Dynamics and geometry of locomotor learning on complex terrain

Locomotion on natural terrain requires animals to navigate irregular surfaces with sparse footholds, yet most theoretical and experimental work has focused on locomotion on flat surfaces. We ask how locomotor theory generalizes to complex terrain, and what constitutes locomotor learning in this setting.

We longitudinally tracked paw trajectories of mice walking on a motorized rung wheel and modeled inter-limb coordination as a system of weakly coupled oscillators whose target stepping rate takes discrete values imposed by rung geometry. Individual limbs switch between fast and slow stepping frequencies largely independently, revealing a high-dimensional coordination landscape organized around metastable regimes rather than a single stable attractor. We propose that the dynamical landscape is shaped by a locomotor stability objective with two components: an instantaneous stability margin, evaluated continuously along the state trajectory, and a catastrophic cost that represents the regime-specific probability of a stability collapse, which may lead to a fall. The choice of each limb's stepping regime minimizes combined cost within anatomical constraints.

Over sessions, fast stepping regimes are progressively abandoned in favor of slower regimes, while coordination within regimes becomes more precise. We conclude that both effects are driven by increased precision in single-limb swing timing, with downstream effects on regime selection and catastrophic cost. Finally, we relate these behavioral dynamics to complex spiking activity in a small population of cerebellar Purkinje cells. Together, these findings show that locomotor learning reshapes the behavioral manifold as mice progressively favor regions associated with lower expected stability cost.