Dynamic modeling and numerical simulations of a passive robotic walker using Euler-Lagrange method

The two main important factors to be considered while designing an efficient biped robot are human like gait cycle and energy efficiency. The researchers have sought the solution through passive dynamic walking which can provide highly energy efficient model for biped locomotion exhibiting human like gait under gravity. By adding actuation at some joints, the passive dynamic walking robot can walk stably on level ground. In this paper, we present numerical simulation of a simple robotic dynamic walker using Matlab. We derived the equation of motion using Euler-Lagrange method. We first demonstrate that a simple passive biped walker, vaguely resembling human legs, can walk down a shallow slope without any actuation and control. Later, we extended the passivity property to active dynamic walkers on level ground. Our model is the simplest special case of the passive-dynamic models pioneered by McGeer (1990a). It has two rigid massless legs hinged at the hip, a pointmass at the hip, and point-masses at the feet. After nondimensionalizing the governing equations, the model has only one free design parameter, the ramp slope γ. This model shows stable walking modes similar to more elaborate models, but allows some use of analytic methods to study its dynamics.