A Vexing Question in Motor Control: The Degrees of Freedom Problem

Abstract

The human “marionette” is extremely complex and multi-articulated: anatomical redundancy (in terms of Degrees of Freedom: DoFs), kinematic redundancy (movements can have different trajectories, velocities, and accelerations and yet achieve the same goal, according to the principle of Motor Equivalence), and neurophysiological redundancy (many more muscles than DoFs and multiple motor units for each muscle). Although it is quite obvious that such abundance is not noxious at all because, in contrast, it is instrumental for motor learning, allowing the nervous system to “explore” the space of feasible actions before settling on an elegant and possibly optimal solution, the crucial question then boils down to figure out how the nervous system “chooses/selects/recruits/modulates” task-dependent subsets of countless assemblies of DoFs as functional motor synergies. Despite this daunting conceptual riddle, human purposive behavior in daily life activities is a proof of concept that solutions can be found easily and quickly by the embodied brain of the human cognitive agent. The point of view suggested in this essay is to frame the question above in the old-fashioned but still seminal observation by Marr and Poggio that cognitive agents should be regarded as Generalized Information Processing Systems (GIPS) and should be investigated according to three nearly independent but complementary levels of analysis: 1) the computational level, 2) the algorithmic level, and 3) the implementation level. In this framework, we attempt to discriminate as well as aggregate the different hypotheses and solutions proposed so far: the optimal control hypothesis, the muscle synergy hypothesis, the equilibrium point hypothesis, or the uncontrolled manifold hypothesis, to mention the most popular ones. The proposed GIPS follows the strategy of factoring out shaping and timing by adopting a force-field based approach (the Passive Motion Paradigm) that is inspired by the Equilibrium Point Hypothesis, extended in such a way to represent covert as well overt actions. In particular, it is shown how this approach can explain spatio-temporal invariances and, at the same time, solve the Degrees of Freedom Problem.