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Optimal Workloop Energetics of Muscle-Actuated Systems: An Impedance Matching View

Figure 2

Solution of the optimal control problem.

This is an example solution for a time horizon of seconds, corresponding to an oscillation frequency of 5 Hz. Plots show the bang-bang control inputs [dimensionless] and corresponding activation [dimensionless], muscle forces [N], time-varying stiffnesses [N/m], the motion of the mass-spring-damper system (displacement, velocity, and the net power imparted per kg of muscle), and the resulting workloop. In the plots, blue traces pertain to the agonist muscle, the red traces to the antagonist muscle, and black traces refer to the net effects of both muscles and the load. Note that this particular solution exhibits co-activation as evidenced by the degree of overlap in the activation signals, and also in the control signals. This co-activation was required to stiffen the overall system to accommodate the relatively high-frequency of excitation required.

doi: https://doi.org/10.1371/journal.pcbi.1000795.g002