Coregionalised Locomotion Envelopes - A Qualitative Approach

‘Sharing of statistical strength’ is a phrase often employed in machine learning and signal processing. In sensor networks, for example, missing signals from certain sensors may be predicted by exploiting their correlation with observed signals acquired from other sensors [1]. For humans, our hands move synchronously with our legs, and we can exploit these implicit correlations for predicting new poses and for generating new natural-looking walking sequences. We can also go much further and exploit this form of transfer learning, to develop new control schemas for robust control of rehabilitation robots. In this short paper we introduce coregionalised locomotion envelopes a method for multi-dimensional manifold regression, on human locomotion variates. Herein we render a qualitative description of this method. We have previously considered novel control strategies for powered ankle-foot prostheses, using a data-driven approach, which employs a combination of Gaussian processes regression and impedance control [2]. Therein we learned the nonlinear functions, which dictate how locomotion variables temporally evolve using the aforementioned nonparametric method, and regress that surface over several velocities to create a manifold, per variable. The joint set of manifolds, as well as the temporal evolution of the gait-cycle duration is what we termed a locomotion envelope. For full notational and methodological details, please consult that paper, as we build upon it extensively herein and will not repeat background material. The problem with our initial approach is that it did not consider the dependency (or correlation) of the input training variables or the output training variables, instead, assuming that regression variates are independent (strictly i.i.d.). Our initial approach is not an uncommon first pass. Indeed, consider the remarks by Mai & Commuri [4] on the topic of commercially available below-knee controlled prostheses: In general, control algorithms neglect the dynamics of the ankle joint, the interaction of the ankle with the remaining healthy joints of the residual limb, and the effect of the ground reaction torque. These devices are based on the linearized dynamics of the joint and use proportional-derivative control with fixed control gains. ∗Corresponding author. ar X iv :1 80 3. 04 96 5v 1 [ st at .M L ] 1 3 M ar 2 01 8