Predictor-Based Compensation for Electromechanical Delay During Neuromuscular Electrical Stimulation

Abstract

Abstract-Electromechanical delay (EMD) is a biological artifact that arises due to a time lag between electrical excitation and tension development in a muscle. EMD is known to cause degraded performance and instability during neuromuscular electrical stimulation (NMES). Compensating for such input delay is complicated by the unknown nonlinear muscle force-length and muscle force-velocity relationships. This paper provides control development and a mathematical stability analysis of a NMES controller with a predictive term that actively accounts for EMD. The results are obtained through the development of a novel predictor-type method to address the delay in the voltage input to the muscle. Lyapunov-Krasovskii functionals are used within a Lyapunov-based stability analysis to prove semi-global uniformly ultimately bounded tracking. Experiments on able-bodied volunteers illustrate the performance and robustness of the developed controller during a leg extension trajectory following task.

Robust compensation of electromechanical delay during neuromuscular electrical stimulation of antagonistic muscles

“…These nonlinear methods have improved performance over linear control methods. Robust nonlinear control of NMES is especially more relevant, and controllers have been developed to compensate for the nonlinear and uncertain muscles dynamics [5,7], time-varying phenomena such as muscle fatigue [19], and electromechanical delay [18,19].…”

“…In results such as [4,6,19], the EMD was modeled as an input delay in the musculoskeletal dynamics. Input delays can cause performance degradation and system instability, such as during human stance experiments [20].…”

“…Recently, a robust compensation control method was developed for an uncertain input delayed system with additive disturbances [21] and it suggests that a PD/PID controller can be augmented with a delay compensator that contains a finite integral of past control values to transform the delayed system into a delay-free system. Modified PD/PID controllers have been extended to compensate for EMD during NMES [18,19].…”

“…A proportional-derivative (PD)-type closed-loop controller with delay compensation (DC) to deal with the EMD was designed for stimulating antagonistic muscle pairs in a musculoskeletal system. Unlike previous controllers that produce joint flexion with the help of gravity [9,18,19] or controlled by correctional forces such as robot arms [22,24], the developed controller will flex and extend a limb joint by stimulating agonist and antagonist muscles. The controller is designed to transition smoothly between the stimulation of the antagonist muscles.…”

Predictor-feedback stabilization of multi-input nonlinear systems

“…Such systems serve as models for the dynamics of traffic [22], [47], teleoperators [24] and robotic manipulators [2], [20], motors [34], [50], multi-agent systems [1], [18], [40], autonomous ground vehicles [39], unmanned aerial vehicles [23] and planar vertical take-off and landing aircrafts [21], [48], and the human musculoskeletal system in applications such as neuromuscular electrical stimulation [32], [38], [51], to name only a few. Motivated by the negative effects of input delays on the stability and performance of such control systems, in this article we present control designs that achieve delay compensation.…”