Optimization of the switching surface for the simplest passive dynamic biped

Recently, it has been proved that a different switching surface can preserve the walking trajectory while varying the walking stability [1], [2]. In this paper, by employing the simplest passive dynamic biped, we optimize the switching surface to maximize the robot´s stability. Here, the stability measure is preferably the size of the basin of attraction, i.e. the collection of all possible initial conditions leading to the system´s equilibrium point. Numerical investigations indicate that the maximum stability is obtained for neither the highest nor the lowest walking speed.