Nonlinear structure of escape-times to falls for a passive dynamic walker on an irregular slope: Anomaly detection using multi-class support vector machine and latent state extraction by canonical correlation analysis

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.