Orbital analysis of passive dynamic bipeds; the effect of model parameters and stabilizing arm

In this paper the effect of different parameters on the periodic orbits of an under-actuated passive biped is studied. The system is designed to follow a periodic orbit in the phase plane, starting from an initial condition and walking down a slope. The dynamic motion of the system is cast as an optimization problem under constraints that impose the periodicity with optimal behavior. The effect of dynamics and kinematics factors such as inertia and length characteristics of the biped and slope angle on the stability and bifurcation phenomena is extensively studied. In the following, it is shown how an under-actuated arm can perfectly synchronize its stabilizing motion with walking. The effect of dynamics parameters of the arm on the locomotion of the biped, stability criteria and the robustness of the whole system is extensively investigated. The results of the paper clearly illustrate the effects of dynamics parameters as well as the stabilizing arm on the stability, energy, and step characteristics of locomotion.