We propose using the kernel dimension reduction (KDR) to extract a low-dimensional feature space for humanoid locomotion tasks. Although humanoids have many degrees of freedom, task relevant feature spaces can be much smaller than the number of dimension of the original state space. We consider an application of the proposed approach to improve the locomotive performance of humanoid robots using an extracted low-dimensional state space. To improve the locomotive performance, we use a reinforcement learning (RL) framework. While RL is a useful non-linear optimizer, it is usually difficult to apply RL to real robotic systems - due to the large number of iterations required to acquire suitable policies. In this study, we use the extracted low-dimensional feature space for RL so that the learning system can improve task performance quickly. The kernel dimension reduction method allows us to extract the feature space even if the task relevant mapping is non-linear. This is an essential property to improve humanoid locomotive performance since stepping or walking dynamics involves highly nonlinear dynamics. We show that we can improve stepping and walking policies by using a RL method on an extracted feature space by using KDR.
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