Online identification and nonlinear control of the electrically stimulated quadriceps muscle

Abstract

A new approach for estimating nonlinear models of the electrically stimulated quadriceps muscle group under non-isometric conditions is investigated. The model can be used for designing controlled neuro-prostheses. In order to identify the muscle dynamics (stimulation pulsewidth -active knee moment relation) from discrete-time angle measurements only, a hybrid model structure is postulated for the shankquadriceps dynamics. The model consists of a relatively well known time-invariant passive component and an uncertain time-variant active component. Rigid body dynamics, described by the Equation of Motion (EoM), and passive joint properties form the time-invariant part. The actuator, i.e. the electrically stimulated muscle group, represents the uncertain time-varying section. A recursive algorithm is outlined for identifying online the stimulated quadriceps muscle group. The algorithm requires EoM and passive joint characteristics to be known a priori. The muscle dynamics represent the product of a continuous-time nonlinear activation dynamics and a nonlinear static contraction function described by a Normalised Radial Basis Function (NRBF) network which has knee-joint angle and angular velocity as input arguments. An Extended Kalman Filter (EKF) approach is chosen to estimate muscle dynamics parameters and to obtain full state estimates of the shank-quadriceps dynamics simultaneously. The latter is important for implementing state feedback controllers. A nonlinear state feedback controller using the backstepping method is Preprint submitted to Control Engineering Practice 16 July 2004explicitly designed whereas the model was identified a priori using the developed identification procedure.

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

“…These nonlinear methods were proved to have enhanced performance over linear control methods in previous researches [4][5][6][7][8][9][16][17][18]. Among these nonlinear control techniques, robust nonlinear control of NMES in [5,7] is especially more relevant given the nonlinear and uncertain muscle dynamics, time-varying phenomena such as muscle fatigue [19], and electromechanical delay [18,19].…”

“…Examples of linear control methods include proportional integral derivative (PD/PID), linear quadratic Gaussian control, pole placement method, gain scheduling control method [13][14][15]. Nonlinear control methods [4][5][6][7][8][9][16][17][18] have also been recently developed for NMES. These nonlinear methods have improved performance over linear control methods.…”

“…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].…”

“…NMES artificially contracts muscle groups by applying external stimulation current. Closed-loop control of NMES can be used to generate advanced functional tasks (in this case NMES is also called functional electrical stimulation (FES)) such as walking [2,3], single leg extension [4][5][6][7][8][9], and upper extremity grasping and reaching [10][11][12].…”

In Vivo Identification of Skeletal Muscle Dynamics with Nonlinear Kalman Filter: Comparison between EKF and SPKF

“…The main objective of this paper is to develop an experimental computational method to identify unknown internal parameters from the limited information. For such identification of nonlinear system, extended Kalman filter (EKF) has often been used for skeletal muscle [17] and cardiac muscle identification [18]. It can work when the model is not complicated and not highly nonlinear.…”