Online Discrimination of Nonlinear Dynamics with Switching Differential Equations

TL;DR

This paper introduces a model for recognizing different nonlinear dynamic processes, such as walking or running, in real-time by combining switching differential equations with brain-inspired mechanisms, enabling online discrimination of motions.

Contribution

It proposes a novel switching nonlinear differential equation model using Hopfield networks and dynamic primitives, suitable for real-time inference of dynamic states.

Findings

Successful online discrimination of walking and running in synthetic data.

Effective application of unscented Kalman filter for real-time inference.

Model capable of handling transitions between different dynamic processes.

Abstract

How to recognise whether an observed person walks or runs? We consider a dynamic environment where observations (e.g. the posture of a person) are caused by different dynamic processes (walking or running) which are active one at a time and which may transition from one to another at any time. For this setup, switching dynamic models have been suggested previously, mostly, for linear and nonlinear dynamics in discrete time. Motivated by basic principles of computations in the brain (dynamic, internal models) we suggest a model for switching nonlinear differential equations. The switching process in the model is implemented by a Hopfield network and we use parametric dynamic movement primitives to represent arbitrary rhythmic motions. The model generates observed dynamics by linearly interpolating the primitives weighted by the switching variables and it is constructed such that standard filtering algorithms can be applied. In two experiments with synthetic planar motion and a human motion capture data set we show that inference with the unscented Kalman filter can successfully discriminate several dynamic processes online.