Biped gait optimization using spline function based probability model

A new estimation of distribution algorithm (EDA) with spline kernel function (EDA_S) is proposed to optimize biped gait for a nine-link humanoid robot. Gait synthesis of the biped locomotion is firstly formulated as a multi-constraint optimization problem with consideration of two objectives, including zero-moment point (ZMP) for dynamically stable locomotion and driving torque for energy efficiency. The parameters to be optimized are joint coordinates at transition poses between three successive phases. Rather than searching in joint angle permutation space directly, the proposed method approximates the probability distribution by Catmull-Rom (CR) cubic spline function and updates them with gradient descent learning strategy. The effectiveness of EDA_S for biped gait optimization has been successfully tested on the simulated model of a humanoid soccer robot. It is shown that the flexible kernel with the updating rule is able to remarkably accelerate the learning speed with comparison to the traditional EDA