Isabelle Thomassin-Naggara

Luc Ceugnart

Anne Tardivon

Laurent Verzaux

Corinne Balleyguier

Patrice Taourel

Brigitte Séradour

Brigitte Seradour

What's the place of artificial intelligence?]

Keywords:

ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

Introduction

En 2019, le Conseil National Professionnel de Radiologie présentait lors de JFR (Journées Francophones de Radiologie) de printemps l'état de l'art des solutions d'intelligence artificielle et faisait un certain nombre de propositions pour une bonne intégration au sein de la campagne de dépistage du système français [START_REF] Thomassin-Naggara | Artificial intelligence and breast screening: A position paper for the French radiological community[END_REF]. En deux ans, les publications sur le sujet se sont multipliées avec une dynamique exponentielle et un élargissement de l'offre à la disposition des radiologues. Cependant, la plupart des solutions proposées ont fait l'objet d'une mise sur le marché avant même la diffusion d'études évaluant la solution en pratique clinique. Ainsi, il semble pertinent de faire le point sur les différentes possibilités offertes par l'intelligence artificielle aujourd'hui en se plaçant dans le contexte des problématiques posées par la campagne de dépistage français : les difficultés liées à la dématérialisation et la diminution de l'apport de la seconde lecture en rapport avec la diffusion de la tomosynthèse mammaire (entre 700 et 800 appareils aujourd'hui en France). Plusieurs types d'utilisations de l'intelligence artificielle se déclinent aujourd'hui dans la pratique de la mammographie de dépistage. Tout d'abord, de nombreuses solutions d'intelligence artificielle ont été développées pour améliorer le ratio qualité image-dose d'irradiation. Ces solutions ont été développées par les différents constructeurs et permettent de réduire l'irradiation. Certaines de ces solutions portent sur le système de reconstruction primaire et sont centrées sur l'optimisation du rapport signal sur bruit, d'autres sur l'optimisation du positionnement des patientes (notamment en améliorant la compression mammaire, responsable à 75 % de la dose d'irradiation). Ces dernières ont aussi l'avantage d'améliorer le Work-Flow en créant une alerte de « Cliché Techniquement Insuffisant (CTI) » auprès du manipulateur, ce qui permet de refaire immédiatement le cliché au lieu d'attendre la demande du radiologue. Ces solutions ne font l'objet d'aucun débat et se placent dans un processus d'innovation technologique inhérent à toute technique d'imagerie. L'essentiel des questionnements actuels porte sur la façon d'intégrer les solutions d'intelligence artificielle dédiées à l'interprétation de la mammographie et de la tomosynthèse mammaire. L'interprétation radiologique est une part significative du rôle du radiologue, dont les fonctions sont multiples (discussion de l'indication de l'examen, choix de l'examen pertinent, optimisation de l'image radiologique, échange avec les médecins correspondants, communication avec le patient). On peut schématiquement diviser en trois grands types d'utilisation des logiciels d'intelligence artificielle pour l'interprétation mammographique (figure 1) : l'approche « Standalone » où les études opposent et comparent la performance diagnostique d'un modèle d'intelligence artificielle à la lecture humaine, l'approche dite « Radiologue augmenté » où est étudiée la valeur ajoutée qu'apporte un système d'intelligence artificielle à la performance du lecteur humain et enfin l'utilisation des systèmes d'intelligence artificielle comme outil de triage pour sélectionner les mammographies normales et peu denses. Enfin, de nombreux travaux portent sur la capacité de l'intelligence artificielle à aller au-delà des informations radiologiques appréhensibles par l'humain et tentent de mieux définir le niveau de risque de chaque femme pour mieux adapter son suivi (type et rythme). Ainsi, de nombreux travaux sont menés pour tester des modèles prédictifs basés sur des modèles de deep learning appliqués à la mammographie en comparaison avec les modèles conventionnels utilisés aujourd'hui.

L'intelligence artificielle pour détecter un cancer du sein en 2021

Modèle d'utilisation en « Standalone » Après un enthousiasme classique devant toute nouvelle technologie, largement relayée par une communication grand public, une revue systématique récente portant sur douze études correspondant à 131 822 femmes dépistées a comparé la performance de 36 solutions d'intelligence artificielle en mammographie à celle du radiologue. Cette étude rapportait que 94 % des logiciels d'intelligence artificielle étaient moins pertinents qu'un radiologue [START_REF] Freeman | Use of artificial intelligence for image analysis in breast cancer screening programmes: systematic review of test accuracy[END_REF]. Cette étude mettait en lumière également le faible niveau méthodologique (risque de biais, inquiétude portant sur l'applicabilité en routine clinique) de la plupart des études. On constate aujourd'hui une explosion du nombre de publications relatives à l'utilisation de l'intelligence artificielle pour le diagnostic de cancer du sein qui est décorrélé avec l'utilité qu'y trouve les radiologues dans leur quotidien [START_REF] Philpotts | Advancing artificial intelligence to meet breast imaging needs[END_REF]. L'expérience des Computed Aided Diagnosis (CAD) au début des années 2000 a montré à quel point il est fondamental de tester l'utilité de ces systèmes en routine clinique. Ceci explique le faible degré de confiance des radiologues dans les systèmes d'intelligence artificielle et c'est peu probable que ce soit le type d'utilisation envisagée dans le futur. Une étude récente a montré qu'une utilisation des systèmes d'intelligence artificielle en standalone permettait d'atteindre une sensibilité identique au radiologue pour la détection de cancer mais péchait par leur manque de spécificité et notamment lorsqu'ils étaient appliqués sur les coupes de tomosynthèse [START_REF] Romero-Martín | Stand-alone use of artificial intelligence for digital mammography and digital breast tomosynthesis screening: a retrospective evaluation[END_REF]. Le dépistage du cancer du sein repose aujourd'hui sur une approche multimodale et notamment sur la combinaison mammographie et échographie justement pour pallier le manque de spécificité. Vouloir remplacer le diagnostic actuel basé sur les couples mammographie et échographie par un modèle d'intelligence artificielle basé uniquement sur la mammographie ne peut pas fonctionner et c'est ce qu'a très bien démontré l'étude prospective multicentrique (INSPIiRED003) [START_REF] Pfob | The importance of multi-modal imaging and clinical information for humans and AI-based algorithms to classify breast masses (INSPiRED 003): an international, multicenter analysis[END_REF] avec une performance de l'approche classique humaine multimodale (AUROC = 0,95) supérieure à celle d'un modèle d'intelligence artificielle standalone (AUROC 0,90). Les auteurs concluaient qu'une des pistes serait de construire des modèles d'intelligence artificielle multimodalités [START_REF] Pfob | The importance of multi-modal imaging and clinical information for humans and AI-based algorithms to classify breast masses (INSPiRED 003): an international, multicenter analysis[END_REF]. Trois autres pistes d'amélioration pourraient être envisagées : la prise en considération des antériorités et l'intégration de la notion d'asymétrie que peu de solutions proposent aujourd'hui. La troisième piste consiste en l'analyse des clichés de tomosynthèse plutôt que des clichés de mammographie, ce qui permettrait de plus d'améliorer la sensibilité de détection, en particulier en cas d'acquisition de double incidence [START_REF] Raya-Povedano | AI-based strategies to reduce workload in breast cancer screening with mammography and tomosynthesis: a retrospective evaluation[END_REF].

Ceci pose un problème à l'heure actuelle puisque l'utilisation de la tomosynthèse mammaire n'est toujours pas validée pour le dépistage du cancer du sein en France. Elle est réalisée par de nombreux radiologues pour caractériser une anomalie détectée en mammographie (puisque plus performante et moins irradiante que le cliché en compression localisé) [START_REF] Tagliafico | One-to-one comparison between digital spot compression view and digital breast tomosynthesis[END_REF] mais ceci est source de difficulté pour le second lecteur, qui ne dispose pas de ces clichés, dans un contexte où le protocole de contrôle qualité tarde à se mettre en place de façon correcte. Il est aujourd'hui bien démontré que la tomosynthèse mammaire permet d'améliorer le taux de détection et de diminuer le taux de rappel en ajout de la mammographie numérique mais également de la mammographie synthétique [START_REF] Giampietro | Accuracy and Effectiveness of Mammography versus Mammography and Tomosynthesis for Population-Based Breast Cancer Screening: A Systematic Review and Meta-Analysis[END_REF], ce qui permet de pallier la problématique de l'augmentation de dose. d'intelligence artificielle seul [START_REF] Schaffter | Evaluation of combined artificial intelligence and radiologist assessment to interpret screening mammograms[END_REF][START_REF] Jiang | Artificial intelligence applied to breast mri for improved diagnosis[END_REF] grâce à une augmentation de la sensibilité et de la spécificité [START_REF] Rodríguez-Ruiz | Detection of breast cancer with mammography: effect of an artificial intelligence support system[END_REF]. Les système CAD deep learning permettent une meilleure détection des cancers sur les acquisitions de tomosynthèse que sur les acquisitions de mammographie [START_REF] Mendel | Transfer learning from convolutional neural networks for computer-aided diagnosis: a comparison of digital breast tomosynthesis and full-field digital mammography[END_REF]. De plus, ces systèmes CAD présentent l'avantage d'accélérer le temps de lecture en aidant le radiologue à identifier la coupe optimale où l'anomalie est détectée en tomosynthèse [START_REF] Conant | Improving accuracy and efficiency with concurrent use of artificial intelligence for digital breast tomosynthesis[END_REF][START_REF] Van Winkel | Impact of artificial intelligence support on accuracy and reading time in breast tomosynthesis image interpretation: a multireader multi-case study[END_REF] qu'il s'agisse d'un vrai positif ou d'un faux positif qui sera alors plus facilement et plus rapidement négativé par le radiologue sans besoin de clichés ou d'examens complémentaires. Quelles que soient les solutions, le temps de lecture est réduit de façon significative (entre 30 et 50 %) avec un gain de sensibilité par patient et par lésion [START_REF] Van Winkel | Impact of artificial intelligence support on accuracy and reading time in breast tomosynthesis image interpretation: a multireader multi-case study[END_REF]. Les performances des solutions d'intelligence artificielle semblent identiques entre les acquisitions de mammographie 2D et les mammographies synthétiques [START_REF] Lee | Application of artificial intelligence-based computerassisted diagnosis on synthetic mammograms from breast tomosynthesis: comparison with digital mammograms[END_REF] mais sont variables en fonction du type d'image. L'expérience quotidienne montre qu'il existe un grand nombre de faux positifs sur la détection de microcalcifications alors que les solutions semblent plus au point pour la détection et la caractérisation des masses et des distorsions et ce particulièrement sur les acquisitions de tomosynthèse. Ceci est bien corrélé avec la littérature qui a bien montré qu'un système d'intelligence artificielle est plus performant que le radiologue pour détecter les masses (90 % versus 78 %) et les distorsions ou asymétries (90 % versus 50 %), avec donc une supériorité du système d'intelligence artificielle pour les cancers de stade T1 N0 [START_REF] Kim | Changes in cancer detection and false-positive recall in mammography using artificial intelligence: a retrospective, multireader study[END_REF].

L'intelligence artificielle : outil de triage

Le dépistage du cancer du sein en France repose actuellement sur la réalisation d'une mammographie systématique qui permet de détecter sept à huit cancers pour 1 000 femmes en France. Le programme français repose sur la réalisation d'une double lecture avec une seconde lecture par un expert radiologue qui permet de détecter en moyenne plus de 6 % des cancers, non décelés lors de la première lecture. Cette seconde lecture est donc nécessaire mais rend plus complexe et plus cher le programme de dépistage organisé. Actuellement en France, le coût de la deuxième lecture correspondrait à un cinquième du coût global de la campagne de dépistage, soit 12 millions d'euros. En effet, l'absence de solution de dématérialisation fonctionnelle sur le plan national conduit à un coût humain important dépendant notamment de la volumétrie du nombre d'examens envoyés en seconde lecture (acheminement de dossiers papier, affichage de film sur négatoscope. . .). De plus, l'attente du résultat de la deuxième lecture peut être anxiogène pour les patientes. Des évolutions de la L2 sont indispensables à court terme auxquelles les solutions d'intelligence artificielle devraient contribuer ou participer. Deux études récentes suggèrent que dans 20 % des cas, l'intelligence artificielle permettrait d'exclure à 100 % le diagnostic de cancer (VPN = 100 %). Ainsi, une combinaison, premier lecteur et intelligence artificielle, permettrait d'atteindre une sensibilité équivalente à celle du couple premier et deuxième lecteur dans 20 % des cas, ce qui rendrait une seconde lecture inutile [START_REF] Rodriguez-Ruiz | Can we reduce the workload of mammographic screening by automatic identification of normal exams with artificial intelligence? A feasibility study[END_REF][START_REF] Lång | Identifying normal mammograms in a large screening population using artificial intelligence[END_REF]. Une autre étude plus récente portant sur une cohorte de 15 986 patientes (taux de détection 6/1 000) a comparé plusieurs stratégies en incluant la tomosynthèse. Dans cette étude, l'utilisation de l'intelligence artificielle uniquement pour 70 % des examens n'entraînait pas de perte de sensibilité ou de spécificité et permettait un gain de temps significatif. Aussi, les auteurs avaient testé trois stratégies : double lecture mammographique, simple lecture tomosynthèse et double lecture tomosynthèse. L'introduction de l'intelligence artificielle rendait faisable en termes de temps de lecture humaine la double lecture tomosynthèse par une diminution de la volumétrie du nombre d'examens à lire. Enfin, cette étude confirmait que la double lecture tomosynthèse par rapport aux deux autres stratégies présentait une meilleure sensibilité (84,1 % contre 79,5 % en simple lecture tomosynthèse et 69 % en double lecture mammographique) et un meilleur taux de rappel par rapport à la double lecture mammographie (3,7 contre 4,2) [START_REF] Raya-Povedano | AI-based strategies to reduce workload in breast cancer screening with mammography and tomosynthesis: a retrospective evaluation[END_REF]. Ces données sont intéressantes mais doivent être pondérées par le fait qu'une seule solution d'intelligence artificielle a été évaluée (Transpara, ScreenPoint) et que méthodologiquement la plupart des études comportent de nombreux biais qui doivent nous rendre prudents quant à l'applicabilité de ces hypothèses [START_REF] Freeman | Use of artificial intelligence for image analysis in breast cancer screening programmes: systematic review of test accuracy[END_REF]. Une revue systématique publiée dans Radiology a montré l'extrême variabilité des résultats portants sur les études ayant évalué les systèmes d'intelligence artificielle comme outil de triage puisque le nombre de mammographies considérées comme lisibles seulement par l'intelligence artificielle variait de 7 à 91 % avec un taux de cancers manqués qui variait de 0 à 7 % [START_REF] Hickman | Machine learning for workflow applications in screening mammography: systematic review and meta-analysis[END_REF]. Enfin, la plupart des solutions d'intelligence artificielle actuellement sur le marché ne font pas d'évaluation de la qualité image préalable à l'interprétation. Or, l'une des principales fonctions de la seconde lecture est d'identifier les clichés techniquement insuffisants. Des solutions sont en cours d'évaluation pour proposer cette fonctionnalité (Exemple HERA-MI). Enfin l'intelligence artificielle permettrait-elle d'améliorer l'efficacité du dépistage en diminuant le taux de cancer de l'intervalle ? La réponse semble être oui puisque deux publications concordantes avec deux logiciels différents (Transpara/Profound AI iCAD) démontrent une diminution potentielle d'environ 50 % des cancers de l'intervalle grâce aux solutions d'intelligence artificielle [START_REF] Lång | Can artificial intelligence reduce the interval cancer rate in mammography screening?[END_REF][START_REF] Graewingholt | Retrospective analysis of the effect on interval cancer rate of adding an artificial intelligence algorithm to the reading process for two-dimensional fullfield digital mammography[END_REF]. De plus, un score élevé du modèle d'intelligence artificielle serait un meilleur facteur prédictif que les modèles conventionnels d'évaluation du risque basés sur la densité et les facteurs de risque pour prédire la survenue de cancer de l'intervalle (OR = 2 versus OR = 1,59) [START_REF] Dembrower | Effect of artificial intelligence-based triaging of breast cancer screening mammograms on cancer detection and radiologist workload: a retrospective simulation study[END_REF]. Enfin, une approche combinant modèle intelligence artificielle et densité mammaire permettrait de mieux prédire la survenue des cancers de l'intervalle au cours des douze mois suivants que chacune des approches séparées [START_REF] Wanders | Interval cancer detection using a neural network and breast density in women with negative screening mammograms[END_REF].

L'intelligence artificielle pour prédire un cancer du sein dans le futur

Une autre piste d'utilisation des modèles d'intelligence artificielle appliqués à la mammographie est de mieux définir le risque individuel pour adapter la meilleure stratégie de dépistage. Plusieurs études sont en cours pour définir de nouvelles stratégies de dépistage basées sur le risque personnalisé [START_REF] Pashayan | Personalized early detection and prevention of breast cancer: ENVISION consensus statement[END_REF], dont la plus connue aux Etats-Unis est l'étude WISDOM [START_REF] Eklund | The WISDOM personalized breast cancer screening trial: simulation study to assess potential bias and analytic approaches[END_REF] et en Europe, l'étude « My Pebs », qui a la particularité d'inclure la densité mammaire radiologique dans la prédiction du risque [START_REF] Rossi | Validation of a new fully automated software for 2D digital mammographic breast density evaluation in predicting breast cancer risk[END_REF]. Des résultats concordent sur l'apport de logiciels d'intelligence artificielle appliqués à la mammographie pour prédire le risque. Des études préliminaires avaient montré la supériorité d'un logiciel de deep learning par rapport aux modèles classiques de régression logistique combinant les facteurs de risques classiques de cancer du sein et ceux du modèle de Tyrer Cuzick [START_REF] Yala | A deep learning mammographybased model for improved breast cancer risk prediction[END_REF]. Plus récemment, une large étude norvégienne basée sur la cohorte KARMA a prouvé qu'un logiciel de d'intelligence artificielle combinant densité mammaire, microcalcifications, présence de masses mammographiques et l'âge était plus performant que toutes les autres techniques conventionnelles d'évaluation du risque (Polymorphisme génomique, modèle de Gail, modèle de Tyrer-Cusick). De plus, la prédiction du risque du modèle d'intelligence artificielle était améliorée lorsqu'il était combiné aux facteurs de risque classiques [START_REF] Eriksson | Identification of women at high risk of breast cancer who need supplemental screening[END_REF].

  Modèle d'utilisation type « Radiologue augmenté »Le deuxième type d'approche consiste à savoir si la performance du radiologue avec solution d'intelligence artificielle est supérieure à celle sur radiologue sans intelligence artificielle. Cette problématique, soulevée lors de la diffusion aux États Unis des premiers Computed Aided Diagnosis (CAD) avait fait l'objet de deux grandes études[START_REF] Fenton | Influence of computer-aided detection on performance of screening mammography[END_REF][START_REF] Lehman | Diagnostic accuracy of digital screening mammography with and without computeraided detection[END_REF] qui avaient mis fin à l'utilisation des premières solutions d'intelligence artificielle en démontrant une diminution de performance des radiologues par augmentation du taux de faux positifs et de biopsies pour lésions bénignes. Les études basées sur les nouvelles solutions CAD développées à partir de modèle de deep learning, sont concordantes pour démontrer une supériorité du radiologue aidé de l'intelligence artificielle par rapport au radiologue seul ou au système

Figure 1

 1 Figure 1

L

  'intelligence artificielle pourrait ainsi contribuer à mieux définir les populations à risque intermédiaire entre celui de la population générale et celui des groupes à très haut risque ainsi qu'un groupe de patientes à très bas risque où l'on pourrait envisager d'espacer le suivi. En conclusion, l'intelligence artificielle pourrait devenir une aide quotidienne pour le radiologue afin d'améliorer la qualité d'image et son interprétation. Des études complémentaires sont nécessaires pour voir comment utiliser au mieux ces nouvelles solutions pour les intégrer à la campagne de dépistage en France. Les solutions d'intelligence artificielle doivent être évaluées en première lecture et en seconde lecture, cette seconde option rend la dématérialisation obligatoire de tout le flux et la nécessité que le contrôle qualité soit pris en compte dans les logiciels d'intelligence artificielle. Déclaration de liens d'intérêts : Isabelle Thomassin-Naggara : lectures rémnunérées Bard, Bracco, Bayer, Canon, Fujifilm, GE, Guerbet, GSK, Hologic, ICAD, Incepto, Roche, Siemens. Luc Ceugnart : organisateur et intervenant FORCOMED association de formation continue en imagerie, responsable de la formation obligatoire au Depistage Organisé du cancer du sein. Anne Tardivon : intervenante FORCOMED association de formation continue en imagerie (Depistage Organisé du cancer du sein) Laurent Verzaux, Corinne Balleyguier, Patrice Taourel et Brigitte Seradour déclarent ne pas avoir de lien d'intérêt.

Bull Cancer 2022: 109 tome 109 > n87-8 > juillet 2022


D Bouvet

G Garcia

B J Gorham
email: b.j.gorham@uel.ac.uk

D Bétaille
email: david.betaille@lcpc.fr

3-D localization of pavers in a Computer Integrated Road Construction context

This paper presents a navigation system providing 3-D position and spatial attitude data for outdoor vehicles. Our system uses an odometer and an automatic laser theodolite, the data of which are fused using a Kalman filter. We show through different experiments carried out with the Sessyl test station that the high accuracies required for some civil-engineering tasks are fully satisfied, provided the beacons are properly positioned.

Introduction

The Computer Integrated Road Construction (CIRC) aims to share a common numerical geometrical data base from the design, through all the site operations up to the quality control of the geometry of the structure. It relies upon the following technologies: Computer Aided Design (CAD), automatic control, shortrange wireless communication and real-time positioning. In this context, a recently completed EU Brite-Euram research project resulted in the successful development of new control and monitoring systems for road construction equipment, to be integrated into compactors (CIRCOM) and asphalt pavers (CIRPAV) as target applications [START_REF] Peyret | The computer integrated road construction project[END_REF]. Designing an automatic process that takes the initial CAD road design and translates this into a finished product, a road built to specification, requires the provision in real-time of position and attitude information for the different machines. On compactors, an integrated system has been developed, using dead-reckoning sensors (Doppler radar, encoder and fibre-optic gyrometer) in addition to RTK GPS, unable to work continuously when alone (particularly under the bridges). A maximum deviation of 20 cm was obtained for 100 m long masks, which meets the CIRCOM specifications [START_REF] Pampagnin | Architecture of a GPS-based guiding system for road compaction[END_REF]. On asphalt pavers, RTK GPS precision was not sufficient and IMRU developed the measurement system Laserguide, designed to meet the project specification for the spatial parameters of the paver, namely ±30 mm in x and y, ±10 mm in z, and ±0.1 • in pitch and roll. The paper describes the additional developments that have been performed by IRCCyN, UEL and LCPC outside the framework of CIRC, in terms of localization algorithm. It is organised as follows. The Laserguide is described in section 2. Section 3 details the choice of representation of the mobile robot 3-D posture and proposes a 3-D evolution model. The modelling of the Laserguide measurements is also presented and the resulting localisation algorithm based on Extended Kalman Filtering (EKF) is derived. Problematic situations for the initial localization by theodolite are also presented. Results of tests carried out on a mobile platform are given in section 4 and are followed by conclusions in section 5.

The Laserguide

Existing solutions

Some possible, currently available, solutions to the problem of providing the necessary position and attitude information for the paver were considered initially. The first of these was GPS, and after some careful study, was ultimately rejected for the following reasons. The cost of establishing a Base Station, together with its high speed and often long-range radio link, as well as a minimum of one mobile receiver per vehicle, is often significant in relation to the actual cost of the vehicles themselves. Moreover, the system is dependent on the field of view of its receivers and this seldom can be guaranteed without interruption during a day's operations. In some circumstances that prevail, in Scandinavian countries for instance, where a roadway is to be constructed through forests or in cuttings, the satellite receivers are unable to detect sufficient satellites to obtain a fix over periods of several hours. In addition to shadow zones where insufficient signals are received, multi-path errors can be significant in the environment of a work-site. These effects allow measurements data to be produced but the noise factor associated with the position data can become unacceptably high. Furthermore, and following a loss of lock between an individual mobile receiver and the Base Station, there can be a significant delay in restoring the full communication ability of the system. This is particularly relevant to operation of a paver which cannot pause whilst guidance information is interrupted. Practical accuracies quoted for 3-D co-ordinates from a GPS receiver in this dynamic mode are between ±5 and ±10 mm for both x and y, and between ±20 and ±30 mm in the z parameter (height) -well short of the requirements of the new control systems for paving. However, these can be improved under certain conditions [START_REF] Peyret | Highprecision application of GPS in the field of realtime equipment positioning[END_REF]. In addition, information concerning vehicle tilts and heading can be obtained, albeit of less than the required accuracy, by using a pair of spaced GPS receivers fixed to opposite corners of the vehicle. The other system considered for automatic guidance of the paver is a Robotic Total Station (RTS) [START_REF] Bayer | Leitdrahtlose navigation von baumaschinen[END_REF]. The attainable dynamic accuracies of the respective commercial systems are very similar. They are generally equivalent to a standard error in direction of ±5 arc seconds, and in distance measured, to ±6 mm. The only mode of use for RTS instruments in vehicle guidance so far reported is that where the instrument is established in a fixed position at the rear and to one side of the vehicle. The measurements are automatically undertaken to a single target prism rigidly fixed to part of the vehicle chassis, or in the case of a road paver, to part of the 'screed'. Both update rate for the measurements and dynamic accuracy requirements for x, y and z are easily met. However, use of a single RTS instrument cannot at present provide real-time spatial attitude information for a moving road paver. Accordingly, it is common to employ either on-board sensors for heading and tilts or to use two targets on the vehicle, for example, one back right and the other front left, and consequently operate two RTS instruments simultaneously [START_REF] Booth | Surveying and construction machine control systems[END_REF]. A further necessary feature of use is provision of a radio data link to communicate the measurement information from instrument to vehicle. In practice, a RTS determines its own position and orientation in relation to the local site survey reference system before finding and locking on automatically to the vehicle target prism. Thereafter, the prism is tracked as the vehicle moves and the xyz co-ordinate information for the target is transmitted regularly to the vehicle computer for onboard control or display. Clearly, in this process, the RTS is dedicated to only one vehicle at a time. Further, the intrinsic accuracy limit in the instrument measures of vertical angles, for this single-ended measurement system operating in site conditions, ensures that a required accuracy of ±5 mm in target height cannot be achieved beyond about 250 metres range.

A new approach

In view of these shortcomings of the current systems, and more particularly, since there appears to be limited scope for their improvement in the context of site-vehicle guidance, it was decided to develop a fundamentally different approach. The technique chosen was one based on an automatic laser theodolite, developed by, and first given a public demonstration in 1983 as an RTS in, what is now the University of East London. Earliest publication of the main features of this instrument is given in [START_REF] Gorham | Method and apparatus for determining position[END_REF][START_REF] Gorham | A novel method of digital height transfer using a laser[END_REF]. Since then, the technology has been developed in applications to surveying, robot calibration and automatic tunnel guidance. A features summary of Laserguide is given below. The theodolite operates by continuous scanning of a compound laser beam comprising a pair of mutually inclined fans. The rotation of the beam is monitored internally by a single electronic angle encoder. When either of the fan beam components strikes an elec-Figure 1: A CIRPAV demonstration: the Laserguide is mounted on a trolley drawn by the asphalt paver and equipped with an encoder wheel tronic or passive retro-reflecting target, the instantaneous reading of the encoder is latched and recorded. There is almost no limit to the number of targets whose directions can be measured per sweep of the laser beams. For site vehicle guidance, the sweep rate is 1 or 2 Hz, and for short-range position monitoring, it can be increased to some 30 Hz. The repeatable pointing accuracy per target is between 1 and 2 arc seconds for ranges up to 100 metres in good optical sight conditions, and in this respect, compares favourably with current performance of commercial RTS instruments [START_REF] Gorham | A new technique of position fixing for site vehicles[END_REF]. When the first prototype system (Laserguide Mk I) was developed for paver guidance, the instrument was designed to be set up at the rear and to one side of the paver as for a conventional RTS. A fixed array of photocells constituted the staff unit and was mounted on the rear of the paver. An infra-red laser pulse transmitter was used to convey every sixth angular minute marker from the instrument encoder to the staff. Time interpolation at the staff enabled a computation of the respective direction vectors to an accuracy of 1 to 2 arc seconds. The six spatial parameters of the staff were computed at the staff, and these could be translated into spatial parameters for the supporting paver. The first phase of testing of Laserguide Mk I used the Sessyl facility at LCPC and took place during May 1998. However, although providing more real-time spatial information than a conventional RTS, and delivering data of comparable accuracy, this configuration also suffered from the same practical disadvantage; namely, guidance was lost while the instrument was moved forward to a new set-up. Obviously, the use of two instruments operating in leap-frog fashion does provide a solution, but it is a crude and expensive one. Accordingly, and in order better to exploit the capability of a Laserguide system to measure to multiple targets in a short space of time, it was decided to mount the instrument directly on the vehicle itself or on a towed sled or trolley (Laserguide Mk II; see figure 1). Here, the electronic targets of the staff are replaced by a number of local survey beacons distributed along the edges of the site, a configuration which provides uninterrupted real-time vehicle guidance. The beacons are established along a line of known points along both sides of the road trajectory. Their positions must be known accurately in terms of site global x, y and z co-ordinates although they do not have to be set out in a strictly regular spatial pattern. The scanning Laserguide measures the directions of each of the beacons struck by its beams, and this data is used to compute the instrument position and attitude. The minimum number of beacons necessary to provide this information is three, although a redundancy of at least one beacon becomes a practical requirement. These beacons, which have been developed for use with Laserguide, are robotic optical transponders. They seek and maintain their pointing towards the scanning laser instrument on the paver and, each time an integral photocell is struck by one of the sweeping fan beams, they transmit a very short optical pulse back towards the instrument. These 'reflections' latch the single integral angle encoder used to generate the six spatial parameters of the instrument and correspondingly of its underlying road surface. The Laserguide instrument and one of its four associated robotic beacons provided for the field tests at LCPC in November 1999 are shown in figure 2.

3-D localization by EKF

From the measured directions of the beacons struck by the laser beams, it is possible to compute by spatial resection the Laserguide and vehicle 3-D postures. As we will see in subsection 3.4, this approach is used to evaluate the initial position and attitude of the asphalt paver. But for real-time positioning, an Extended Kalman Filter is used. Indeed, fusing the Laserguide angles with the measurements of an additional encoder wheel presents several advantages. First, it allows to maintain an estimation of the vehicle 3-D posture even when angle measurements are unavailable (either because the beacons are temporary masked by another vehicle, or because the theodolite measurements are erroneous). Secondly, it is possible to take into account the angles issued by the theodolite one at a time contrary to quasi-static approaches where several measurements are used simultaneously, as if corresponding to a single position and attitude of the paver. And finally, although the Laserguide scanning rate is 1 Hz, integrating measurements of the complementary sensor allows to provide position and attitude data at a higher frequency.

Definition of the 3-D pose and kinematic model of the vehicle

Six independent variables are generally required to describe the 3-D posture (position and attitude) of a vehicle. For our application, the position is defined by the co-ordinates (x, y, z) of the centre M of the encoder wheel in the reference frame R 0 , and for the attitude, the roll-pitch-heading angles have been chosen. As a consequence, the 3-D posture is defined by:

x = [x, y, z, R, P, H] t (1)
From this choice of representation a kinematic model adapted to the asphalt pavers was derived. Since these are very slow machines (about 10 cm/s) working on smooth terrain with very progressive gradient variations, the vehicle is assumed to move between instants t i-1 and t i on an inclined plane defined by the roll and pitch angles R i-1 and P i-1 . The movement on this plane is considered as an elementary translation δ followed by an elementary rotation of speed ω. Since an unique encoder wheel is used, only δ is measured and ω is estimated by EKF. Denoting T s the sampling

α a α b (P s ) (P a ) (P b ) a b x S y S z S S θ ρ B k ( S x k , S y k , S z k )
rotation axis Figure 3: Sensor modelling period, the resulting evolution model is given by:

x i = x i-1 + δ i cos(P i-1 ) cos(H i-1 ) y i = y i-1 + δ i [cos(R i-1 ) sin(H i-1 ) + . . . cos(H i-1 ) sin(P i-1 ) sin(R i-1 )] z i = z i-1 + δ i [sin(H i-1 ) sin(R i-1 ) + . . . -cos(H i-1 ) cos(R i-1 ) sin(P i-1 )] R i = R i-1 P i = P i-1 H i = H i-1 + T s • ω i-1 ω i = ω i-1 (2)
or by the vector equation:

x a i = f (x a i-1 , u i ) ( 3
)
where f is the prediction function, u the system input (here only δ), and x a the augmented state vector:

x a = [x, y, R, P, H, ω] t (4)
Actually, the evolution model and the proprioceptive measurement are assumed to be corrupted by uncorrelated white Gaussian noises of mean zero and known variances:

x a i = f (x a i-1 , u i + β i ) + α i ( 5
)
where α is the model noise of covariance matrix Q α , and β the input noise of variance Q β .

Laserguide modelling and observation equations

The Laserguide is modelled as shown on figure 3. The fan-shaped laser beams are denoted (P a ) and (P b ). The sensor centre S is given by the intersection of (P a ) and (P b ) with the rotation axis z S . An encoder allows to measure the rotation angle ρ with a precision of 1 arc second. Angle θ is given by θ = ∠( aS b) and vector x S is such that x S = a when ρ = 0. The frame F S associated with the sensor is given by (S, x S , z S ∧ x S , z S ).

Each laser beam emitter is associated with an IR receiver oriented along axis a (resp. b). Thus, whenever the Laserguide receives a pulse from a beacon, it is possible to know which laser beam has struck the target by checking which receiver has detected the signal. The corresponding encoder reading is denoted ρ a or ρ b . When the laser beams strike beacon B k , the corresponding angular measurements ρ a,k and ρ b,k are given by:

s a,k = -S x k S z k cot(α a ) + . . . S y k ( S x 2 k + S y 2 k ) -S z 2 k cot(α a ) 2 c a,k = S y k S z k cot(α a ) + . . . S x k ( S x 2 k + S y 2 k ) -S z 2 k cot(α a ) 2 ρ a,k = arctan2(s a,k , c a,k ) (6) s b,k = -S x k S z k cot(α b ) + . . . S y k ( S x 2 k + S y 2 k ) -S z 2 k cot(α b ) 2 c b,k = S y k S z k cot(α b ) + . . . S x k ( S x 2 k + S y 2 k ) -S z 2 k cot(α b ) 2 ρ b,k = arctan2(s b,k , c b,k ) -θ (7)
where S b k = [ S x k , S y k , S z k , 1] t are the homogeneous co-ordinates of beacon B k in the sensor frame F S . Actually, only the beacon co-ordinates 0 b k in the reference frame are known, and the homogeneous coordinates S b k are given by:

S b k = S T M • M T 0 (x) • 0 b k (8)
The homogeneous transformation matrix S T M is fixed once and for all after calibration of the Laserguide in the vehicle frame F M and the homogeneous transformation matrix M T 0 depends on the 3-D posture x of the vehicle. Finally, the Laserguide observations at observation instant t j can be rewritten in the following form:

Z j = g a|b,k (x a j ) + γ j ( 9
)
where γ is a white Gaussian noise of mean zero and variance Q γ , Z the system scalar output, and g a|b,k the observation function, the expression of which depends on the laser beam which struck the beacon and on the particular beacon struck by the beam.

Localization by Kalman filtering

Since the evolution and observation functions f and g a|b,k are nonlinear, an extended Kalman filter is used to compute the estimation xa of the augmented state vector and the associated covariance matrix P of the estimate error.

At each sampling period, the state estimate is predicted from the input readings δ:

xa i|i-1 = f (x a i-1|i-1 , δ i ) P i|i-1 = A i P i-1|i-1 A t i + B i Q β B t i + Q α ( 10
)
with the following Jacobian matrices:

A i = ∂f(x a , u) ∂x a x a =x a i-1|i-1 ,ui=δi (11)
B i = ∂f(x a , u) ∂u x a =x a i-1|i-1 (12)
And whenever a laser beam strikes beacon B k , this prediction is corrected as follows:

xa i|i = xa i|i-1 + K i Z i -g a|b,k (x a i|i-1 ) P i|i = P i|i-1 -K i C a|b,k i P i|i-1 (13)
where the jacobian matrix C a|b,k i is given by:

C a|b,k i = ∂g a|b,k (x a ) ∂x a x a =x a i|i-1 (14)
and the Kalman gain K i is defined by:

K i = P i|i-1 (C a|b,k i ) t • C a|b,k i P i|i-1 (C a|b,k i ) t + Q γ -1 (15)
Actually, the IR pulses sent to the Laserguide are unsigned, which means that the beacons are undistinguishable. The chi-squared distribution test provides a mean to know which target has been detected before processing the updating step.

For each beacon B k , k = 1 . . . N, the so-called Mahalanobis distance is computed as follows:

d k i = |Z i -g a|b,k (x a i|i-1 )| C a|b,k i P i|i-1 (C a|b,k i ) t + Q γ (16)
In the case of a linear system corrupted by white Gaussian noises of mean zero, and with a 1-dimensional innovation, the Mahalanobis distance d has a 99.7% probability to be lower than 3 [START_REF] Maybeck | Stochastic Models, Estimation and Control[END_REF]. Despite the fact that in our application, the system is nonlinear, we have kept this threshold. As a consequence, k such that d k i < 3 indicates which beacon has been struck by laser beam (P a ) or (P b ) at instant t i . The resulting localization algorithm is given by:

Initialization: xa 0|0 , P 0|0 for i = 1, 2, . . . do δ i ← odometer measurement A i ← ∂f (x a ,u) ∂x a x a =x a i-1|i-1 ,u=δi B i ← ∂f (x a ,u) ∂u x a =x a i-1|i-1 xa i|i-1 ← f (x a i-1|i-1 , δ i ) P i|i-1 ← A i P i-1|i-1 A t i + B i Q β B t i + Q α xa ← xa i|i-1 P ← P i|i-1 for each angular measurement Z performed be- tween t i-1 and t i do for each beacon B k do C a|b, k i ← ∂g a|b,k (x a ) ∂x a x a =x a d k i ← |Z(j)-g a|b,k (x a )| C a|b,k i P (C a|b,k i ) t +Qγ end for if min(d k i ) < 3 then l ← arg mind k i K i ← P (C a|b,l i ) t C a|b,l i P (C a|b,l i ) t + Q γ -1 xa ← xa + K(i)[Z(i) -g a|b,l (x a )] P ← P -K(i) C

Localization initialization

To work properly, the EKF requires a good estimation xa 0|0 of the initial state vector. Since the paver is assumed to be motionless when starting its work, we have ω0|0 = 0 rad/s. The initial 3-D posture x0|0 is computed from the full direction vector (both horizontal and vertical direc- When motionless, the Laserguide is equivalent to a theodolite, i.e. an instrument which can measure the azimuth and elevation angles of a given target. These angles are computed from the Laserguide measures ρ a,k and ρ b,k as follows:

Beam (P a ) Beam (P b ) Beacon B k ρ a,k ρ b,k λ k σ k x S y S S
λ k = ρ a,k + arctan     tan(α a ) tan(α b ) sin(ρ a,k -ρ b,k -θ) 1- tan(α a ) tan(α b ) cos(ρ a,k -ρ b,k -θ)     σ k = arctan tan(α a )• sin(λ k -ρ a,k ) (17)
If one tries to solve the localization problem directly by writing the equations that involve the position and attitude of the vehicle, one obtains a complex system of six nonlinear equations with six unknowns. Actually, as shown in [START_REF] Le Corre | SIREM: the absolute location of civil-engineering equipment[END_REF], it is possible to reduce this system to a problem with 3 unknowns by introducing the distances between the sensor and the beacons as new variables.

Let r k be the distance from the origin of the sensor frame S to beacon B k . The co-ordinates of B k in the sensor frame are given by:

S x k = r k cos(λ k ) cos(σ k ) S y k = r k sin(λ k ) cos(σ k ) S z k = r k sin(σ k ) (18)
By writing the (known) distances d ij between beacons B i and B j , three equations of the following form are obtained:

α ij = r i /r j + r j /r i -d 2 ij /(r i • r j ) (19) λ 1 σ 1 λ 2 σ 2 λ 3 σ 3 x S y S z S S r 1 r 2 r 3 B 1 B 2 B 3 d 12 d 23 d 31
α ij = 2(cos(σ i ) cos(λ i ) cos(σ j ) cos(λ j ) + . . . cos(σ i ) sin(λ i ) cos(σ j ) sin(λ j ) + sin(σ i ) sin(σ j )) (20)
Finding the values r k provides the co-ordinates of the beacons in the sensor frame. If one defines a frame F B associated with the three non aligned beacons, one can compute the homogeneous transformation S T B . Knowing 0 T B and M T S , it is easy to obtain the homogeneous transformation matrix 0 T M and hence, the spatial position and orientation of the vehicle in the work site frame:

0 T M (x) = 0 T B • S T -1 B • S T M (21)
As a consequence, the whole problem lies in finding the good association beacons-angles (recall that the beacons are unsigned) and in determining the proper distances r 1 , r 2 and r 3 . The algorithm dealing with this issue is not discussed here, but it works provided the theodolite is not stopped on the cylinder generated by the circle passing by the three beacons and normal to the plane containing these beacons. This can be shown by studying the observability of the following system, defined from equation (20):

α = h(r) (22)
where the system output is α = [α 12 , α 23 , α 31 ] t and the state vector is r = [r 1 , r 2 , r 3 ] t . The property of observability for a dynamical system is related to the possibility to reconstruct the state information given the inputs and outputs of the system. In the specific case of static localisation using theodolite, the problem is simple to study, since the dimension of the output vector equals the dimension of the state vector r. In this case, one simply finds the non observable situations by checking the rank of the jacobian matrix ∂h ∂r .

Its determinant is given by the following expression:

∆ = r 2 1 -r 2 2 +d 2 12 r 2 1 r2 r 2 2 -r 2 1 +d 2 12 r1r 2 2 0 0 r 2 2 -r 2 3 +d 2 23 r 2 2 r3 r 2 3 -r 2 2 +d 2 23 r2r 2 3 r 2 1 -r 2 3 +d 2 31 r 2 1 r3 0 r 2 3 -r 2 1 +d 2 31 r3r 2 1 (23)
In a frame denoted F 123 , the origin of which is the centre of the circle of radius R passing through the three beacons, and the z axis of which is orthogonal to the plane containing these beacons, the homogeneous co-ordinates of beacon B k and the theodolite centre S are given by:

123 b k = [R cos(θ k ), R sin(θ k ), 0, 1] t (24) 123 s = [ρ cos(θ), ρ sin(θ), h, 1] t (25)
Hence, we have:

r 2 i = R 2 + ρ 2 + h 2 -2Rρ cos(θ i -θ) (26) d 2 ij = 2R 2 (1 -cos(θ i -θ j )) (27)
With this choice of representation, the numerator of determinant ∆ is given after simplification by:

(R 2 -ρ 2 ) (sin(θ 1 -θ 2 ) + sin(θ 2 -θ 3 ) + sin(θ 3 -θ 1 )) 2 (28)
which means that ∆ = 0 ⇔ ρ = R, since θ 1 = θ 2 , θ 2 = θ 3 and θ 3 = θ 1 .

As a consequence, the whole set of non-observable positions with a theodolite is contained in the cylinder generated by the circle passing through the three beacons and orthogonal to the plane containing these beacons, which means that near this cylinder, the accuracy of the estimation of the initial position falls drastically.

Experimental results

The Sessyl station

To evaluate the Laserguide performances, we have used the Sessyl station, which is the localization systems test and research facility of the Laboratoire Central des Ponts et Chaussées. Its main objective is to support the research work and localization systems assessments carried out in the field of site robotics and • GPS receivers, absolute, differential and Real-Time Kinematic,

• radio positioning systems using ground beacons,

• optical systems using laser triangulation, such as the Laserguide,

• levelling systems using laser plane, etc.

It consists of a closed track composed of a metal rail fixed upon a concrete wall and a mobile carriage moving on it. The upper part of the carriage is a platform which can be controlled in height, pitch and roll by three jacks and which supports the tested localization system. The computation of the Sessyl reference trajectory requires a static calibration. To this end, a SOKKIA NET 2 theodolite was used to perform a static survey of 300 positions of the carriage around the track. The curvilinear abscissa of each station (distance travelled by Sessyl along the track from the origin of the reference frame F 0 ) was also computed using the measurements of the theodolite. During a test, the following data are stored with a frequency of 64 Hz:

• the position of the platform relative to the carriage (with three position transducers),

• the attitude of the platform (directly measured with two inclinometers), • the distance travelled by SESSYL along the track (with an encoder, the resolution of which is 3 mm, and which is corrected every 10 to 15 m),

• the time (with one millisecond resolution).

Since the trajectory followed by the carriage is perfectly known, it is possible to reconstruct at each sampling period the complete 3-D posture of the platform in the reference frame F 0 . Table 1 summarizes the main features of Sessyl. For further details on this station, the reader is referred to [START_REF] Peyret | A new facility for testing accurate positioning systems for road construction robotics[END_REF].

Tests and results

Although only three beacons are needed to localize the mobile platform, a fourth one has been settled (see figure 7) and it is used in the positioning computations.

Several tests have been carried out. The data issued by all sensors are recorded and post-processed so as to compare the reference 3-D posture of the Sessyl platform with its estimation by our 3-D localization algorithm. The movements of the mobile platform have been programmed as follows:

• tests 1, 2 and 3: one or two complete laps at constant speed (10 cm/s) without height, gradient and cross-fall variations,

• test 4: one complete lap without height, gradient and cross-fall variations, but with numerous stops, so as to simulate the real motions of a paver on site,

• tests 5 and 6: one complete lap at constant speed with variations of the cross-fall angle,

• tests 7 and 8: variations of height and gradient angle. The platform movements are programmed so as to simulate a vehicle moving on a road with a variable slope. The first validation is to verify that the platform rotation speed ω is properly estimated by the EKF. The comparison of the estimate ω with the output of a fibre-optic gyro fixed on Sessyl shows that both speeds are almost identical and confirms that, with the Laserguide, an encoder wheel is sufficient to evaluate the 3-D posture of asphalt pavers. The second validation consists in seeing to what extent the positioning requirements defined in the framework of the CIRC project are satisfied. To this end, the following percentages have been calculated:

• estimations within the planimetric tolerance:

(x Sessylx) 2 + (y Sessylŷ) 2 ≤ 3 cm,

• estimations within the altimetric tolerance: |z Sessyl -ẑ| ≤ 1 cm,

• estimations within the R-positioning tolerance:

|R Sessyl -R| ≤ 0.1 • ,
• estimations within the P -positioning tolerance:

|P Sessyl -P | ≤ 0.1 • ,
• fully satisfying position estimations,

• fully satisfying attitude estimations,

• fully satisfying posture estimations. Yet, these performances can be drastically reduced in particular conditions. The test presented in the following subsection illustrates this phenomenon.

Additional test

Our concern was to evaluate the EKF behaviour when the asphalt paver moves through the cylinder problematic for the initial localization. To this end, three beacons have been positioned so that the resulting cylinder intersects the Sessyl track. As figure 8 testifies, the positioning accuracy drops when the carriage approaches the cylinder and the Laserguide performances are strongly degraded (see table 3). To avoid such a phenomenon, one will have to make sure that four beacons are always visible for the Laserguide and that these beacons do not belong to the same circle.

Conclusion

In order to determine precisely and in real-time the 3-D co-ordinates and spatial attitude of asphalt pavers, a localisation system, which fuses by Kalman filtering measurements issued by an odometer and an automatic laser theodolite, is proposed. Through the different experiments carried out with the evaluation station Sessyl, it has been shown that a second proprioceptive sensor was not necessary to evaluate the rotation speed of the machine in the rolling plane, since its estimation by the extended Kalman filter precisely corresponds to the outputs of a fibre-optic gyro fixed on the station. Moreover, with this navigation algorithm, 95% of the estimated postures meet the accuracy requirements, namely ±3 cm in x and y, ±1 cm in z and ±0.1 • in pitch and roll. As a comparison, the positioning error of the previous method, based on quasi static 3-D localization, had for standard deviation σ = 4 cm in x and y, and σ = 2 cm in z. We see that the improvement is really significant with only one additional encoder wheel.

Figure 2 :

 2 Figure 2: The Laserguide mounted on station Sessyl and one of the robotic beacons

  α a and α b are the tilt angles of half-planes (P a ) and (P b ). The plane containing S and orthogonal to the rotation axis is denoted (P c ). Vector a is defined by (P s )∩(P a ) = [S, a) and vector b by (P s )∩(P b ) = [S, b).

Figure 4 :

 4 Figure 4: Azimuth and elevation angles of beacon B k and corresponding Laserguide angular measures

Figure 5 :

 5 Figure 5: Variables involved in the computation of the initial 3-D posture

Figure 6 :

 6 Figure 6: The Sessyl station

Figure 7 :

 7 Figure 7: 3-D position of the Sessyl platform and location of the four beacons for a test with height and gradient variations

Figure 8 : 3 -

 83 Figure 8: 3-D position of the Sessyl platform and location of the three beacons for the additional test. The areas where the planimetric error exceeds 3 cm are visible in the xy plane.

Table 1 :

 1 Movement amplitude and accuracy of the Sessyl station

	Degree of freedom Amplitude Accuracy (±2σ)
	x	81 m	±5 mm
	y	16 m	±5 mm
	z	30 cm	±2 mm
	R	6 •	±0.07 •
	P	6 •	±0.05 •
	H	360 •	±0.1 •

Table 2

 2

	reports the positioning accuracy of the Laser-
	guide. Tests 4 and 8 excepted, more than 95% of
	the estimated 3-D postures satisfy the requirements
	defined by the end-users of a localization system for
	asphalt pavers.

Table 2 :

 2 Percentages of estimations within the fixed tolerances

Table 3 :

 3 Percentages of estimations within the fixed tolerances for the additional test

	Test	xy	z	R	P	xyz RP	all
	9	80.3 99.9 98.9 99.9 80.3 98.8 79.2


Patrice Berthod

Lionel Aranda

A Vernière

Thermo-mechanical Behavior of HEA Alloys Containing Interdendritic MC Carbides

ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

Introduction

The casting route allows obtaining in situ composites which combine a HEA dendritic matrix and an interdendritic network of MC carbides. This association bring the simultaneous benefit of the intrinsic good creep resistance of the HEA matrix and of the delayed {steady state to tertiary} transition of creep regime given by the improved cohesion between neighbor dendrites resulting from script-like carbides. However, the difference in thermal expansion behavior between matrix and carbides may induce curious geometrical behavior of the whole alloy at high temperature, as earlier observed for cobaltbased

Chemical compositions & as-cast microstructures of the alloys [3-5]

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Thermo-mechanical Behavior of HEA Alloys Containing Interdendritic MC Carbides

Patrice Berthod 1,2 , Lionel Aranda 2 , Anne Vernière 1,2 1 Faculté des Sciences et Technologies, Campus Victor Grignard, F-54500 VANDOEUVRE-LES-NANCY (France) [START_REF] Berthod | Thermal expansion of chromium-rich iron-based or iron/nickel -based alloys reinforced by tantalum carbides[END_REF] Institut Jean Lamour, CNRS (UMR 7198), 2 allée André Guinier, Campus Artem, F-54000 NANCY (France)

patrice.berthod@univ-lorraine.fr

Dimensional behaviors during heating up to 1200°C and during the following {1 hour}-isothermal stage

• "Mn1Cr1" and "Mn0.5Cr1.5": linear expansion up to 1200°C

• Less Mn / more Cr seems to decrease thermal expansion (24 × 10 -6 K -1 down to 18 × 10 -6 K -1 )

• "Mn1Cr1TaC" : linear expansion up to 1200°C

• "Mn0.5Cr1.5TaC": linear expansion up to 950°C, then slowed expansion followed by inversion

• "Mn1Cr1HfC" : linear expansion up to 850°C, then slowed expansion followed by inversion • "Mn0.5Cr1.5HfC": linear expansion up to 650°C, then slowed expansion followed by inversion

• For the carbides-containing alloys (except "Mn1Cr1TaC"), during the isothermal stage at 1200°C, the dimensional contraction goes on, but slower and slower, leading to a relative stabilization

Conclusion

The The corresponding supplemental proceeding TMS is available; see pp.679-688.

[ 1 ]

 1 and {iron and/or nickel}-based alloys [2]. This work aims to investigate the dimensional behavior of MC-strengthened HEA alloys at high temperature during heating as well as during an isothermal stage at H.T., in order to observe the possible consequences of the internal interaction between matrix and carbides resulting from differential thermal expansion. Effectively, in contrast with the carbides-free quinary HEA alloys based on Co, Ni, Fe, Mn and Cr, the alloys based on these HEA and added with TaC or HfC carbides can be expected to behave similarly to the TaC-containing Co-based and Fe(Ni)-based alloys evocated above.

  "Mn1Cr1" is the original Cantor's alloy (equimolar in Co, Ni, Fe, Cr and Mn) in a conventionally cast version; "Mn0.5Cr1.5" is a modified version resulting from a decrease in Mn (× 0.5 → 10 at.%) and an increase in Cr (× 1.5 → 30 at.%) ; both of them are single-phased • "Mn1Cr1TaC" and "Mn0.5Cr1.5TaC" are developed from the quinary "Mn1Cr1" and "Mn0.5Cr1.5" alloys respectively; they additionally contain 4 wt.% Ta and 0.25 wt.% C; their matrixes are similar to the two quinary alloys (except the additional presence of about 1 wt.%Ta in solid solution); eutectic TaC carbides, located in the interdendritic spaces, are present in their microstructures • "Mn1Cr1HfC" and "Mn0.5Cr1.5HfC" are the "Mn1Cr1" and "Mn0.5Cr1.5" alloys modified by the addition of 4 wt.% Hf and 0.25 wt.% C; their matrixes are similar to the two quinary alloys described above (notably: no Hf in solid solution); eutectic HfC carbides are present in the interdendritic spaces; some blocky HfC carbides -probably of a pre-eutectic nature -also formed, forming clusters.

  presence of carbides obviously led to the high temperature visco-plastic deformation of the matrix under the compressive stresses applied by the carbides, until the total decrease of the tensile stresses which developed in the carbide network during the first part of heating. These MC-reinforced HEA alloys are thus affected by the phenomena of matrix/carbides interactions and internal stresses development previously observed for Co, Fe or Ni-based alloys containing carbides with similar characteristics. Such behavior can cause problems of dimensional precision as well as of internal deterioration of the alloys, especially in situation of thermal cycling.

Acknowledgements:

Nassima Chenikha, Corentin Gay and Pauline Spaeter for their help for synthesizing some of the alloys.