Disturbance rejection is one of the most important abilities required for biped walkers. In this study, we propose a method for dynamic programming of biped walking and apply it to a simple passive dynamic walker (PDW) on an irregular slope. The key of the proposed approach is to employ the transient dynamics of the walker just before approaching the falling state in the absence of any controlling input, and to derive the optimal control policy in the low-dimensional latent space. In recent our study, we found that such transient dynamics deeply relates to the basin of attraction for a stable gait. By patching latent coordinates to such a structures in each Poincaré section and defining the reward function according to the survive time of the transient dynamics, so-called escape-times, we construct a Markov decision process (MDP) for the PDW and obtain an optimal policy using a dynamic programming (DP). We will show that the proposed method actually succeeds in controlling the PDW even if the degree of disturbance is relatively large and the dimensionality of coordinates is reduced to lower ones.

Falls that occur during walking are a significant problem from the viewpoints of both medicine and robotics engineering. It is very important to predict falls in order to prevent the falls or minimize the ensuing damage from them. In this study, we investigate the structure of the escape-times from walking to falling of a passive dynamic biped walker on a slope in a 2D plane with irregularities. We find that the structure lies on a manifold with high nonlinearity in state space that cannot be analyzed by linear methods under the assumption of a Gaussian distribution. Therefore, we first apply an extension of the support vector machine (SVM) to characterize its nonlinear structure, which enables us to predict imminent falls. Next, we find a latent space which describes the essential dynamics of the passive walker in a lower-dimensional space using canonical correlation analysis (CCA). There is wide applicability of this work for monitoring walking anomalies of both robots and human beings.