Intermittent control of unstable multivariate systems

Abstract

A sensorimotor architecture inspired from biological, vertebrate control should (i) explain the interface between high dimensional sensory analysis, low dimensional goals and high dimensional motor mechanisms and (ii) provide both stability and flexibility. Our interest concerns whether single-input-single-output intermittent control (SISO_IC) generalized to multivariable intermittent control (MIC) can meet these requirements.We base MIC on the continuous-time observer-predictorstate-feedback architecture. MIC uses event detection. A system matched hold (SMH), using the underlying continuoustime optimal control design, generates multivariate open-loop control signals between samples of the predicted state. Combined, this serial process provides a single-channel of control with optimised sensor fusion and motor synergies. Quadratic programming provides constrained, optimised equilibrium control design to handle unphysical configurations, redundancy and provides minimum, necessary reduction of open loop instability through optimised joint impedance. In this multivariate form, dimensionality is linked to goals rather than neuromuscular or sensory degrees of freedom. The biological and engineering rationale for intermittent rather than continuous multivariate control, is that the generalised hold sustains open loop predictive control while the open loop interval provides time within the feedback loop for online centralised, state dependent optimisation and selection.

The effect of fear of falling on vestibular feedback control of balance

“…This analysis uses a previously published model, which represents the standing human as a three-segment model with a head and trunk segment (HAT), a thigh and a shank segment Loram et al 2015Loram et al , 2016. Mechanical segment properties (link mass, length, centre of mass location, radius of gyration) are taken from Winter (2009).…”

“…Mechanical segment properties (link mass, length, centre of mass location, radius of gyration) are taken from Winter (2009). To simplify exposition of effects we used passive springs of 100% gravitational stiffness, which by definition eliminates the gravitational effect on segment rotations from the vertical Loram et al 2015Loram et al , 2016. All simulations began with zero link angle from the vertical and zero velocity for all segments.…”

Intermittent control of unstable multivariate systems with uncertain system parameters

“…where Qt is a positive semi-definite matrix representing appropriate weights for each state [8]. E is thus a continuously evolving scalar norm of the prediction error ehp.…”

“…For this system each segment has four physical parameters: mass (m), link length (l), CoM location (c), and radius of gyration (r) with values taken from Figure 4.1 and Table 4.1 of [9]. The controller is designed using linear quadratic regulation as described previously [3,8].…”

“…There are many ways to measure such a discrepancy. Following [7,8], we compute a quadratic function of the prediction error ehp, such that E>1 triggers sampling of the observed state xo…”