On the nonholonomic nature of human locomotion

Abstract

In the kinematic realm, wheeled robot's determining characteristic lies in its nonholonomic constraint. Indeed, the wheels of the robot unequivocally force the robot vehicle to move tangentially to its main axis. Here we test the hypothesis that human locomotion can also be partly described by such a nonholonomic system. This hypothesis is inspired by the trivial observation that humans do not walk sideways: some constraints of different natures (anatomical, mechanical. . .) may restrict the way humans generate locomotor trajectories. To model these constraints, we propose a simple differential system satisfying the so called rolling without sliding constraint. We validated the proposed model by comparing simulated trajectories with actual (recorded) trajectories obtained from goal-oriented locomotion of human subjects. These subjects had to start from a pre-defined position and direction in space and cross over to a distant porch so that both initial and final positions and directions were controlled. A comparative analysis was successfully undertaken by making use of numerical methods to compute the control inputs from actual trajectories. To achieve this, three body segments were used as local reference frames: head, pelvis and torso. The best simulations were obtained using the last body segment. We therefore suggest an analogy between the steering wheels and the torso segment, meaning that for the control of locomotion, the trunk behavior is constrained in a nonholonomic manner. Our approach allowed us to successfully predict 87 percent of trajectories recorded in seven subjects and might be particularly relevant for future pluridisciplinary research programs dealing with modeling of biological locomotor behaviors.

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.…”

“…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. We assume that every admissible locomotion trajectory is solution of a control system that describes the dynamics, exploiting the nonholonomic nature of human locomotion [3]. Among these trajectories, the chosen one minimizes a cost that has to be sought in a particular class L of functionals.…”

“…2. Examples of trajectories for several final positions, drawn by using the data recorded by Arechavaleta et al [3] (with the kind permission of the authors).…”

“…System (1) captures the nonholonomic nature of the human locomotion pointed out in [3], which is valid when the subject walks toward a far enough target point. Note also that the paths (x, y) are parameterized by arc-length.…”