Linear combinations of nonlinear models for predicting human–machine interface forces

Abstract.

 This study presents a computational framework that capitalizes on known human neuromechanical characteristics during limb movements in order to predict human–machine interactions. A parallel–distributed approach, the mixture of nonlinear models, fits the relationship between the measured kinematics and kinetics at the handle of a robot. Each element of the mixture represented the arm and its controller as a feedforward nonlinear model of inverse dynamics plus a linear approximation of musculotendonous impedance. We evaluated this approach with data from experiments where subjects held the handle of a planar manipulandum robot and attempted to make point-to-point reaching movements. We compared the performance to the more conventional approach of a constrained, nonlinear optimization of the parameters. The mixture of nonlinear models accounted for 79±11% (mean ±SD) of the variance in measured force, and force errors were 0.73 ± 0.20% of the maximum exerted force. Solutions were acquired in half the time with a significantly better fit. However, both approaches suffered equally from the simplifying assumptions, namely that the human neuromechanical system consisted of a feedforward controller coupled with linear impedances and a moving state equilibrium. Hence, predictability was best limited to the first half of the movement. The mixture of nonlinear models may be useful in human–machine tasks such as in telerobotics, fly-by-wire vehicles, robotic training, and rehabilitation.