Symmetry and order parameter dynamics of the human odometer

Prior research has shown that bipedal gaits can be modeled using differential equations grouped by symmetry. Primary gaits like walking and running exhibit dihedral symmetry, while secondary gaits like gallop-walk show cyclic symmetry. These symmetry classifications have been used to test human odometry, a system for estimating distance traveled. Earlier studies suggested that distance estimates remain consistent within the same symmetry class but change when switching classes. No prior work had resolved whether these findings apply to treadmill locomotion or whether symmetry dynamics influence measurement consistency. This gap motivated the current investigation into the symmetry and dynamics of human odometer function.

The researchers aimed to test whether symmetry-based distance estimation patterns in human odometry remain consistent when locomotion occurs on a treadmill rather than overground. They also sought to assess the dynamics of sequentially coupled measure and report phases. By treating relative velocity as an order parameter and symmetry class differences as imperfection parameters, the study aimed to determine whether symmetry dynamics affect odometer accuracy. The goal was to confirm whether the human odometer operates with consistent symmetry and dynamics regardless of whether the person or the ground is in motion.

The study used treadmill locomotion to replicate prior overground experiments. Participants performed walking and running gaits, categorized by symmetry class. Distance estimates were collected during measure and report phases. Relative velocity was tracked as an order parameter, while symmetry class differences served as imperfection parameters. The researchers compared distance estimates within and across symmetry classes. They assessed whether switching symmetry classes at the report phase altered measured distance. The study design involved sequential coupling of measure and report phases to analyze dynamic interactions.

Results showed that distance estimates remained consistent within the same symmetry class during treadmill locomotion. Switching symmetry classes at the report phase compressed or inflated measured distance, with changes equal in magnitude. The pattern mirrored prior overground findings. Relative velocity acted as an order parameter, while symmetry class differences functioned as imperfection parameters. The dynamics of sequentially coupled measure and report phases were preserved. Distance estimation symmetry and dynamics were consistent whether the odometer was in motion relative to a stationary ground or stationary relative to a moving ground. These findings suggest a unified mechanism for human odometer function.

The authors propose that human odometer function operates with consistent symmetry and dynamics regardless of locomotion context. The results suggest that distance estimation remains stable within symmetry classes but shifts predictably when switching classes. The study confirms that symmetry-based patterns observed in overground locomotion also apply to treadmill locomotion. Relative velocity and symmetry class differences function as key parameters in odometer dynamics. The findings support the idea that the human odometer is governed by symmetry-based principles. The authors suggest that these dynamics remain consistent across different reference frames. No prior work had resolved whether symmetry dynamics influence odometer accuracy in treadmill settings. The results align with prior studies in overground contexts.