Analysis and Control of the Dynamic Walking of the Compass Biped Walker Using Poincaré Maps: Comparison Between Two Design Approaches

The present work aspires to summarize and compare previous findings treating the analyze and control of the human-like passive walking dynamics of the compass-gait biped walker (CGBW). Our development is based on examining the impulsive hybrid nonlinear dynamics (IHNLD) describing the walking process of the CGBW and defining a linear dynamics around a period-1 passive hybrid limit cycle (p1-PHLC). Based on Taylor series approximation, we analytically demonstrate several expressions of the the Poincaré map (PM) and controlled Poincaré map (CPM). The control of the passive walking of the CGBW is the main objective behind this paper. Therefore, we present two approaches leading to stabilize period-1 fixed point of the PMs and particularly we will compare between two control laws and promote their low energy consumption.