive mechanism by means of the Poincar & eacute; map. Nevertheless, it is very difficult (and even impossible) to establish the exact closed form of the Poincar & eacute; mapping. This paper is concerned with the development of an improved closed-form analytical expression of the impact-to-impact Poincar & eacute; map for analyzing the complex walking behavior of the passive-dynamics biped walker and its stability. Our methodology consists in linearizing and then approximating the hybrid dynamics of the compass-gait biped robot around a predefined hybrid limit cycle. Based on the second-order Taylor series expansion, we design first an enhanced closed-form expression of the Poincar & eacute; map as well as an analytical expression for the computation of the step period of the bipedal locomotion. Furthermore, a simplification of these developed expressions is presented by decreasing the dimension. We provide also an expression of the Jacobian matrix for investigating the stability of the period-1 fixed point of the designed simplified Poincar & eacute; map. At the end of this work, we illustrate some simulation results in order to evaluate the validity of the new developed expression of the impact-to-impact Poincar & eacute; map in analyzing the stability and the complex walking behavior of passive-dynamics compass biped robot. (c) 2021 Elsevier Inc. All rights reserved.

Automated summary

This paper aims to develop an improved closed-form analytical expression for analyzing the complex walking behavior and stability of a passive-dynamics biped walker. By linearizing and approximating the hybrid dynamics, an enhanced closed-form expression of the Poincaré map and an analytical expression for the computation of step period are designed. A simplification of these expressions is achieved by decreasing dimension and providing a Jacobian matrix expression for investigating the stability of the designed simplified Poincaré map.