Robustness analysis of nonlinear biped control laws via singular perturbation theory

The gait and stability analysis of a complex biped model using nonlinear techniques is presented. The overall dynamics of the system is treated analytically using singular perturbation theory and phase plane techniques. The unperturbed dynamical system corresponds to a reduced model of the biped vehicle where only a few components play a major role in determining the gross behavior of the biped dynamics. Since the dynamics of the reduced model is relatively easy to understand analytically, the approach followed is to design control laws for the reduced biped via nonlinear limit cycles and to treat more complicated system models as perturbations to this reduced model. The reduced control law is shown to be robust to small perturbation. However, simulations indicate that the robustness to dynamical perturbation can be quite large.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">></ETX>