Linear combinations of nonlinear models for predicting human-machine interface forces.

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.