  The study of motion in animals and robots has been aided by insights from
geometric mechanics. In friction dominated systems, a mechanical "connection"
can provide a high fidelity mechanical model. The connection is a co-vector
(Lie algebra) valued map on the configuration space of the system. As such,
empirically estimating a global model of the connection requires a truly
exhaustive collection of experiments, and is thus prohibitive on all systems
with even a moderate number of degrees of freedom. In this work, insights from
data driven oscillator theory enable us to define a framework for estimating a
local model of a connection in the vicinity of observed animal and robot gait
cycles. The estimates are produced directly from motion capture data of a
stochastically perturbed cyclic behavior. We demonstrate the model extraction
process under noisy, experiment-like conditions by simulating planar
multi-segment serpentine swimmers in a low Reynolds number (viscous-friction)
environment. Following this, we assess model accuracy in the presence of
observation error. Validating our method's capability to produce accurate
models in the presence of simulated system and observational noise motivates
its usage on real robotic and biological systems.
