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The Inactivation Principle: Mathematical Solutions Minimizing the Absolute Work and Biological Implications for the Planning of Arm Movements
An important question in the literature focusing on motor control is to determine
which laws drive biological limb movements. This question has prompted numerous
investigations analyzing arm movements in both humans and monkeys. Many theories
assume that among all possible movements the one actually performed satisfies an
optimality criterion. In the framework of optimal control theory, a first
approach is to choose a cost function and test whether the proposed model fits
with experimental data. A second approach (generally considered as the more
difficult) is to infer the cost function from behavioral data. The cost proposed
here includes a term called the absolute work of forces, reflecting the
mechanical energy expenditure. Contrary to most investigations studying
optimality principles of arm movements, this model has the particularity of
using a cost function that is not smooth. First, a mathematical theory related
to both direct and inverse optimal control approaches is presented. The first
theoretical result is the Inactivation Principle, according to which minimizing
a term similar to the absolute work implies simultaneous inactivation of
agonistic and antagonistic muscles acting on a single joint, near the time of
peak velocity. The second theoretical result is that, conversely, the presence
of non-smoothness in the cost function is a necessary condition for the
existence of such inactivation. Second, during an experimental study,
participants were asked to perform fast vertical arm movements with one, two,
and three degrees of freedom. Observed trajectories, velocity profiles, and
final postures were accurately simulated by the model. In accordance,
electromyographic signals showed brief simultaneous inactivation of opposing
muscles during movements. Thus, assuming that human movements are optimal with
respect to a certain integral cost, the minimization of an absolute-work-like
cost is supported by experimental observations. Such types of optimality
criteria may be applied to a large range of biological movements