A Nonlinear Dynamics-Based Estimator for Functional Electrical Stimulation: Preliminary Results From Lower-Leg Extension Experiments

Abstract

Miniature inertial measurement units (IMUs) are wearable sensors that measure limb segment or joint angles during dynamic movements. However, IMUs are generally prone to drift, external magnetic interference, and measurement noise. This paper presents a new class of nonlinear state estimation technique called state-dependent coefficient (SDC) estimation to accurately predict joint angles from IMU measurements. The SDC estimation method uses limb dynamics, instead of limb kinematics, to estimate the limb state. Importantly, the nonlinear limb dynamic model is formulated into state dependent matrices that facilitate the estimator design without performing a Jacobian linearization. The estimation method is experimentally demonstrated to predict knee joint angle measurements during functional electrical stimulation of the quadriceps muscle. The nonlinear knee musculoskeletal model was identified through a series of experiments. The SDC estimator was then compared to an Extended Kalman filter (EKF), which uses a Jacobian linearization and a rotation matrix method, which uses a kinematic model instead of the dynamic model. Each estimator’s performance was evaluated against the true value of the joint angle, which was measured through a rotary encoder. The experimental results showed that the SDC estimator, the rotation matrix method, and EKF had root mean square errors of 2.70°, 2.86°, and 4.42°, respectively. Our preliminary experimental results show the new estimator’s advantage over the EKF method but a slight advantage over the rotation matrix method. However, the information from the dynamic model allows the SDC method to use only one IMU to measure the knee angle compared to the rotation matrix method that uses 2 IMUs to estimate the angle.

Dynamic Feedback Control And State Observers For A Knee Rehabilitation Device Using Soft Action

“…presented with control purposes and also for parameter estimation (see e.g. Allen et al (2017), Luo et al (2017), Brahmi et al (2018)). Estimators allow quantifying nonmeasurable variables, so they are indeed used in control applications for rehabilitation devices.…”

Simultaneous exercise recognition and evaluation in prescribed routines: Approach to virtual coaches

“…EKFs are the KF variation that most frequently appear in motion analysis. EKFs are used for the sensor fusion of gyroscopes and accelerometers in order to estimate the joints orientation [8], [38], [66], [70], [72], [92], [96], joints orientation and location [55], [76], [79], [88], [108] and segment orientation [77], [78]. Researchers also use EKFs to fuse gyroscope and accelerometer data with magnetometer measurements to estimate the orientation of joints [138], [142] or segments [117], [118], [135], [140], [145].…”

“…Another common approach for the error reduction in most of biomechanical models is to take into account the anatomic parameters, such as the joints location with respect to the sensors or the segments length [8], [17], [19], [20], [23]- [26], [35], [37], [38], [46], [46], [64], [73], [76]- [79], [83], [87]- [89], [91]- [96], [98], [99], [105]- [108], [119], [129], [132], [137], [138], [143], [150], [151], [154]. Fig.…”

An Enhanced Model Free Adaptive Control Approach for Functional Electrical Stimulation Assisted Knee Joint Regulation and Control

“…They developed a robust controller to ensure cadence tracking efficiency by adjusting the parameter variation in the model. These models, however, only approximate the dynamics of the limb and do not account for the dynamic response of the muscle to the exogenous electrical stimulus, necessitating the implementation of a compensator [8] in the FES controller network.…”