I might be way out my league here, but anyway…
The above “equation” is not the same as “minimize the sum of muscle forces”, because you minimize the objective function (G). This objective function only consider maximal activity of the muscles. Hence, a min/max formulation. To solve for the sub-maximally activated muscles they have implemented an iterative scheme that is described in the (unfortunately hard to come by) article:
[li]M. Damsgaard, J. Rasmussen & S.T. Christensen (2001): Inverse dynamics of musculo-skeletal systems using an efficient min/max muscle recruitment model. Proceedings of IDETC: 18-th Biennial Conference on Mechanical Vibration and Noise, Pittsburgh, September 9-13, 2001.[/li][/ul]
But I guess you simply could say that you minimize the normalized muscle force, then it might be easier to understand the concept.
The Min/Max muscle recruitment will try to minimize the activation of the maximal activated muscle in the model. This will lower the activation envelope, which is the maximum relative load of any muscle in the system.
Here is an explanation from the muscle recruitment tutorial:
“This would physiologically be a minimum fatigue criterion because fatigue is likely to happen first in the muscle with the maximum relative load, and it makes physiological sense that the body might work that way. It would mean that the body would maximize its endurance and precisely this criterion might decide survival of the fittest in an environment where organisms are competing with each other for limited resources”
Concerning the muscle lever arm, the min/max reqruitment will try to make use of all muscles with a usefull momentarm, as a soon as a muscle has a usefull moment arm it may be activated and help lower the activations of the other muscles. This will happen even if the momentarm is very small.
If this behaviour is undesired a polynomial criteria can be used, this is a sum of muscle activations lifted in a user defined power. With a very high power it will resemble the min/max criteria but when lowing the power, muscles with smaller momentarms will in general gradually be left unused, because the objective is a summation and it will have cost to have a muscle activated, so if it does not help significantly it will be left inactive.