Recurrent Gait of Anthropomorphic, Bipedal Walkers

This thesis explores the dynamics of two bipedal, passive-walker models that are free to move in a three-dimensional environment. Specifically, two rigid-bodied walkers that can sustain anthropomorphic gait down an inclined plane with gravity being the only source of energy were studied using standard dynamical systems methods. This includes calculat-ing the stability of periodic orbits and varying the system parameter to create bifurcation diagrams and to address the persistence of a periodic solution under specific parameter vari-ations. These periodic orbits are found by implementing the Newton-Raphson root solving scheme. The dynamical systems associated with these periodic orbits are not completely smooth. Instead, they include discontinuities, such as those produced due to forces at foot contact points and during knee hyper-extension. These discontinuities are addressed in the stability calculations through appropriate discontinuity mappings. The difference between the two walker models is the number of degrees of freedom (DOF) at the hip. Humans possess three DOF at each hip joint, one DOF at each knee joint, and at least two DOF at each ankle joint. The first walker model studied had revolute joints at the hips and knees and completely locked ankles. To make the walking motion mor