Modeling Verticality Estimation During Locomotion

Abstract

In this thesis, a nonlinear model of the vestibular system is proposed, with special reference to humans and other locomoting animals. The vestibular system is essential for stable locomotion since it provides idiothetic measurements of spatial orientation that are needed for postural control. The model was constructed from general considerations regarding the Newton-Euler dynamics governing the three-dimensional movements of bodies constrained to oscillate in non-inertial frames, such as the otoliths, which were modeled as spherical damped pendula. Two configurations were considered. The medial model considered only one inner ear located in the center of a head. The lateral model considered two inner ears located laterally with respect to the center of rotation of the head. The differences between these two models were analyzed and the importance of having two vestibular organs discussed. To this end, a nonlinear algebraic observability test was used to verify whether the reconstruction of the head orientation with respect to the gravitational vertical was possible from otoliths measurements only. It could be shown that in order for the head vertical orientation to be observable, the head had to be stabilized during locomotion. Moreover, it was shown that the gravitoinertial ambiguity inherent to inertial idiothetic sensing could be resolved if the head was horizontally stabilized. These results were applied to solve the head vertical orientation estimation problem in the linearized case (Luenberger observer, Kalman filter) as well as in the nonlinear case (Extended Kalman filter, Newton method based observation). These observers were designed and tested in simulations. The simulations indicated that the estimation errors were smaller and the observers converged faster when head was stabilized during locomotion, leading to a nonlinear, combined observation-control system that could be stabilized with respect to the gravitational vertical based on no other information than the prior knowledge of the Newton-Euler dynamics. The results were further tested with a specifically designed experimental setup that comprised an actuated gimbal mechanism to represent the head-neck articulation and a liquid-based inclinometer that represented the otoliths organs. The findings derived from this research would be helpful for analyzing spatial perception in humans and animals, and for improving the perceptual capabilities of robotic systems, such as humanoid robots, rough terrain vehicles, or free-moving drones.Keywords: vestibular system, head-neck system, nonlinear system, observation, estimation, verticality, spatial perception, locomotion, humanoid robot. 3 RésuméDans cette thèse, nous proposons un modèle non-linéaire du système vestibulaire, en particulier chez l'humain et autres animaux mobiles. Le système vestibulaire est essentiel pour une locomotion stable dans la mesure où il fournit des mesures idiothétiques d'orientation spatiale nécessairesà la stabilité posturale. Le développement du modèle est basé sur l...

The Yoyo-Man

“…It can be understood then that stabilizing the head facilitates the fusion of visual and vestibular information. Recent studies also show that head stabilization improves the accuracy of estimation of the vertical direction by vestibular-like inertial sensor (Farkhatdinov et al, 2013). Head stabilization improves perturbation detection and safety supervision.…”

Idiothetic Verticality Estimation Through Head Stabilization Strategy

“…The understanding of how verticality estimation and head stabilization are achieved in biological systems may lead to better design and control of robotic systems, such as humanlike and animal-like walking robots, or free-roaming drones. The problem of modeling verticality estimation by a nonlinear Newton-method-based observer as well as an extended Kalman filter was previously addressed in [16,17]. Here, we show empirically that the platform-inertial-measurement system-a strongly nonlinear system that we model in Section II and III-in closed-loop with a linear controller-observer pair yields local linearization of an otherwise fully nonlinear observer-based closed-loop system.…”

Review of Anthropomorphic Head Stabilisation and Verticality Estimation in Robots

“…We suggest that a stabilised robotic head may improve the quality of inertial measurements of the sensors located in this head. First of all, we suppose that the head stabilised independently from the motion of the trunk will be less affected by external forces and disturbances which may occur during locomotion [51,52]. Second, if the head is stabilised in upright vertical position, then at least one of the axis of inertial sensors will be aligned with gravitational acceleration.…”