Non-linear estimation is easy

Fliess, Michel; Join, Cédric; Sira‐Ramírez, Hebertt

doi:10.1504/ijmic.2008.020996

Cited by 308 publications

(197 citation statements)

References 78 publications

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“…This is classically used for parametric estimation [15] and fault diagnosis and fault tolerant control in noisy environment [9] since many years. More recently, this approach is used for marginal applications such as the curvature extrema detection [16].…”

Section: A Existing Approachmentioning

confidence: 99%

“…The third sensor is classically scanning horizontally to the ground in order to detect other obstacles. The other contribution of this paper is an original distance-based approach for algebraic derivative calculation based on [9] and adapted to laser sensor constraint. This work has been developed in the framework of the Personal Intelligent City Accessible Vehicle (PICAV) project.…”

Section: Introductionmentioning

confidence: 99%

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Step and curb detection for autonomous vehicles with an algebraic derivative-based approach applied on laser rangefinder data

Pollard

Pérez

Nashashibi

2013

2013 IEEE Intelligent Vehicles Symposium (IV)

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Abstract-Personal Mobility Vehicles (PMV) is is an important part of the Intelligent Transportation System (ITS) domain. These new transport systems have been designed for urban traffic areas, pedestrian streets, green zones and private parks. In these areas, steps and curbs make the movement of disable or mobility reduced people with PMV, and with standard chair wheels difficult. In this paper, we present a step and curb detection system based on laser sensors. This system is dedicated to vehicles able to cross over steps, for transportation systems, as well as for mobile robots. The system is based on the study of the first derivative of the altitude and highlights the use of a new algebraic derivative method adapted to laser sensor data. The system has been tested on several real scenarios. It provides the distance, altitude and orientation of the steps in front of the vehicle and offers a high level of precision, even with small steps and challenging scenarios such as stairs.

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Section: A Existing Approachmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Step and curb detection for autonomous vehicles with an algebraic derivative-based approach applied on laser rangefinder data

Pollard

Pérez

Nashashibi

2013

2013 IEEE Intelligent Vehicles Symposium (IV)

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“…R. Kalman developed an observability theory for linear stationary systems [110,112] [95], and many other researchers. More recently, M. Fliess has showed that the concept of identifiability is strongly connected with the notion of observability [52,67].…”

Section: Nonlinear Observability 311 Definitionsmentioning

confidence: 99%

Modeling Verticality Estimation During Locomotion

Farkhatdinov

Michalska

Berthoz

et al. 2013

Romansy 19 – Robot Design, Dynamics and Control

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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...

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“…Moreover, for stability reasons, we chose to employ exponentially stable dynamics instead of constant dynamics. It is shown that the proposed approach is realisable thanks to the finite time differentiator as, for example, the one proposed in [6,7] (but for these methods, the delay appears due to the data acquisition frame) or High Order Sliding Mode (HOSM) [18,9].…”

Section: Introductionmentioning

confidence: 99%

Observabilty singularities and observer design: dual immersion approach

et al. 2016

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It is well-known that, for nonlinear systems, the observability is often only a local property and depends on the input. Moreover, it is often required that the observer be of the same dimension as the original system. A direct consequence of this requirement is that it enlarges the set of observability singularities. If, on one hand, it is impossible to observe the state variables that are structurally unobservable, it is, however, possible to overcome the observability singularities introduced by the constraints on the observer design. In this paper, we propose a novel dual immersion method which allows to reduce the set of observability singularities. In addition, a step by step design of a high order sliding mode observer based on the proposed dual immersion approach is presented. Finally, a thorough analysis and discussion on the simulation results with respect to a non-autonomous system is given.

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Non-linear estimation is easy

Cited by 308 publications

References 78 publications

Step and curb detection for autonomous vehicles with an algebraic derivative-based approach applied on laser rangefinder data

Step and curb detection for autonomous vehicles with an algebraic derivative-based approach applied on laser rangefinder data

Modeling Verticality Estimation During Locomotion

Observabilty singularities and observer design: dual immersion approach

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