Robust Discrete-Time H∞ Control for Unsupported Paraplegic Standing: Experimental Results

Abstract

This paper develops a design approach, based on sampled data H ∞ -robust feedback control, for stabilisation of the upright posture of paraplegic persons standing. The subject stands in a special apparatus which braces the knee and hip joints. Stabilising torque at the ankle joint is produced by electrical stimulation of the paralyzed calf muscle of both legs using surface electrodes. The goal in this setup is for the subject to stand without the need to hold on to an external support for stability: we call this “unsupported standing”. The apparatus allows measurement of ankle moments and inclination angle. The control structure therefore has an inner loop providing high-bandwidth control of ankle moment, and an outer loop which stabilises the inclination angle. This problem involves a significant degree of uncertainty because of the nonlinear and time-varying response of the electrically stimulated muscles. We therefore focus here on robust H ∞ -control design for the angle control loop, using a discrete-time formulation.