Ground reaction force estimation of a prosthetic leg using optimized derivative-free Kalman filter

Abstract

Artificial Prosthesis Systems assists injured patients to improve their quality of life. For proper utilization of these artificial systems, accurate estimation of external forces and state vectors are required for feedback control. Existing works estimate ground reaction forces using load cells and extended Kalman filter. However, load cells are expensive, bulky and prone to errors, whereas the filter has some inherent limitations which occur as a result of the truncation of higher order terms brought about by local linearization using first-order Taylor-series approximation and also requires Jacobian computation. We propose a robust Kalman filtering approach known as an optimized derivative-free Kalman filter for the estimation of states and ground reaction forces of a prosthesis system for transfemoral (TF) amputees. The system has four degrees of freedom (vertical displacement, thigh angle, knee angle and ankle angle). The plant is transformed to its linear equivalent using differential flatness. Grasshopper optimization algorithm was employed to optimize the parameters of the derivative-free Kalman filter by minimizing the root mean square estimation error of the nonlinear filter. Four measurement sensors were used (vertical displacement, thigh angle, knee angle and ankle angle) and the performance of the prosthesis system in normal gait mode was examined. The designed filter was simulated on Matlab R2018a and the results are compared with extended Kalman filter and unscented Kalman filter. The superiority of our method in estimating the joint angle reference, the GRFs and the reduction of material cost are shown when compared with existing methods. The optimized derivative-free Kalman filter recorded an average RMSE improvement of 99.85% and 99.77% estimation in joint angles and GRFs when computed and compared to existing methods.