An Optimality Principle Governing Human Walking

Abstract

Abstract-In this paper, we investigate different possible strategies underlying the formation of human locomotor trajectories in goal-directed walking. Seven subjects were asked to walk within a motion capture facility from a fixed starting point and direction, and to cross over distant porches for which both position and direction in the room were changed over trials. Stereotyped trajectories were observed in the different subjects. The underlying idea to attack this question has been to relate this problem to an optimal control scheme: the trajectory is chosen according to some optimization principle. This is our basic starting assumption. The subject being viewed as a controlled system, we tried to identify several criteria that could be optimized. Is it the time to perform the trajectory? The length of the path? The minimum jerk along the path?. . . We found that the variation (time derivative) of the curvature of the locomotor paths is minimized. Moreover, we show that the human locomotor trajectories are well approximated by the geodesics of a differential system minimizing the L 2 norm of the control. Such geodesics are made of arcs of clothoids. The clothoid or Cornu spiral is a curve, whose curvature grows with the distance from the origin.

On Inverse Optimal Control Problems of Human Locomotion: Stability and Robustness of the Minimizers

“…This very natural property has been highlighted in the experiments performed by Laumond et al [2][3][4].…”

“…This paper focuses on the inverse optimal control problem associated with the goal-oriented human locomotion. In the approach initiated in [2][3][4], goal-oriented human locomotion is 1072-3374/**/****-0001 c 20** Springer Science+Business Media, Inc. understood as the motion in the 3-D space of both its position (x, y) and its orientation θ of a person walking from an initial point (x 0 , y 0 , θ 0 ) to a final point (x 1 , y 1 , θ 1 ) (see Figure 1). We take advantage here of the analysis carried out in a previous work [10] (see also [6]) in modeling the human locomotion by means of optimal control problems.…”

Eye tracking for locomotion prediction in redirected walking

“…By using standard models of human locomotion [1,2], it is possible to obtain an expected reference path to each of the targets. Once the user starts moving, the observed movement can be compared to the simulated reference trajectories and a prediction can be made.…”

“…They propose to use a model of human locomotion to generate a set of reference trajectories to all possible targets the moment the user starts to walk and then compare the observed trajectory to them while the user walks. In the following evaluation the models by Arechavaleta et al [1] and Fink et al [2] are used to generate these reference trajectories. In addition, they presented different schemes for comparing the observed path to the reference trajectories, the most promising ones are based on Dynamic Time Warping (DTW) and the cost-based method.…”

Feature-Based Prediction of Trajectories for Socially Compliant Navigation

“…For instance, Arechavaleta et al [1] present a nonholonomic motion model that minimizes the norm of the accelerations along the trajectory, assuming humans navigate as efficiently as possible. Mombaur et al [19] add an additional cost component, penalizing the time to reach the target.…”