  Movement in biology is often achieved with distributed control of coupled
subcomponents, e.g. muscles and limbs. Coupling could range from weak and
local, i.e. decentralized, to strong and global, i.e. centralized. We developed
a model-free measure of centralization that compares information shared between
control signals and both global and local states. A second measure, called
co-information, quantifies the net redundant information the control signal
shares with both states. We first validate our measures through simulations of
coupled oscillators and show that it successfully reconstructs the shift from
low to high coupling strengths. We then measure centralization in freely
running cockroaches. Surprisingly, extensor muscle activity in the middle leg
is more informative of movements of all legs combined than the movements of
that particular leg. Cockroach centralization successfully recapitulates a
specific model of a strongly coupled oscillator network previously used to
model cockroach leg kinematics. When segregated by stride frequency, slower
cockroach strides exhibit more shared information per stride between control
and output states than faster strides, indicative of an information bandwidth
limitation. However, centralization remains consistent between the two groups.
We then used a robotic model to show that centralization can be affected by
mechanical coupling independent of neural coupling. The mechanically coupled
bounding gait is decentralized and becomes more decentralized as mechanical
coupling decreases while internal parameters of control remain constant. The
results of these systems span a design space of centralization and
co-information that can be used to test biological hypotheses and advise the
design of robotic control.
