  Research on assistive technology, rehabilitation, and prosthesis requires the
understanding of human machine interaction, in which human muscular properties
play a pivotal role. This paper studies a nonlinear agonistic-antagonistic
muscle system based on the Hill muscle model. To investigate the
characteristics of the muscle model, the problem of estimating the state
variables and activation signals of the dual muscle system is considered. In
this work, parameter uncertainty and unknown inputs are taken into account for
the estimation problem. Three observers are presented: a high gain observer, a
sliding mode observer, and an adaptive sliding mode observer. Theoretical
analysis shows the convergence of the three observers. To facilitate numerical
simulations, a backstepping controller is employed to drive the muscle system
to track a desired trajectory. Numerical simulations reveal that the three
observers are comparable and provide reliable estimates in noise free and noisy
cases. The proposed schemes may serve as frameworks for estimation of complex
multi-muscle systems, which could lead to intelligent exercise machines for
adaptive training and rehabilitation, and adaptive prosthetics and
exoskeletons.
