Time optimality in the control of human movements

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Abstract
In a simulation study the control of maximally fast goal directed movements has been analyzed. For a simple linear model it is shown that the presence of a third input block reduces the movement duration. The time optimal size of the third block depends on the ratio of a neuromuscular time constant (first-order lag) and movement time. As a second step a non-linear muscle model was simulated. By an optimization of input parameters it was found that the time optimal input, as expected, switches between maximal agonist and maximal antagonist activation. As for the linear model, a third phase was required for an optimal movement. It was found that the third phase serves to compensate the slowly decaying antagonist force. Also an input similar to experimentally found activation patterns was simulated. This input contains a silent period between the first two bursts and the second and the third burst have submaximal amplitudes. This input led to a near time optimal movement with a duration 9% larger than the minimal duration but with largely reduced muscle forces. This suggests that a criterion is minimized which also takes into account the effort spent. Including gravity in the model indicates optimality of a silent period between the third phase and a final agonist activity to resist gravity. When assuming different dynamics for agonist and antagonist, the optimal switch times for agonist and antagonist no longer coincide, also after the three block pattern some extra activity is required to obtain a cancellation of the slowly decaying force in agonist and antagonist.