The nonholonomic nature of human locomotion: a modeling study

This work presents a differential system which accurately describes the geometry of human locomotor trajectories of humans walking on the ground level, in absence of obstacles. Our approach emphasizes the close relationship between the shape of the locomotor paths in goal-directed movements and the simplified kinematic model of a wheeled mobile robot. This kind of system has been extensively studied in robotics community. From a kinematic perspective, the characteristic of this wheeled robot is the nonholonomic constraint of the wheels on the floor, which forces the vehicle to move tangentially to its main axis. Humans do not walk sideways. This obvious observation indicates that some constraints (mechanical, anatomical...) act on human bodies restricting the way humans generate locomotor trajectories. To model this, we propose a differential system that respects nonholonomic constraints. We validate this model by comparing simulated trajectories with actual (recorded) trajectories produced during goal-oriented locomotion in humans. Subjects had to start from a pre-defined position and direction to cross over a distant porch (position and orientation of the porch were the two manipulated factors). Such comparative analysis is undertaken by making use of numerical methods to compute the control inputs from actual trajectories. Three body frames have been considered: head, pelvis and trunk. It appears that the trunk can be considered as a kind of a steering wheel that steers the human body with a delay of around 0.2 second. This model has been validated on a database of 1,560 trajectories recorded from seven subjects. It opens a promising route to better understand the human locomotion via differential geometry tools successfully experienced in mobile robotics