Nonlinear modelling of FES-supported standing up in paraplegia for selection of feedback sensors
This paper presents analysis of the standing-up manoeuvre in paraplegia considering the body supportive forces as a potential feedback source in functional electrical stimulation (FES)-assisted standing-up. The analysis investigates the significance of arm, feet, and seat reaction signals to the human body center-of-mass (COM) trajectory reconstruction. The standing-up behavior of eight paraplegic subjects was analyzed, measuring the motion kinematics and reaction forces to provide the data for modeling. Two nonlinear empirical modeling methods are implemented— Gaussian process (GP) priors and multilayer perceptron artificial neural networks (ANN)—and their performance in vertical and horizontal COM component reconstruction is compared. As the input, ten sensory configurations that incorporated different number of sensors were evaluated trading off the modeling performance for variables chosen and ease-of-use in everyday application. For the purpose of evaluation, the root-mean-square difference was calculated between the model output and the kinematics-based COM trajectory. Results show that the force feedback in COM assessment in FES assisted standing-up is comparable alternative to the kinematics measurement systems. It was demonstrated that the GP provided better modeling performance, at higher computational cost. Moreover, on the basis of averaged results, the use of a sensory system incorporating a six-dimensional handle force sensor and an instrumented foot insole is recommended. The configuration is practical for realization and with the GP model achieves an average accuracy of COM estimation 16 1.8 mm in horizontal and 39 3.7 mm in vertical direction. Some other configurations analyzed in the study exhibit better modeling accuracy, but are less practical for everyday usage. Index Terms—Artificial neural network (ANN), center of mass (COM), feedback, functional electrical stimulation (FES), Gaussian process (GP), mixture models, paraplegia, position tracking, standing-up.