Filtering with rhythms: Application to estimation of gait cycle

Abstract

The aim of this paper is to describe a coupled oscillator model for Bayesian inference. The coupled oscillator model comprises of a large number of oscillators with meanfield coupling. The collective dynamics of the oscillators are used to solve an inference problem: the empirical distribution of the population encodes a 'belief state' (posterior distribution) that is continuously updated based on noisy measurements. In effect, the coupled oscillator model works as a particle filter.The framework is described here with the aid of a model problem involving estimation of a walking gait cycle. For this problem, the coupled oscillator particle filter is developed, and demonstrated on experimental data taken from an Ankle-foot Orthosis (AFO) device.

Synchronization in complex networks of phase oscillators: A survey

“…Since alternating current (AC) circuits are naturally modeled by equations similar to (1), some electric applications are found in structure-preserving (Bergen and Hill, 1981;Sauer and Pai, 1998) and networkreduced power system models (Chiang et al, 1995;Dörfler and Bullo, 2012b), and droop-controlled inverters in microgrids (Simpson-Porco et al, 2013). Algorithmic applications of the coupled oscillator model (1) include limit-cycle estimation through particle filters (Tilton et al, 2012), clock synchronization in decentralized computing networks (Simeone et al, 2008;Baldoni et al, 2010;, central pattern generators for robotic locomotion (Aoi and Tsuchiya, 2005;Righetti and Ijspeert, 2006;Ijspeert, 2008), decentralized maximum likelihood estimation (Barbarossa and Scutari, 2007), and human-robot interaction (Mizumoto et al, 2010). Further envisioned applications of oscillator networks obeying equations similar to (1) include generating music (Huepe et al, 2012), signal processing (Shim et al, 2007), pattern recognition (Vassilieva et al, 2011), and neuro-computing through micromechanical (Hoppensteadt and Izhikevich, 2001) or laser (Hoppensteadt and Izhikevich, 2000;Wang and Ghosh, 2007) oscillators.…”

“…The continuum-limit model has enjoyed a considerable amount of attention by the physics and dynamics communities. Related controltheoretical applications of the continuum-limit model are estimation of gait cycles (Tilton et al, 2012), spatial power grid modeling and analysis (Mangesius et al, 2012), and game theoretic approaches (Yin et al, 2012).…”

Multi-dimensional feedback particle filter for coupled oscillators

“…Apart from this paper, the problem of estimating phase variables appears in our own prior work [15], which applies the feedback particle filter to estimating a single phase variable associated with a walking gait cycle. In [13], a computational method, Phaser, is described based on taking a Hilbert transform and applying a Fourier series based correction (see also [6]).…”

A coupled oscillators-based control architecture for locomotory gaits

“…The methodology of this paper is a synthesis of several papers from our research group at the University of Illinois: the feedback particle filtering methodology for diffusion appears in [30], [29], [28]; its application to the problem of phase estimation is described in [24], [26]; a feedback particle filter-based approach to optimal control of partially observed diffusions is the subject of [21], [25]. In the present paper, we bring together these research threads to propose a CPG architecture for control of locomotion.…”

“…Estimation using CPG: The estimation problem is to construct a nonlinear filter for estimating the instantaneous phase θ (t), given a time-history of noisy measurements. The problem is solved numerically by constructing a coupled oscillator feedback particle filter; cf., [24], [26]. The coupled oscillator filter comprises of N stochastic processes {θ i (t) : 1 ≤ i ≤ N}, where the value θ i (t) ∈ [0, 2π] is the state of the i th oscillator at time t. For large N, the empirical distribution of the population approximates the posterior distribution of the θ (t).…”