Velocity/curvature relations along a single turn in human locomotion

Neuroscientific approaches have provided an important invariant linking kinematics and geometry in locomotion: a power law controls the relation between radius of curvature and velocity of the trajectory followed. However, these trajectories are predefined and cyclic. Consequently, they cannot be considered as fully natural. We investigate whether this relationship still exists in one unconstrained turn, which can be compared to an everyday life movement. Two different approaches were developed: an intra-individual one along each turn of each trial and an inter-individual one based on a specific instant for which a subject's trajectory goes through its maximal curvature. Eleven subjects performed turns at three gait speeds (natural, slow, fast). The intra-individual approach did not lead to any power law between velocity and curvature along one single trial. Notwithstanding, the inter-individual approach showed a power law between the whole couples "minimal radius of curvature/associated velocity". Thus, the speed/curvature relation is more a "long term" motor control law linked to the turning task goal rather than a "short term" one dealing with trajectory following all the time of the motion.