Stable Nonlinear Control of an Agonist-Antagonist Muscle-Driven System

We introduce an asymptotically stable nonlinear controller for a two-muscle system with an agonist-antagonist arrangement. A Hill model with series and parallel elasticity is used for each muscle. The controller is based on a combination of backstepping and algebraic virtual control matching to determine final activation control signals. Two definitions for the synthetic input used in the first backstepping stage are considered: a scalar form and a vector form. A novel feature of the vector approach is the ability to incorporate a minimum-effort optimality criterion as a way of resolve actuation redundancy. Minimum effort criteria reflect well-established biomechanical principles of human movement. The proposed approach is scalable and can serve as a “working controller” to facilitate studies in the field of human-machine interactions, including machine control systems and biomechanical state estimation.