48 research outputs found
Motion Planning for Kinematic systems
In this paper, we present a general theory of motion planning for kinematic
systems. This theory has been developed for long by one of the authors in a
previous series of papers. It is mostly based upon concepts from subriemannian
geometry. Here, we summarize the results of the theory, and we improve on, by
developping in details an intricated case: the ball with a trailer, which
corresponds to a distribution with flag of type 2,3,5,6.
This paper is dedicated to Bernard Bonnard for his 60th birthday
A bisector line field approach to interpolation of orientation fields
We propose an approach to the problem of global reconstruction of an orientation field. The method is based on a geometric model called "bisector line fields", which maps a pair of vector fields to an orientation field, effectively generalizing the notion of doubling phase vector fields. Endowed with a well chosen energy minimization problem, we provide a polynomial interpolation of a target orientation field while bypassing the doubling phase step. The procedure is then illustrated with examples from fingerprint analysis
Continuous-Discrete High-Gain Extended Kalman Filter for Mobile Robots with Asynchronous Outputs
International audienceThis paper details the implementation of an asynchronous high-gain Kalman filter on a mobile robot test platform. The presented study consists of reconstructing the path followed by a mobile robot. The observer algorithm is tailored from our previous theoretical developments to fit the problem under consideration. Two experiments of path reconstruction are carried out, using respectively a predefined trajectory and a joystick controlled trajectory. The estimation results are presented after offline processing. They show that our algorithm can be applied with success in the field of mobile robot navigation in the presence of asynchronous measurements
Le filtre de Kalman Ă©tendu Ă grand-gain adaptatif et ses applications
The work concerns the âobservability problemââthe reconstruction of a dynamic processâs full state from a partially measured stateâ for nonlinear dynamic systems. The Extended Kalman Filter (EKF) is a widely-used observer for such nonlinear systems. However it suffers from a lack of theoretical justifications and displays poor performance when the estimated state is far from the real state, e.g. due to large perturbations, a poor initial state estimate, etc. . . We propose a solution to these problems, the Adaptive High-Gain (EKF). Observability theory reveals the existence of special representations characterizing nonlinear systems having the observability property. Such representations are called observability normal forms. A EKF variant based on the usage of a single scalar parameter, combined with an observability normal form, leads to an observer, the High-Gain EKF, with improved performance when the estimated state is far from the actual state. Its convergence for any initial estimated state is proven. Unfortunately, and contrary to the EKF, this latter observer is very sensitive to measurement noise. Our observer combines the behaviors of the EKF and of the high-gain EKF. Our aim is to take advantage of both efficiency with respect to noise smoothing and reactivity to large estimation errors. In order to achieve this, the parameter that is the heart of the high-gain technique is made adaptive. Voila, the Adaptive High-Gain EKF. A measure of the quality of the estimation is needed in order to drive the adaptation. We propose such an index and prove the relevance of its usage. We provide a proof of convergence for the resulting observer, and the final algorithm is demonstrated via both simulations and a real-time implementation. Finally, extensions to multiple output and to continuous-discrete systems are given.Le travail porte sur la problĂ©matique de lâobservation des systĂšmes â la reconstruction de lâĂ©tat complet dâun systĂšme dynamique Ă partir d'une mesure partielle de cet Ă©tat. Nous considĂ©rons spĂ©cifiquement les systĂšmes non linĂ©aires. Le filtre de Kalman Ă©tendu (EKF) est lâun des observateurs les plus utilisĂ©s Ă cette fin. Il souffre cependant dâune performance moindre lorsque l'Ă©tat estimĂ© nâest pas dans un voisinage de l'Ă©tat rĂ©el. La convergence de lâobservateur dans ce cas nâest pas prouvĂ©e. Nous proposons une solution Ă ce problĂšme : lâEKF Ă grand gain adaptatif. La thĂ©orie de lâobservabilitĂ© fait apparaĂźtre lâexistence de reprĂ©sentations caractĂ©risant les systĂšmes dit observables. Câest la forme normale dâobservabilitĂ©. LâEKF Ă grand gain est une variante de lâEKF que lâon construit Ă base dâun paramĂštre scalaire. La convergence de cet observateur pour un systĂšme sous sa forme normale dâobservabilitĂ© est dĂ©montrĂ©e pour toute erreur dâestimation initiale. Cependant, contrairement Ă lâEKF, cet algorithme est trĂšs sensible au bruit de mesure. Notre objectif est de combiner lâefficacitÂŽe de lâEKF en termes de lissage du bruit, et la rÂŽeactivitÂŽe de lâEKF grand-gain face aux erreurs dâestimation. Afin de parvenir Ă ce rĂ©sultat nous rendons adaptatif le paramĂštre central de la mĂ©thode grand gain. Ainsi est constituĂ© lâEKF Ă grand gain adaptatif. Le processus dâadaptation doit ĂȘtre guidĂ© par une mesure de la qualitĂ© de lâestimation. Nous proposons un tel indice et prouvons sa pertinence. Nous Ă©tablissons une preuve de la convergence de notre observateur, puis nous lâillustrons Ă lâaide dâune sĂ©rie de simulations ainsi quâune implĂ©mentation en temps rĂ©el dur. Enfin nous proposons des extensions au rĂ©sultat initial : dans le cas de systĂšmes multi-sorties et dans le cas continu-discret
Adaptive high-gain extended kalman filter and applications
The work concerns the ``observability problemâ --- the reconstruction of a dynamic process's full state from a partially measured state--- for nonlinear dynamic systems. The Extended Kalman Filter (EKF) is a widely-used observer for such nonlinear systems. However it suffers from a lack of theoretical justifications and displays poor performance when the estimated state is far from the real state, e.g. due to large perturbations, a poor initial state estimate, etcâŠ
We propose a solution to these problems, the Adaptive High-Gain (EKF).
Observability theory reveals the existence of special representations characterizing nonlinear systems having the observability property. Such representations are called observability normal forms. A EKF variant based on the usage of a single scalar parameter, combined with an observability normal form, leads to an observer, the High-Gain EKF, with improved performance when the estimated state is far from the actual state. Its convergence for any initial estimated state is proven. Unfortunately, and contrary to the EKF, this latter observer is very sensitive to measurement noise.
Our observer combines the behaviors of the EKF and of the high-gain EKF. Our aim is to take advantage of both efficiency with respect to noise smoothing and reactivity to large estimation errors. In order to achieve this, the parameter that is the heart of the high-gain technique is made adaptive. \textit{Voila}, the Adaptive High-Gain EKF.
A measure of the quality of the estimation is needed in order to drive the adaptation. We propose such an index and prove the relevance of its usage. We provide a proof of convergence for the resulting observer, and the final algorithm is demonstrated via both simulations and a real-time implementation. Finally, extensions to multiple output and to continuous-discrete systems are given
A bisector line field approach to interpolation of orientation fields
International audienceWe propose an approach to the problem of global reconstruction of an orientation field. The method is based on a geometric model called "bisector line fields", which maps a pair of vector fields to an orientation field, effectively generalizing the notion of doubling phase vector fields. Endowed with a well chosen energy minimization problem, we provide a polynomial interpolation of a target orientation field while bypassing the doubling phase step. The procedure is then illustrated with examples from fingerprint analysis
On the stability of a differential Riccati equation for continuous-discrete observers
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A Real-Time Adaptive High-Gain EKF, Applied to a Quadcopter Inertial Navigation System
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Consumption minimisation for a car-like robot: Case study for a non-flat road profile
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