A Method to Estimate the Basin of Attraction of the System with Impulse Effects: Application to the Biped Robots

摘要

A new method is presented for the estimation of the basin of attraction of the system with impulse effects. This method is called Poincare-like-alter-cell-to-cell mapping method. This method synthesizes and generalizes the theories of the simple cell mapping and the Poincare mapping. Since the robustness of the system can be estimated by the size of the basin of attraction, then the optimal configurable parameter can be estimated by using this method. In the end, the basin of attraction of the simplest walking model is obtained with this method, when the mass proportion of upper legs and lower legs is increased. Simulation tests verify the validity of this method. The simulations show that the size of basin of attraction of the simplest walking model diminishes with increasing the configurable parameter that is mass proportion of upper legs and lower legs. In addition, the size of basin of attraction of the system with impulse effects is not directly related to the convergence rate of recovering from a small disturbance.