Bénédicte Batrancourt
email: benedicte.batrancourt@upmc.fr

Michel Dojat
email: michel.dojat@ujf-grenoble.fr

Bernard Gibaud
email: bernard.gibaud@irisa.fr

Gilles Kassel
email: gilles.kassel@u-picardie.fr

A core ontology of instruments used for neurological, behavioral and cognitive assessments

Keywords: Biomedical ontology, Artefact ontology, Knowledge Representation, Neuroscience, Brain

Neurosciences are progressively moving into a mass computational intensive era with the fusion of numerous large heterogeneous data sets from cellular to system level. To process and share this mass of information in a consistent and computational amenable form, computerized techniques -among them, ontologies -are currently designed to store, analyze and access this information. Recently, we proposed a multi-layered and multi-components ontology to deal with MR images and regions-of-interest that can be represented onto the images. In the present paper, we extend our initial ontology by adding a core ontology of subject data acquisition instruments modeling neuroclinical, neuropsychological and neurobehavioral tests used for neurological, behavioral and cognitive skills assessment. This ontology deals with instruments per se as specific artefacts, their variables and measured scores, and actions performed using instruments. In the paper, we underline the major aspects of our approach and emphasize its potential interest as a semantic reference for various neuroscience applications.

Introduction

Similarly to other biomedical scientists, neuroscientists collect facts, use knowledge (what they currently know about these facts) and then make inferences to produce new knowledge and facts [START_REF] Bodenreider | Bio-ontologies: current trends and future directions[END_REF]. As a consequence, there is a crucial need for computerized techniques to store, manage, analyze and share this information [START_REF] Ascoli | Mobilizing the base of neuroscience data: the case of neuronal morphologies[END_REF] [START_REF] Van Horn | Multisite neuroimaging trials[END_REF]. Alike bioinformatics with in silico experiments [START_REF] Stevens | Using OWL to model biological knowledge[END_REF], neuroscience is progressively moving into a mass computational intensive era with fusion of various large heterogeneous data sets from cellular to system level [START_REF] Martone | E-neuroscience: challenges and triumphs in integrating distributed data from molecules to brains[END_REF]. These datasets are often disseminated in various medical centers and carried out in highly distributed environments such as grids [START_REF] Small | Database-managed grid-enabled analysis of neuroimaging data: the CNARI framework[END_REF] [START_REF] Van Horn | Multisite neuroimaging trials[END_REF]. Many research groups in various institutions make strong efforts to develop federated and distributed infrastructures for biomedical imaging data [START_REF] Barillot | Federating Distributed and Heterogeneous Information Sources in Neuroimaging: The NeuroBase Project[END_REF][14] [START_REF] Keator | BIRN Function, BIRN Morphometry, A national human neuroimaging collaboratory enabled by the Biomedical Informatics Research Network (BIRN)[END_REF]. To process the mass of information in a consistent and computational amenable form, ontologies have become recently very important in neurosciences [START_REF] Laird | Lost in localization? The focus is meta-analysis[END_REF] [START_REF] Temal | Towards an ontology for sharing medical images and regions of interest in neuroimaging[END_REF]. The prominent effort in this direction is currently done via the Biomedical Informatics Research Network (BIRN) which proposes, based on an ontology-based vocabulary called BIRNLex a unified representation of the biomedical domains typically used to describe neuroscience data [START_REF] Bug | The NIFSTD and BIRNLex Vocabularies: Building Comprehensive Ontologies for Neuroscience[END_REF]. This ontological effort is driven by the OBO (Open Biomedical Ontologies) initiative that promotes shared biomedical ontologies [START_REF] Smith | The OBO Foundry: coordinated evolution of ontologies to support biomedical data integration[END_REF].

In Neuroscience, imaging plays a central role providing information about brain structure and function. Among the different imaging modalities, Magnetic Resonance Imaging (MRI) strongly contributes to studying the healthy and the pathological brain, from both anatomical and functional perspectives and appears as the cornerstone of most cognitive studies [START_REF] Logothetis | What we can do and what we cannot do with fMRI[END_REF]. In parallel with MRI images, questionnaires and batteries of tests are currently used to assess the neurological state of the subjects as well as their cognitive and behavioural performances. All these instruments focus on specific brain functions, which rely on specific anatomical structures or pathways, so they can be used in diagnosing brain dysfunction or damage and measuring intensity/severity of a subject's trait (e.g. behavioral, personality, psychological, psychopathological) [START_REF] Lezak | Neuropsychological Assessment[END_REF]. Such tests and questionnaire-based interviews are complementary to MR images to investigate the correlation between measures of brain structure and function, derived from MR image analysis, and neurological, cognitive and behavioural traits, highlighted by test-and questionnaire-based assessments [START_REF] Evans | Brain Development Cooperative Group, The NIH MRI study of normal brain development[END_REF].

Recently, we proposed a multi-layered ontology (named OntoNeuroLOG) to deal with MR images and regions-of-interest that can be represented onto the images [START_REF] Temal | Towards an ontology for sharing medical images and regions of interest in neuroimaging[END_REF]. In the present paper, we extend our initial ontology by adding a new component to model the general characteristics of the neuroclinical, neuropsychological and behavioral tests and scores mostly used. To our knowledge, this significant effort represents the first attempt to model this kind of data. This core ontology is currently specialized for sharing data between four French neuroimaging centres through the federated NeuroLOG architecture 2The paper is organized as follows: in the next section we remind of the most generic modules of OntoNeuroLOG onto which our Instrument ontology relies, especially the foundational ontology DOLCE , leading to the conceptualization of specific classes of instruments.

3 [START_REF] Kassel | A formal ontology of artefacts[END_REF] and a formal ontology of artefacts recently designed . We then detail our main contribution, an ontology of subject data acquisition instruments, including instruments per se as specific technical artefacts, with their variables and scores associated, and actions performed using an instrument. In the Discussion section we underline the major aspects of our approach and emphasize in Conclusion its potential interest as a semantic reference for various neurosciences applications.

with different levels of abstraction. Schematically, three levels can be identified: at the most abstract level, the foundational DOLCE ontology [START_REF] Masolo | The WonderWeb Library of Foundational Ontologies and the DOLCE ontology[END_REF] provides a set of abstract concepts (e.g. physical object, event, quality) and relations (e.g. parthood, constitution) for structuring (by specialization) any type of domain. At this level, DOLCE is supplemented by a few ontologies such as a formal ontology of artefacts [START_REF] Kassel | A formal ontology of artefacts[END_REF]. At an intermediate level, "core" domain ontologies [START_REF]Proceedings of the EKAW'04 Workshop on Core Ontologies in Ontology Engineering[END_REF] define generic and central concepts in various domains such as medical images [START_REF] Temal | Towards an ontology for sharing medical images and regions of interest in neuroimaging[END_REF] or programs and software [START_REF] Lando | An ontological investigation in the field of computer programs[END_REF]. Lastly, at the most specific level, the previously mentioned ontologies are then specialized to define more specific concepts in the field of neuroimaging and image processing tools, respectively.

We adopt two different modeling languages for specifying our ontologies. At a developmental stage, modeling choices are specified -in the context of OntoSpec methodology [START_REF] Kassel | Integration of the DOLCE top-level ontology into the OntoSpec methodology[END_REF] -by means of a semi-informal language which is semantically rich and includes temporally-indexed relations and meta-properties of the OntoClean methodology [START_REF] Guarino | An Overview of OntoClean[END_REF]. At run-time, the ontologies are encoded in a dialect of OWL -OWL-Lite augmented with rules -which is semantically much poorer than the former but allows for effective automatic inferences (the semantic search engine Corese [START_REF] Corby | Querying the Semantic Web with Corese Search Engine[END_REF] is currently used within the NeuroLOG project).

The new ontology of subject data acquisition instruments is situated at the intermediate level of core ontologies. Its definition relies on abstract primitives provided by generic ontologies (a list of these modules is presented in Table 1). Furthermore, it is used to model classes of specialized instruments (e.g. neuroclinical and neuropsychological instruments) which correspond to "domain" ontologies.

In the following part of this section, we remind of the main structuring principles and concepts provided by the modules of Table 1. 4 With respect to our notation, the informal labels on DOLCE's categories appear in the text in the Courrier new font with First Capital Letters for the concepts and a javaLikeNotation for relations. The same conventions apply for all the ontologies presented in the paper.

, that is to say entities that cannot be instantiated (e.g. "my car") rather than universals (e.g. "being a car"). Four subdomains of Particulars are distinguished (see Fig. 1):

Endurants are entities "enduring in time" 5Perdurants are entities "occurring in time" (e.g. your reading of this article) in which Endurants temporarily participate.

. Within Endurants, Physical Objects (e.g. a printed copy of an article) are distinguished from Non-Physical Objects (e.g. the contents of this article), this distinction corresponding to a difference between two realities or modes of existence for the entities. Basically, Non-Physical Objects exist insofar as agents speak about them. The domain of Non-Physical Objects covers entities whose existence depends on either an individual (for Mental Objects)o r a community of agents (for Social Objects).

Endurants and Perdurants have Qualities that we perceive and/or measure (e.g. the weight of the printed copy of an article, the time it takes for you to read this article). Note that these Qualities are inherent to the entity that bears them, since they are characteristic for it and they are present throughout the course of the entity's existence.

Qualities take "values", called Quales (e.g. 25 grams, 20 minutes) within quality region spaces. As a complement to DOLCE, our "Participation role" module specializes the participation relation to account for specific ways in which Endurants temporally participate in Perdurants (e.g. isAgentOfAt, isInstrumentOfAt, isResultOfAt) and such relations, in turn, are used to define participation roles specializing the concept Endurant (e.g. Agent, Instrument, Result).

Within the domain of Perdurants, Actions have been informally introduced into DOLCE-Lite-Plus as Accomplishments that "exemplify the intentionality of an agent" [START_REF] Masolo | The WonderWeb Library of Foundational Ontologies and the DOLCE ontology[END_REF]. With the aim of conceptualizing the notion of artefact and subsequently the notion of subject data acquisition instrument, we introduced two specializations of these Actions. These specializations rely on a distinction between two kinds of intentions.

Following on from Searle [START_REF] Searle | Intentionality[END_REF], contemporary philosophers distinguish between two overall kinds of intention -a "prior intention" and "intention-in-action", to borrow Searle's terms -which differ according to their temporality, role and content [START_REF] Pacherie | The content of intentions[END_REF]. A prior intention consists in planning an action (prior to the realization of the action) and then rationally controlling the action. It relies on a conceptual representation of the type of action to be performed, comprising an objective (i.e. a goal) and, optionally, a means of achieving it (i.e. a plan). Once the action has been initiated, the intention-in-action consists in the continuous guidance and control of the initiated action by relying on a descriptive, context-sensitive representation of the said action.

Taking into account current knowledge on the phenomenology of actions [START_REF] Pacherie | The phenomenology of action: A conceptual framework[END_REF], we first assimilate Actions to processes controlled by an intention (intention-in-action and/or prior intention); these contrast with Happenings which lack an intentional cause. We then introduce two specializations of Actions. Firstly, Deliberate Actions are initiated by a prior intention comprising a conceptual representation of the intended goal. Secondly, within Deliberate Actions, Successful Actions are carried out to completion and lead to their intended result.

I&DA

I&DA is a core ontology in the domain of information content entities and their physical materialization that was initially built for classifying documents by their contents [START_REF] Fortier | Managing knowledge at the information level: an ontological approach[END_REF]. I&DA extends DOLCE by introducing three main types of entities (see Fig. We are going to see (in Section 3) that Propositions and Concepts correspond to the intrinsic nature of our instruments. Before that, we extend DOLCE in another way to account for the intentional nature of these instruments and their function.

Artefacts

The notion of artefact that we adopt elaborates on the common philosophical notion of an "entity intentionally made or produced for some reason" [START_REF] Hilpinen | Artifact. Stanford Encyclopedia of Philosophy[END_REF]. Analyzing the notions of intention and reason, this leads us to identify different classes of entities we find important to clearly distinguish and define [START_REF] Kassel | A formal ontology of artefacts[END_REF] (see Fig. 3):

Firstly, we contrast entities resulting from an action of production (Producing Consequents) with entities that are not intentionally produced (Happening Consequents). Among the latter figure Experimental Artefacts (which are unwanted results).

Secondly, according to whether the intention of production is a prior intention or not, Artefacts are distinguished from Non-Targeted Objects (the latter result from Non-Deliberate Actions of production, e.g. routines).

Thirdly, different kinds of reasons for producing Artefacts (hence different kinds of Artefacts) are considered: (i) conveying an emotion and being of aesthetic interest, for works of art, (ii) enabling their author (or another agent) to do something, for "functional" or Technical Artefacts. The latter are Artefacts to which a Function is ascribed, taking a Function to be an "acknowledged capacity to enable the realization of a kind of action" [START_REF] Kassel | A formal ontology of artefacts[END_REF].

It is important to note that DOLCE's distinction between Physical and Non-Physical Objects transcends the domain of Artefacts. Indeed, the latter are defined by the origin of their existence (i.e. their intentional production) rather than a mode of existence. This difference explains why we are able to distinguish between physical artefacts (e.g. an oscilloscope, an image acquisition equipment) and nonphysical artefacts (e.g. the content of an article, a subject data acquisition instrument).

To sum up, Technical Artefacts have -at least -a triple nature as entities (i) possessing an internal essence (be it physical, social or cognitive), (ii) having been intentionally (and successfully) produced, and (iii) having necessarily a Function. With the modules presented in this section in hand, we now have at our disposal a minimal set of conceptual primitives which enables us to tackle the modeling of the domain of neurological, neuropsychological and behavioral instruments.

Our core ontology of instruments

In the core ontology we propose, instruments per se are considered as specific technical artefacts, with their own variables and scores associated, and actions performed using an instrument as specific conceptual actions.

Instrument-based assessments

An Instrument-Based Assessment action corresponds to an administration of an instrument or a 'testing' (to use the term recommended by [START_REF]Recent Developments Affecting the Disclosure of Test Data and Materials: Comments Regarding the 1996 Statement on the Disclosure of Test Data[END_REF]). The conceptualization of this action plays a pivotal role, linking together a large number of entities (cf. Fig. 4): a Healthcare Professional (for instance clinical neuropsychologist or neurologist), as Agent; the Subject about whom data are acquired and, more widely, the context in which this acquisition is performed (i.e. an Examination within a Study); the used instrument prescribing which data are to be acquired and how; results obtained following questions raised and/or tests performed.

These actions commonly take two forms according to whether they solicit an authentic production from the Subject (e.g., a reflex, a performance such as drawing, or a 500-meter walk), for Test-Based Assessments, or they consist in an interview, an inventory, for Questionnaire-Based Assessments. Assessments are then specialized according to the type of acquired data (e.g., psychological, behavioral, neuroclinical), mirroring in part the instruments taxonomy (cf. Fig. 5). The raison d'être of this specialization is to take into account specifications of the evidence of competence (knowledge, skills, abilities, specialties) that would be expected from someone seeking qualification as a test user.

Subject data acquisition instruments

The instruments used to evaluate the state of subjects clearly are technical artefacts. For their conceptualization, we follow our theory of the threefold nature of technical artefacts [START_REF] Kassel | A formal ontology of artefacts[END_REF]. This prompts to describe them as being:

Intangible artefacts, i.e. propositional contents including "clearly defined methods and instructions for administration or responding, a standard format for data collection, and well-documented methods for scoring, analysis, and interpretation of results" [START_REF]CDISC (Clinical Data Interchange Standards Consortium)[END_REF]. Technical artefacts allowing to explore entities related to the state of the subject -these categories of entities correspond to the Domain(s) of the instrument. Social artefacts intentionally created, adopted for use, then adapted and maintained by a community ascribing them the status of standard.

As the definition adopted from [START_REF]CDISC (Clinical Data Interchange Standards Consortium)[END_REF] indicates, we are faced to complex propositional contents. As an illustration of this complexity, some Instruments are explicitly composed of Sub-instruments exploring sub-or related domains (see Fig. 5). For example, to explore the multidimensional aspect of memory, the General Memory Index of the Wechlser Memory Scale-III (WMS-III) -a composite instrument designed to explore several memory abilities -is based on the delayed recall performances of several core "memory" tests, like the Visual Memory Test or the Verbal Memory Test [START_REF] Wechsler | Weschsler Adult Intelligence Scale-III[END_REF]. Such a composition is also found for Instruments which assess a restricted set of cognitive functions. For example, the Mini-Mental State (MMS) [START_REF] Folstein | Mini Mental State[END_REF], which is probably the most widely used instrument for dementia [START_REF] Lezak | Neuropsychological Assessment[END_REF], is structured according to a set of several items such as the MMS Orientation Test, the MMS Registration Test or the MMS Language Tests. Moreover the MMS Language Tests consist of several items such as the MMS Oral Order Language Test or the MMS Written Order Language Test. This indicates that even an Instrument which addresses a relatively small domain may be structurally complex. Such a structure is important to model because, according to the context, only some parts of an instrument may be administrated.

The effects of brain disorders being rarely confined to a single behavioral dimension or functional system [START_REF] Lezak | Neuropsychological Assessment[END_REF], Instrument-Based Assessments focus on different issues: neurological disorders (e.g. weakness, stiffness or visual impairments), cognitive impairments (e.g. aphasia, failure of judgment, lapse of memory), and other behavioral disorders (e.g. personality change, reduced mental efficiency or depression). Functionally, Instruments explore entities (their Domain(s)) which are of different ontological nature (e.g., states, abilities, cognitive functions, behaviors). For instance the memory is a cognitive function, while the depression is a Subject's pathological state. Moreover, an Instrument can be designed to explore one or several domains (Mono-domain vs Multi-domain Instrument). Generally, the goal with a Multi-domain Instrument is to integrate into one index the scores obtained by the patient while exploring different dimensions or functional systems. For instance, the MMS, which addresses the Global Cognitive efficiency, tries to obtain a global measure while exploring a whole set of domains: orientation, calculation, language, memory, praxia. Formally, a Domain is modeled as an individual concept which classifies classes of entities.

Instrument variables

Instrument variables are themselves Subject data acquisition artefacts. They carry two fundamental characteristics of the related instrument. First, they define what is being explored and measured using this instrument, represented by an explored Domain and a measured Quality, respectively. A distinction is introduced between Main variables, which explore the same Domain as the related instrument (i.e. same cognitive function or trait of the subject), and Secondary variables, which provide complementary information. Variables may also be categorized as Sex dependent variables, Age dependent variables, and Cultural skill dependent variables. When, for a variable, a typical value from a population of reference is available, the measured value can be standardized and stored in the corresponding score associated to the variable.

Second, Instrument variables define the range of allowed score values, with a basic distinction between Coded variables, which register Coded scores, and Numerical variables that register Numerical scores. The former are associated to a set of allowed Coded variable values, which are parts of the definition of the instrument. The latter, Numerical variables, can take any value in a certain range (which may be specified using min and max values). For instance, the MMS Calculation variable is a Numerical variable belonging to the range [0;5]. The Pessimistic thoughts variable of the Montgomery-Asberg Depression Rating Scale (MADRS) [START_REF] Montgomery | A new depression scale designed to be sensitive to change[END_REF] is a Coded variable with the following Coded variable values {0 = 'No pessimistic thoughts', 2 = 'Fluctuating ideas of failure, self-reproach or selfdepreciation', 3 = 'Persistent self-accusation, or definite but still rational ideas of guilt or sin. Increasingly pessimistic about the future', 6 = 'Delusions of ruin, remorse or irredeemable sin. Self-accusations, which are absurd and unshakable'}. Values are Propositions denoting, e.g., that "the subject has no pessimistic thoughts as measured by the MADRS Pessimistic thoughts variable". In the latter proposition, the term 'subject' does not refer to a particular individual, but to an abstract Subject.

Scores

Scores are Propositions that result from the recording of a particular Subject's cognitive performance (e.g. calculation performance) or a particular Subject's trait intensity (e.g. pessimistic thoughts intensity) during a particular Instrumentbased assessment, in relation to a particular Instrument Variable.F o r instance a Score may correspond to the following propositions: "During one MMS Calculation assessment, Patient X's Calculation performance is equal to 4 as measured by such MMS Calculation variable" or "During one MADRS assessment, Patient X has no pessimistic thoughts as measured by the MADRS Pessimistic thoughts variable".

Scores are divided into Coded scores and Numerical scores. Coded scores specialize the Coded variable values allowed for a particular Coded variable by referring to a particular Subject.

Numerical scores are further categorized as Raw scores, Corrected scores and Standardized scores depending whether they result of the direct registering of the subject's performance, or result of some correction or standardization of such raw scores. One also distinguishes between Scores with (respectively without) unit of measure.

Codes

We have seen that Variable values and Scores are Propositions. To help synthesize these values and offer calculus facilities, these Propositions are usually coded. Let's take, for instance, the Beck Depression Inventory (BDI-III) [START_REF] Beck | Manual for Beck Depression Inventory II (BDI-II)[END_REF], one of the most widely used instruments for measuring the severity of depression. One of its variables measures the sleeping dimension with values such as: "The patient sleeps somewhat more than usual" or "The patient sleeps most of the day". These Propositions are both qualitatively coded (by the respective Qualitative Score codes: 'Minimal' and 'Severe') and quantitatively coded (by the respective Quantitative Score codes: '1a' and '3a'). The latter Codes refer to a number (resp. 1 and 3), therefore enabling applying order relationships.

Discussion

A central quest in current neuroscience is the understanding of relations, under normal or pathological conditions, between brain anatomy and brain function. Brain functions can be mainly explored by neuroimaging, such as functional MRI, and neuropsychology, when concerned with the behavioral expression of brain functions [START_REF] Laird | Lost in localization? The focus is meta-analysis[END_REF]. One of our goal, with the construction of the proposed core ontology, was to define a model supporting the investigation of correlations between MRI based findings and neuroclinical, behavioural and neuropsychological based findings. The latter can be assessed by scores, which register the subject's task ability, cognitive performance or trait intensity. These correlations will be investigated in mining a large collection of data via a federation of heterogeneous and distributed databases (NeuroLOG project). For instance in Alzheimer's disease (AD), Gray Matter (GM) loss in the temporal regions lobes seems correlated with a decrease in Global Cognitive Efficiency (GCE) score. The two widely used instruments to examine the cognitive changes that characterize AD are the Mini Mental State (MMS) and the Mattis Dementia Rating Scale (MDRS) [START_REF] Mattis | Mental status examination for organic mental syndrome in the elderly patient[END_REF]. Indeed, MMS and MDRS are multi-domains instruments because their sub-instruments screen a large set of cognitive skills: attention, orientation, calculation, language, memory, praxia. The MMS and MDRS main variables register a total score which is based on the scores obtained during each of their sub-instrument assessments. Depending on the clinicians habits or the context of the assessment, MMS or MDRS is considered to define the subject's GCE. NeuroLOG's platform allows to search for: "all patients with a low GCE and with T1weigthed images presenting a GM loss temporal lobes ". Firstly, our core ontology allows (i) to retrieve all the Instruments (and their Main variables) that explore the Domain: Global Cognitive Efficiency, and (ii) to scan the entire set of related Scores, while filtering those which have a value less than a cut-off value (the latter is provided by the user and is Instrument and research study dependent). Secondly, images of the patient are retrieved and a specific computational anatomy pipeline is processed to quantify the possible GM volume loss in temporal lobes in the selected images.

The definition of the present core ontology was based on the detailed examination of the common instruments routinely used in three neurology hospital departments in France. We consider this set of instruments as representative of the minimal core that core ontology should support via dedicated sub-ontologies.

Two important modeling choices should be emphasized. The first one concerns the conceptualization of Instruments and the fact that we chose to model specific standard Instruments (e.g. MMS, WMS-III) as classes and not instances. The reason is that, in some centers, administered Instruments do not strictly conform to the defined standard. To account for these variations, local Instruments are modeled as instances of classes, with the latter representing shared properties of standard Instruments. Such properties correspond to structural and functional properties presented in Section 2.2. As a consequence, our core ontology is specialized by subontologies, each accounting for a specific Instrument. In some cases, however, variations become so important that this modeling is no longer adequate. A new standard is then built as a version of a previous one. Such a versioning relation is introduced between the two standards so that we can maintain the class/instances representation. The second modeling choice concerns the distinction between Variable values and Scores. As we have seen, the former are modeled as Propositions (referring to an abstract Subject) which pertain to the definition of Instrument, whereas the latter (referring to a particular Subject) are the result of an Assessment. We therefore have two different propositional contents which are linked by a specialization relation (thanks to this relation, information about Score codes is only attached to Variable values). It is important to note that Scores are moreover characteristic of Assessments (i.e. two Assessments do not share the same Score). This choice enlarges our model with a greater number of instances. However, when requesting to a given a Score, we directly obtain its specific context (Subject, Examination and Study).

Conclusion and perspectives

In this paper, we have proposed a core ontology of instruments which builds upon a conceptual framework comprising the foundational ontology DOLCE and a recently designed ontology of artefacts. Thanks to this building approach and the possibilities of mapping it offers with other biomedical ontologies (such as those based on BFO 6Before it can be used, our core ontology must be complemented with ontologies modeling the actually shared Instruments (more precisely the common properties of shared Instruments, as stressed earlier). This work is in progress. Once these ontologies available, the next step will consist in aligning the different Instruments'

), we would like to stress its potential interest as a semantic reference for various neurosciences applications. instantiations (at the different clinical sites) to a common reference, thanks to the mediator used in the NeuroLOG system (Data Federator, SAP). This will enable to query the actual Subjects' Scores and to correlate such Scores with image findings, which is what the end-users are primarily interested in. A current limitation of our conceptualization of Instruments lies in our preliminary description of the Domains and Qualities respectively explored and measured by Instrument variables. Such Domains and Qualities are modeled as independent concepts, which strongly limits the kind of reasoning that can applied. Our intention is to define ontologies of brain functions and states, as well as ontologies of the Qualities that may be measured during Instrument-based assessments, that will certainly lead to enhanced querying and reasoning capabilities.

4

 4

Figure 1 .

 1 Figure 1. An excerpt of DOLCE's hierarchy of concepts. A solid line between two concepts represents a direct subsumption link. A dashed line reflects the existence of intermediate concepts. A line between two lines indicates that sibling concepts are incompatible

  2):Inscriptions (e.g. printed texts) are knowledge forms materialized by a substance (e.g. ink) and inscribed on a physical support (e.g. a sheet of paper, a hard disk). The peculiarity of these Physical Endurants lies in their intentional nature: Inscriptions count as other entities, Expressions. Expressions (e.g. texts, logical formulae) are non-physical knowledge forms ordered by a communication language. Inscriptions realize Expressions and, like Inscriptions, Expressions are intentional entities conveying contents for agents. Conceptualizations consist of the ultimate means by which agents can reason about a world. Two kinds of Conceptualizations are distinguished: Propositions, as a means of describing a state of affairs; and Concepts, as a means to classify entities. Note that, as for the practical semiotics introduced in the ontology SUMO[START_REF] Pease | Practical Semiotics: A Formal Theory[END_REF], Propositions may encompass the content expressed by sentences, theories, books, and even libraries.

Figure 2 .

 2 Figure 2. An excerpt of I&DA's hierarchy of concepts

Figure 3 .

 3 Figure 3. Core taxonomy of artefacts

Figure 4 .

 4 Figure 4. Taxonomy of Instrument-based assessments.

Figure 5 .

 5 Figure 5. Taxonomy of Subject data acquisition instruments.

Figure 6 .

 6 Figure 6. Taxonomy of Instrument variables.

Figure 7 .

 7 Figure 7. Taxonomy of Scores.

Figure 8 .

 8 Figure 8. Taxonomy of Score codes.

Table 1 .

 1 Domains covered by most generic modules composing OntoNeuroLOG, along with the location of their OntoSpec manifestation (prefix=http://www.laria.u-picardie.fr/IC/Site/IMG/pdf)

	Module		domains	Location of OntoSpec
				manifestation
	Particular	Endurant, perdurant, quality,	prefix/Particular-OS.pdf
		abstract
	Action	Deliberate action, intentional	prefix/Action-OS.pdf
		action,	physical	action,
		conceptual action
	Participant role	Agent, substrate, consequent,	prefix/Participant-role-OS.pdf
		result, instrument
	Function & artefact	Artificial object, functional	prefix/Function-artefact-OS.pdf
		object,	artefact,	technical
		artifact, social artefact
	Inscription & Expression &	Support, inscription, Linguistic	prefix/Inscription-OS.pdf
	Conceptualization	expression, concept, proposition
	1.1 DOLCE
	DOLCE's domain is that of Particulars

see http://neurolog.polytech.unice.fr/doku.php

http://www.loa-cnr.it/DOLCE.html

B. Batrancourt et al. / A Core Ontology of Instruments Used for Assessments

Due to space limitations, we are only able to provide a very brief characterization of DOLCE's categories and we limit ourselves to categories of use in our ontology of instruments.B. Batrancourt et al. / A Core Ontology of Instruments Used for Assessments

http://www.ifomis.org/bfo B. Batrancourt et al. / A Core Ontology of Instruments Used for Assessments

Acknowledgements

This work is funded by the French national research agency (ANR), NeuroLOG project, under contract number ANR-06-TLOG-024.


Michael Defoort
email: michael.defoort@ec-lille.fr

Jorge Palos

Annemarie Kokosy

Thierry Floquet

Wilfrid Perruquetti

Performance-Based Reactive Navigation for Nonholonomic Mobile Robots *

Keywords: Nonholonomic mobile robots, Reactive navigation, Receding horizon planning, Sliding mode control

This paper presents an architecture for the navigation of an autonomous mobile robot evolving in environments with obstacles. Instead of addressing motion planning and control in different contexts, these issues are described in connected modules with performance requirement considerations. The planning problem is formulated as a constrained receding horizon planning problem and is solved in real time with an efficient computational method that combines nonlinear control theory, B-spline basis function and nonlinear programming. An integral sliding mode controller is used for trajectory tracking. Closed-loop stability of the tracking errors is guaranteed in spite of unknown disturbances. It is also shown that this strategy is particularly useful if integral sliding mode control is combined with other methods to further robustify against perturbations. The effectiveness, perfect performance of obstacle avoidance, real time and high robustness properties are demonstrated by experimental results.

Introduction

Wheeled mobile robots (WMRs) have been widely studied in the last two decades due to their practical importance and theoretically interesting properties. Indeed, there are considerable research efforts toward solving mobile robot navigation in different applications in indoor and outdoor environments (see [START_REF] Laumond | Robot Motion planning and Control[END_REF][START_REF] Latombe | Robot Motion Planning[END_REF] and the survey paper [START_REF] Salichs | Navigation of mobile robots: open questions[END_REF]). For some navigation tasks like planetary exploration, robots are required to travel long distances within constrained resources (energy, time. . . ). In such cases, efficient motion planning and control algorithms are needed in order to achieve the goal while meeting certain performance issue, such as geometric-based or time-based criteria.

Although motion planning and control are closely related in the robot navigation problem, they are usually addressed as two separate problems in much of the existing literature. Motion planning consists in generating a collision-free trajectory from the initial to the final desired positions and control is the determination of the physical inputs to the robot motion components. These two problems are typically solved using methods from different areas such as those in artificial intelligence and control theory. Such a separation makes it difficult to address robot performance in a complete application, since the planned trajectory may not be efficiently tracked. This fact can imply that the meaning of optimization in each step is lost. For instance, in a typical time optimal trajectory planning, the open-loop control schemes result in bang-bang or bang-singular-bang controls [START_REF] Chen | Structure of Minimum-Time Control Law for Robotic Manipulators with Constrained Paths[END_REF]. However, the discontinuities of the planned openloop control may not produce a satisfactory path tracking result in practice and will not be applicable to high speed traveling. In this research, we bridge the gap between trajectory planning and motion control.

Many theoretically challenging properties stem from the so-called nonholonomic constraints imposed by the rolling wheels. A survey of nonholonomic control problems can be found in [START_REF] Kolmanovsky | Developments in nonholonomic control problems[END_REF]. Obstacles to the tracking of nonholonomic systems are the uncontrollability of their linear approximation and the fact that the Brockett's necessary condition to the existence of a smooth time-invariant state feedback is not satisfied [START_REF] Brockett | Asymptotic stability and feedback stabilization[END_REF]. To overcome these difficulties, various methods have been investigated: homogeneous and time-varying feedbacks [START_REF] Pomet | Explicit design of time-varying stabilizing control laws for a class of controllable systems without drift[END_REF][START_REF] Samson | Control of chained systems: Application to path following and timevarying point-stabilization of mobile robots[END_REF], sinusoidal and polynomial controls [START_REF] Murray | Nonholonomic Motion Planning: Steering Using Sinusoids[END_REF], piecewise continuous controls [START_REF] Hespanha | Stabilization of nonholonomic integrators via logic-based switching[END_REF], backstepping approaches [START_REF] Jiang | Tracking control of mobile robots: a case study in backsteeping[END_REF] or discontinuous controls [START_REF] Floquet | Higher-order sliding mode stabilization for a class of nonholonomic perturbed systems[END_REF]. However, most of these methods do not provide both fast convergence and good robustness properties. Most of the control laws ensuring exponential or finite time convergence [START_REF] Monaco | An introduction to motion planning under multirate digital control[END_REF] are known to be non-robust under disturbances or modeling errors. On the other hand, control design methodologies like smooth time varying feedback [START_REF] Samson | Control of chained systems: Application to path following and timevarying point-stabilization of mobile robots[END_REF], are quite insensitive to perturbations but imply a slow convergence.

In this paper, we propose a practical scheme for real time motion planning and control of nonholonomic mobile robot moving in an uncertain environment. As illustrated in Fig. 1, the scheme consists of two main parts: (i) a real time collision-free motion planner; (ii) a trajectory tracking controller. For each module, we explicitly address the performance considerations. In implementation, the motion planner dynamically generates the optimal trajectory while the robot runs. High precision motion tracking is achieved by the combination of integral sliding mode control and time varying state feedback. The main results are general and can be applied whenever integral sliding mode control is combined with other techniques to further robustify against disturbances. Experimentations support the validity of the theoretical analysis and show that the performance of a time varying state feedback controller can be increased by this particular strategy.

The outline of this paper is as follows. In Section 2, the navigation problem is defined and the robot's nonholonomic model is described. Motion planning is discussed in Section 3. Trajectory tracking strategy is presented in Section 4. Finally, in Section Figure 1: Block diagram for navigation of a nonholonomic mobile robot with a motion planner and a sliding mode controller. 5, we present the integration of the different modules and the experimental results on a mobile robot.

Problem statement

Modeling of mobile robot

The mobile robot, shown in Fig. 2, is of unicycle-type. The robot body is of symmetric shape and the centre of mass is at the geometric centre C of the body. It has two driving wheels fixed to the axis which passes through C and one passive centrered orientable wheel. The two fixed wheels of radius r, separated by 2R, are independently controlled by two actuators (DC motors) and the passive wheel prevents the robot from tipping over as it moves on a plane. In this paper, we assume that the motion of the passive wheel can be ignored in dynamics of the mobile robot. The centre of mass C, whose coordinates are (x, y), is located at the intersection of a straight line passing through the middle of the vehicle and the axis of the two driving wheels. The configuration of the robot can be described by:

q = [x, y, θ ] T
where θ is its orientation in the global frame. In this paper, kinematics of wheeled-mobile robot are shown under the nonholonomic constraints (see [START_REF] De Wit | Exponential stabilization of mobile robots with nonholonomic constraints[END_REF] for details). The pure rolling and nonslipping nonholonomic conditions are described by: A T (q) q = 0 with A T (q) = -sin θ cos θ 0 .

The kinematic equations can be written as follows:

q = f (q)U (1)
where

f (q) =   cos θ 0 sin θ 0 0 1   , U = [v, w]
T is the control inputs, v and w are the linear and angular velocities, respectively. The relationship between [v, w] T and the left and right velocities w le f t , w right T is described by:

v = r 2 w right + w le f t , w = r 2R w right -w le f t .
(

) 2
Figure 2: Unicycle-type mobile robot At last, the robot has the following dynamic limitations on velocities:

|v| ≤ v max and |w| ≤ w max .

(3)

Problem setup

The following assumptions are made in this study: (i) the robot has on-board sensors which can detect surrounding objects within a range with a small margin of error; (ii) the odometry data from the robot has small errors over short distances; (iii) an on-board camera can update at a slower speed relative to local sensors. It is assumed that the robot knows its initial configuration q initial at the initial time instant t initial and its goal configuration q f inal . The navigation problem is to decide wheel velocity inputs w le f t , w right T within constraint (3) such that the robot starts at initial configuration, moves collision-free according to a certain performance criteria and arrives in a neighbourhood of the final configuration. To solve this problem, one can make the following choices without loss of any generality1 :

• The robot's geometric shape is represented by a 2-D circle of centre C = (x, y) and of radius R. Its motion is controlled but nonholonomic and is represented by the velocity vector U(t). The range of its sensors is also described by a circle centrered at C and of radius R s .

• The i textth object, i = 1, . . . , N o , will be represented by a circle centrered at point

O i = (X i ,Y i ) and of radius r i , denoted by B i (O i , r i ).

Motion planning

Depending on the distance that the robot has to travel, the computation of a complete trajectory from start until finish may be computationally too expensive. Moreover, the environment is partially known and further explored in real time. Therefore, the trajectory has to be computed gradually over time while the mission unfolds. It can be accomplished using an on-line receding horizon planner [START_REF] Mayne | Constrained model predicitive control: Stability and Optimality[END_REF], in which partial trajectories from an initial state toward the goal are computed by solving an optimal control problem over a limited horizon.

Receding horizon planner

Contrary to most of the existing trajectory generation modules, the proposed motion planner explicitly takes into account the real time constraint. Indeed, the mobile robot has a limited time to compute its reference optimal trajectory q re f (t). The time δt allocated to make its decision depends on its perception sensors, its computation delays, etc. The proposed algorithm relaxes the constraint that the final point is reached in the planning horizon. In each receding horizon planning problem, the same planning horizon T p ∈ R + and update period

T c ∈ R + (δt ≤ T c < T p ) are used. At each update, denoted τ k (k ∈ N), τ k = t initial + kT c , (4)
the robot computes an optimal collision-free trajectory satisfying constraints (1) and (3) using only local information.

To distinguish the different trajectories, we introduce the following notations:

q(t, τ k ) : the predicted trajectory over any interval [τ k , τ k + T p ] , q re f (t, τ k ) : the optimal planned trajectory over any interval [τ k , τ k+1 τ k + T c [ , q(t) :
the actual trajectory.

The associated control inputs are U(t, τ k ), U re f (t, τ k ) and U(t).

Remark 1

From the open-loop trajectory and control inputs associated to the planning horizon (i.e q(t, τ k ) and U(t, τ k )), only the part which corresponds to the update horizon is kept (see Fig. 3).

Figure 3: Planning and update horizons

The motion planning problem is solved in two steps:

• an initialisation step before the robot moves,

• a step of iterative computations.

Let the following optimal control problem P τ 0 , associated with the initialisation step, which consists in determining the optimal predicted control inputs u re f (t, τ 0 ) and the optimal predicted trajectory q re f (t, τ 0 ):

min τ 0 +T p τ 0 L( q(t, τ 0 ), u(t, τ 0 ))dt + G( q(τ 0 + T p , τ 0 ), q f inal ), subject to: ∀t ∈ [τ 0 , τ 0 + T p ] ,                ˙ q(t, τ 0 ) = f ( q(t, τ 0 )) U(t, τ 0 ), q(τ 0 , τ 0 ) = q(τ 0 ), U(τ 0 , τ 0 ) = U(τ 0 ), | v(t, τ 0 )| ≤ v max -ε v , | w(t, τ 0 )| ≤ w max -ε w , ( x(t, τ 0 ) -X i ) 2 + ( y(t, τ 0 ) -Y i ) 2 > R + r i , ∀B i (O i , r i ) in the range of sensors,
where L(.) indicates a certain performance criteria (time-based criteria, physics-based criteria, geometric-based criteria, etc.) and G(.) represents a terminal penalty function. The latter should be an estimate of the cost to go from the last predicted state q(τ 0 + T p , τ 0 ) in the planning horizon to the desired final point q f inal .

Remark 2

The inclusion of constants ε v ∈ R + and ε w ∈ R + in the constraints of the motion planning problem guarantees that there is sufficient control authority to track the optimal planned trajectory (see Section 4). This process is then repeated during the robot's movement, over the interval [τ 0 , τ 1 ], and so on until its reaches a neighbourhood of the goal q f inal . As such, new detected obstacles can be taken into account in the next iteration. Over any interval [τ k , τ k+1 ] (k ∈ N), the following optimal control problem P τ k+1 , associated with the (k + 1) th step, which consists in determining the optimal predicted control inputs u re f (t, τ k+1 ) and the optimal predicted trajectory q re f (t, τ k+1 ) is solved:

min τ k+1 +T p τ k+1 L( q(t, τ k+1 ), u(t, τ k+1 ))dt + G( q(τ k+1 + T p , τ k+1 ), q f inal ), (5)
subject to: ∀t ∈ [τ k+1 , τ k+1 + T p ] , ˙ q(t, τ k+1 ) = f ( q(t, τ k+1 )) U(t, τ k+1 ), (6) q(τ k+1 , τ k+1 ) = q(τ k+1 , τ k ), (7)
U(τ k+1 , τ k+1 ) = U(τ k+1 , τ k ), (8) | v(t, τ k+1 )| ≤ v max -ε v , (9) | w(t, τ k+1 )| ≤ w max -ε w , (10)
( x(t, τ k+1 ) -X i ) 2 + ( y(t, τ k+1 ) -Y i ) 2 > R + r i , ∀B i (O i , r i ) in the range of sensors. (11)
Once P τ k+1 is solved, the optimal reference trajectory and control inputs over the interval [τ k+1 , τ k+2 ] , are stored for use at the next module (i.e. trajectory tracking controller).

Remark 3 One can note that constraints [START_REF] Pomet | Explicit design of time-varying stabilizing control laws for a class of controllable systems without drift[END_REF] and ( 8) on the initial conditions need the optimal predicted control inputs U(τ k+1 , τ k ) and trajectory q(τ k+1 , τ k ) computed in the previous step. Therefore, in the proposed strategy, the receding horizon planner is not used in order to reject external disturbances or inherent discrepancies between the model and the real process, as it is usually done [START_REF] Cuzzolaa | An improved approach for constrained robust model predictive control[END_REF]. However, it takes into account the computation time δt. Fig. 4 gives an overview of the receding horizon planner.

Remark 4 A compromise must be done between reactivity and optimality. Indeed, the planning horizon T p must be sufficiently small in order to have good enough results in term of optimality for trajectory planning. However, it must be higher than the update horizon T c in order to guarantee the reactivity and obstacle avoidance for next receding horizon planning problems.

Technique for solving receding horizon planning problems

There are three components to the real time resolution of the optimal control problems P τ k (k ∈ N): determination of the flat outputs, B-spline parametrization and constrained feasible sequential quadratic programming. The key approach is to determine outputs such that equation ( 1) is mapped to a lower dimensional output space. It will imply that the problem becomes computionally more efficient to solve. Using the flatness property of system (1) (see [START_REF] Fliess | Flatness and defect of nonlinear systems: introductory theory and examples[END_REF] for further details about flatness), all system variables can be differentially parameterized by x, y and a finite number of their time derivatives. Indeed, θ , v and w can be expressed by x, y and their first and second time derivatives, i.e.

θ = arctan ẏ ẋ , v = ẋ2 + ẏ2 and w = ÿ ẋ -ẍ ẏ ẋ2 + ẏ2 . ( 12
)
Once the performance criteria (5) and constraints ( 6)-( 11) are mapped into the flat output space, the optimal predicted trajectory is planned in this space (see Fig. 5).

Then, in order to transform the optimal trajectory generation problem into a parameter optimization one, a piecewise polynomial function, B-spline, is adopted to approximate the trajectory. The B-spline functions are chosen as basis functions due to their flexibility and ease of enforcing continuity across breakpoints. B-Spline is the function defined by a series of knots called control knots. In our study, the three-order B-spline basis functions are used to parameterize the trajectory. For problem P τ k , the time interval [τ k , τ k + T p ] is divided into n knot equal segments with n knot + 4 knots to be control knots:

nod 0 = . . . = nod 3 = τ k < nod 4 < . . . < nod n knot +3 = τ k + T p ( 13
)
The trajectories of the flat outputs are written in terms of finite dimensional B-spline curves as:

x(t, τ k ) y(t, τ k ) = 3+n knot ∑ j=1 C j B j,3 (t) (14)
where C j ∈ R 2 are the coefficients of the third-order B-spline and B j,3 is the B-spline

B j,0 (t) = 1 if nod j ≤ t < nod j+1 , 0 otherwise . ∀d ∈ {1, 2, 3}, (15)
B j,d (t) = t -nod j nod j+d+2 -nod j B j,d-1 (t) + nod j+d+1 -t nod j+d+1 -nod j+1 B j+1,d-1 (t).
Finally, the time domain is truncated into smaller intervals by quadratic laws. The optimal coefficients C j are numerically found using the constrained feasible sequential quadratic optimization algorithm [START_REF] Lawrance | User's guide for CFSQP Version 2.5[END_REF]. See [START_REF] Milam | Real time optimal trajectory generation for constrained dynamical systems[END_REF] for a detailed analysis of the efficiency of this approach. To finish, the open-loop control inputs are deduced using equation [START_REF] Floquet | Higher-order sliding mode stabilization for a class of nonholonomic perturbed systems[END_REF].

Trajectory tracking controller

The task, for this module, is to design the wheel velocities such that the robot tracks the reference trajectory generated in the previous one.

Formulation of the tracking problem

The reference trajectory (x r , y r , θ r ), generated by the motion planning algorithm fulfills the differential equation:

  ẋr ẏr θr   =   cos θ r 0 sin θ r 0 0 1   v r w r , ( 16
)
where the desired velocities v r and w r satisfy:

|v r | ≤ v max -ε v and |w r | ≤ w max -ε w .
By directly applying v r and w r , the robot does not follow the reference trajectory with a good accuracy. It is obvious that the real control inputs v and w rely on the state measurements x, y and θ . Due to measurement noise and modeling uncertainties, there are input uncertainties for v and w. That is to say, the actual equation of the robot trajectory fulfills the following uncertain differential equation:

  ẋ ẏ θ   =   cos θ 0 sin θ 0 0 1   v + δ v w + δ w ( 17
)
where δ v and δ w represent the uncertainties. Control inputs v and w must be designed such that system [START_REF] Fliess | Flatness and defect of nonlinear systems: introductory theory and examples[END_REF] follows reference [START_REF] Cuzzolaa | An improved approach for constrained robust model predictive control[END_REF] in spite of the perturbations. In fact, the goal is to asymptotically stabilize the tracking errors e x = x rx, e y = y ry and e θ = θ r -θ to zero while respecting the saturation constraints [START_REF] Salichs | Navigation of mobile robots: open questions[END_REF].

Transforming the tracking errors expressed in the inertial frame to the robot frame, the error coordinates can be denoted as:

  e 1 e 2 e 3   =   cos θ sin θ 0 -sin θ cos θ 0 0 0 1     e x e y e θ   .
Accordingly, the tracking error dynamics is represented by:

ė = f 1 (e,t) + f 2 (e,t)(U + δ ) (18)
where

                           e = [e 1 , e 2 , e 3 ] T , U = [v, w] T , δ = [δ v , δ w ] T , f 1 (e,t) =   v r cos e 3 v r sin e 3 w r   , f 2 (e,t) =   -1 e 2 0 -e 1 0 -1   .
It should be pointed out that such a system cannot be stabilized by continuously differentiable, time-invariant, state feedback control laws. In this paper, we combine integral sliding mode control with time-varying state feedback in order to further robustify against perturbations.

Proposed methodology

The basic idea is to use an integral sliding mode controller to reject the matched perturbation (i.e. perturbations that enter the state equation at the same point as the control inputs). The integral sliding mode control algorithm is designed in two steps [START_REF] Utkin | Integral sliding mode in systems operating under uncertainty conditions[END_REF]:

1. the selection of a suitable integral sliding variable s such that, while sliding, the control objective is fulfilled, 2. the design of corresponding control inputs U constraining the system trajectories to evolve on the sliding surface from the initial time instant.

For system [START_REF] Lawrance | User's guide for CFSQP Version 2.5[END_REF], the control law is defined as follows:

U(q,t) = U 0 (q,t) +U 1 (q,t). ( 19
)
The nominal control U 0 (q,t) is responsible for the performance of the nominal system. U 1 (q,t) is a discontinuous control action that reject the perturbations by ensuring the sliding motion.

Integral sliding mode controller

Let us define the sliding variable s(q,t) = [s 1 (q,t), s 2 (q,t)] T ∈ R 2 as: s(q,t) = P e(t)e(t initial ) -

t t initial ( f 1 (e, ν) + f 2 (e, ν)U 0 (q, ν))dν , ( 20
)
where matrix P ∈ R 2×3 is such that P f 2 (e,t) is invertible for all t ∈ R + . Making P = -1 0 0 0 0 -1 , the above condition is fulfilled. One can note that, at the initial time instant t = t initial , the sliding variable satisfies s(q,t) = 0, such that the controlled system always starts on the sliding surface {s(q,t) = 0}.

Remark 5

To simplify notation, we will omit some of the functions' arguments from now on.

Based on the following Lyapunov function candidate, V = 1 2 s T s, the discontinuous control term can be determined such that V < 0, guaranteeing the attractivity of the sliding surface. One can obtain:

V = s T (P ė -P( f 1 + f 2 U 0 )) = s T (P ( f 1 + f 2 (U + δ )) -P( f 1 + f 2 U 0 )) = s T (P f 2 (U 1 + δ )) = [P f 2 ] T s T (U 1 + δ ) = s 1 -e 2 s 1 + s 2 (U 1 + δ ) < 0
The above condition holds if:

U 1 = -M 1 sign (s 1 ) -M 2 sign (-e 2 s 1 + s 2 ) (21)
where M 1 and M 2 are gain high enough to enforce the sliding motion.

The trajectory evolves on {s = 0} from t = t initial and remains there in spite of the perturbations. To determine the motion equations on the sliding surface, the equivalent control method [START_REF] Utkin | Sliding Modes Control in Electromechanical Systems[END_REF] is used. The time derivative of the sliding variable is:

ṡ = P( ė -f 1 -f 2 U 0 ) = P f 2 (U 1 + δ )
The equivalent control is obtained by solving the equation s = 0 for U 1 :

U 1eq = -δ (22)
By substituting U 1eq for U 1 in [START_REF] Lawrance | User's guide for CFSQP Version 2.5[END_REF], one can obtain the sliding dynamics:

ė = f 1 (e) + f 2 (e)U 0 (23)
Remark 6 From equation ( 23), several conclusions can be drawn. Firstly, the sliding dynamics do not contain the matched perturbation: it has been successfully rejected. Secondly, with respect to the conventional sliding mode control, we have gained some extra degrees of freedom. Indeed, U 0 can be used in order to stabilize the nominal system and to deal with the unmatched perturbation.

Time-varying state feedback controller

The second part of the controller design is to find a saturated control law U 0 such that the sliding dynamics ( 23) is globally asymptotically stable. The chosen control law U 0 has been developed by Jiang in [START_REF] Jiang | Saturated stabilization and track control of a nonholonomic mobile robot[END_REF]. The motivation for such a choice is that this design takes into account the actuator bounds. It is described by:

U 0 = v 0 = v r cos e 3 + λ 3 tanh e 1 w 0 = w r + λ 1 v r e 2
Note that the positive parameters λ 1 , λ 2 and λ 3 can be designed such that the bounds of the controls are met for our controllers. Indeed, it can be seen that:

|v 0 | ≤ v max -ε v + λ 3 , |w 0 | ≤ w max -ε w + λ 1 (v max -ε v ) 2 + λ 2

Remark 7

The control gains can be designed such that the bounds on the control inputs are satisfied. In order to design these constants, a compromise must be found between the optimality, the performance and the robustness with respect to perturbations.

From [START_REF] Latombe | Robot Motion Planning[END_REF], it is straightforward to obtain the wheel velocities:

w right = v-Rw r
w le f t = v+Rw r 5 Experimental results

Experimental setup

The proposed motion planning and control algorithms are implemented on the mobile robot Pekee manufactured at Wany Robotics company (see Fig. 6). An overview of the experimental setup is shown in Fig.

• • • ! • " " # $ " %& '( • ) " " • * " + ) , - • ) " " • * " + )
, - The vehicle's wheelbase is taken to R = 0.3m with v max = 0.8m/s, w max = 5rad/s and the sampling period is 100ms. The computation time δt including the image processing and the motion planning algorithm is about two minutes on the on-board 75MHz PC. In order to decrease the computation delay, we used the socket protocol communication and wireless communication link. The vision data are sent to a Pentium IV 2.4GHz PC for image processing and for the generation of the optimal trajectory. This protocol enables to reduce δt to less than 0.2s.

Experimental results

We run experiments on different environments cluttered with obstacles. The corresponding videos are available at: http://www.isen.fr/∼sst lille/fichiers/Icra.wmv.

In these experiments, obstructed areas are created with circular obstacles in the workspace. Some of them are initially out of view from the robots' on-board sensors and may be discovered during the robot movement. The performance criteria is the length of the traveled distance. For the motion planner, the chosen parameters are described in Tab. 1. Furthermore, the parameters for the tracking algorithm are given in Tab. 2. For comparison purpose, the gains M 1 and M 2 needed to enforce the sliding mode are the same in all the experiments in which they occur.

U 1 = -M 1 s 1 |s 1 |+0.0001 -M 2 -e 2 s 1 +s 2 |-e 2 s 1 +s 2 |+0.0001
Figures 10(a) and 11 depict the executed trajectories in unknown environments. First, the robot visualizes the scene and applies the image processing. The nearest obstacles in view from its on-board sensors are detected. In order to take into account the size of the robot, the radius of these obstacles is increased by 0.3m (dotted lines around obstacles). According to the detected obstacles, a collision-free trajectory is planned. Then, the integral sliding mode controller enables to track the desired trajectory in spite of uncertainties and errors. During the execution, the robot plans, in real time, its next optimal collision-free trajectory by taking into account new information from its infra-red and camera sensors. The effectiveness, perfect performance of obstacle avoidance, real time and high robustness properties are demonstrated by these experimental results.

Figures 8, 9 and 10 highlight the performance for the proposed tracking module. The first experiment is made without using feedback controller. By directly applying the open-loop control inputs, the robot does not follow its planned trajectory due to measurement noise and modeling uncertainties. One can see in Fig. 8(b) that the distance between the actual and planned trajectories, i.e.

(xx r ) 2 + (yy r ) 2 , diverges. The second one is made using only the time-varying state feedback controller. The third experiment is made using the combination "integral sliding mode controller plus the time-varying state feedback controller". One can note that using only the timevarying state feedback controller, the robustness performance is not good enough. The use of an integral sliding mode controller enables to improve the precision motion tracking.

Conclusion

An architecture for real time navigation of an autonomous mobile robot evolving in an uncertain environment with obstacles is proposed. It provides the following practical advantages:

• First, it enables to take into account the dynamic limitations on velocities.

• Further, receding horizon planner is a viable method for real time trajectory generation. Depending on computing resources, the use of flatness, B-spline parametrization and constrained feasible sequential quadratic programming can take less than one second to compute an optimal collision-free trajectory.

• Also, the combination of integral sliding mode control with other methods like time-varying state feedback improves the robustness properties of the closedloop system. Therefore, high precision trajectory tracking is achieved in spite of uncertainties and modeling errors.

Experimental results show the effectiveness of our practical scheme (real time, high robustness properties and good performance for obstacle avoidance).

Figure 4 :

 4 Figure 4: Implementation of the receding horizon planner

Figure 5 :

 5 Figure 5: Flatness and motion planning

e 3 e 3 + λ 2 tanh e 3

 333

7 .

 7 An Intel 486 micro-processor running at 75MHz hosts the integral sliding mode controller written in C. The robot operates under linux real time and its software integrates sensor and communication data. It communicates through wireless Ethernet capable of transmitting data up to 3Mb/s. One miniature color vision camera C-Cam8 is mounted on the robot. A C program accesses the streaming data coming into the frame grabber from the camera and stores the data in a 320 × 240 image file. The robot is also equipped with 15 infra-red sensors used for local identification of the environment and two encoders.

Figure 6 :

 6 Figure 6: Pekee mobile robot

Figure 7 :

 7 Figure 7: Overview of the experimental setup

Figure 8 :

 8 Figure 8: Experimental results without using the trajectory tracking module

Figure 9 :

 9 Figure 9: Experimental results using the time-varying state feedback controller

Figure 10 :

 10 Figure 10: Experimental results using the integral sliding mode and time-varying state feedback controllers

Table 1 :

 1 Parameters of the motion planner

	The discontinuous

Table 2 :

 2 Parameters of the tracking algorithm controls are approximated by:

It is trivial to allow the envelope of either the robot or an obstacle to be represented by union/intersection of several circles. The envelopes could also be polygonal. Mathematically, circular envelopes can be represented by second order inequalities while polygonal envelopes can be described by first order linear inequalities.

This work was partially supported by the Region Nord Pas-de-Calais and the FEDER (European Funds of Regional Development) under Interreg ACOS, the ARCIR Robocoop and the AUTORIS-TAT T31 project.


Thomas Guyet
email: thomas.guyet@imag.fr

Catherine Garbay

Michel Dojat

A Human-Machine Cooperative Approach for Time Series Data Interpretation

This paper deals with the interpretation of biomedical multivariate time series for extracting typical scenarios. This task is known to be difficult, due to the temporal nature of the data at hand, and to the context-sensitive aspect of data interpretation, which hamper the formulation of a priori knowledge about the kind of patterns to detect and their interrelations. A new way to tackle this problem is proposed, based on a collaborative approach between a human and a machine by means of specific annotations. Two grounding principles, namely autonomy and knowledge discovery, support the co-construction of successive abstraction levels for data interpretation. A multi-agent system is proposed to implement effectively these two principles. Respiratory time series data (Flow, Paw) have been explored with our system for patient/ventilator asynchronies characterization studies.

Introduction

In the mass of monitoring data, the detection of specific patterns relative to a significant event requires a time-consuming visual data examination by an expert. The relations between events occurring in various physiological parameters are meaningful but difficult to identify. In addition, the potential generic character of the detected patterns is rarely pointed out. We assume that without the use of a computerized assistant, this mass of data can not be fully exploited. However, the design of such an assistant is difficult because the temporal and multivariate nature of the data at hand and the context-sensitive aspect of data interpretation hamper the formulation of a priori knowledge about the kind of patterns to detect and their interrelations. The number of patterns and their combination to form meaningful situations is potentially very high, making their systematic enumeration and description by a human impossible.

For instance, in the context of patients hospitalized in Intensive Care Unit (ICU) and mechanically ventilated, asynchrony, i.e. a frequent mismatch between the ventilator assistance and the patient demand, has recently been reported [START_REF] Thille | Patient-Ventilator Asynchrony During Assisted Mechanical Ventilation[END_REF]. Automatic asynchrony detection could be used to adjust ventilator settings and then improve mechanical assistance efficiency. However, to model asynchrony patterns for a robust automatic detection, essential information is still missing. R. Bellazzi, A. Abu-Hanna, and J. Hunter (Eds.): AIME 2007, LNAI 4594, pp. [START_REF] Shahar | A Framework for Knowledge-Based Temporal Abstraction[END_REF][START_REF] Augusto | Temporal Reasonning for Decision Support in Medicine[END_REF][START_REF] Fromont | Learning Rules from Multisource Data for Cardiac Monitoring[END_REF][START_REF] Guimarães | A Method for Automated Temporal Knowledge Acquisition Applied to Sleep-Related Breathing Disorders[END_REF][START_REF] Silvent | Multi-Level Temporal Abstraction for Medical Scenarios Construction[END_REF][START_REF] Zupan | Knowledge Based Data Analysis and Interpretation[END_REF][START_REF] Kabanza | Implementing Tutoring Strategies Into a Patient Simulator for Clinical Reasoning Learning[END_REF][START_REF] Lee | Students Assessing their Own Collaborative Knowledge Building[END_REF][START_REF] Morik | Knowledge Discovery and Knowledge Validation in Intensive Care[END_REF][START_REF] Schroeder | A Multi-Agent System to Facilitate Knowledge Discovery: An Application to Bioinformatics[END_REF]2007. c Springer-Verlag Berlin Heidelberg 2007 In this paper, we propose a collaborative human-machine approach to gradually define from the data the significant patterns to detect, and to discover specific temporal relations between events.

Following [START_REF] Salatian | Deriving Trends in Historical and Real-Time Continuously Sampled Medical Data[END_REF], we advocate the use of annotations as an elegant and efficient way for communicating between a human and a machine. Starting from expert annotations, the computer builds its own abstractions and in turn annotates the signals. The human-machine interactions occur at three abstraction levels (e.g. segmented time series, symbolic time series data and scenarios), around which a collaborative approach to the interpretation of time series data is proposed. We implemented our approach using the multi-agent (MA) paradigm. The MA system (MAS) design is based on two grounding principles, namely autonomy and knowledge discovery, which support the construction by the system of data interpretation at successive abstraction levels.

State of the Art

Knowledge-Based Temporal Abstraction. Basically, abstraction transforms initial numerical time series to symbolic time series, which is known to result in a so-called semantic gap. The larger is the gap the more difficult is the abstraction. To fill this gap, as showed by Shahar [START_REF] Shahar | A Framework for Knowledge-Based Temporal Abstraction[END_REF], the abstraction process relies on several mechanisms and uses various types of a priori knowledge. There is a wide literature regarding the way to realize several temporal abstraction levels in medical domains [START_REF] Augusto | Temporal Reasonning for Decision Support in Medicine[END_REF].

For instance, in the Calicot system [START_REF] Fromont | Learning Rules from Multisource Data for Cardiac Monitoring[END_REF], dedicated to cardiac arrhythmias detection, a priori knowledge is introduced to support the discovering of new rules. Neural networks are trained to discover normal or abnormal P-waves and QRScomplexes and translate physiological time series into symbolic time series. Then, the system learns rules with an Inductive Logic Programming method where a priori knowledge and bias can be introduced. The computed rules show complex temporal relations between the symbols attached to the various arrhythmias, which are difficult to understand by an expert. However, ICU data appears unfortunately insufficiently formalized to envisage such a procedure.

Guimarães et al. [START_REF] Guimarães | A Method for Automated Temporal Knowledge Acquisition Applied to Sleep-Related Breathing Disorders[END_REF] propose the TCon method for automated temporal knowledge acquisition applied to sleep-related respiratory disorders. TCon uses machine learning techniques to discover new elementary patterns (rules) from the time series. These rules are then translated, in order to be easily interpretable for the clinician, a central motivation that we share. But we are then facing a trade-off: too much a priori knowledge hampers knowledge discovery, whilst not enough a priori knowledge produces non-coherent or difficult to interpret abstractions.

Step by step validation of the abstraction process by the human expert, based on well-adapted visual representations, has been shown as a way to build robust abstraction process [START_REF] Silvent | Multi-Level Temporal Abstraction for Medical Scenarios Construction[END_REF]. In the same vein, we propose that during the knowledge discovery process, the expert continuously interacts with the learning system to drive the process and extract useful chunks of knowledge.

Collaborative Knowledge Discovery. The development of mutual learning capabilities is a way to solve the previously mentioned trade-off between autonomy and intelligibility. In [START_REF] Zupan | Knowledge Based Data Analysis and Interpretation[END_REF], the authors present the desired cycle of knowledge where clinicians are central actors in knowledge production with a positive impact on the final system. Classical approaches to collaborative knowledge discovery consist either in human-driven machine learning, the clinician acting as an expert, or in computer assisted human learning, the machine acting as a teacher (Intelligent Tutoring Systems). TeachMed [START_REF] Kabanza | Implementing Tutoring Strategies Into a Patient Simulator for Clinical Reasoning Learning[END_REF] for instance is a recent system to support clinical learning. The student is observed and when, for TeachMed, he/she needs assistance a dialog is engaged to help him/her to find the solution. Computers can also serve as a medium for a collaborative mutual learning (Computer-Supported Collaborative Learning) in facilitating interaction between humans [START_REF] Lee | Students Assessing their Own Collaborative Knowledge Building[END_REF]. In [START_REF] Morik | Knowledge Discovery and Knowledge Validation in Intensive Care[END_REF] human and machine are both embedded in a learning cycle. On this basis, they automatically generate in a faster way more reliable guidelines compared to classical methods.

Multi-agent systems exhibit several properties that make them a "natural" framework for the design of such collaborative systems, particularly due to the open character of the MA architecture and to the autonomy of its components. They facilitate the combination of several approaches for distributed problem solving, support the autonomous emergence of new knowledge and may naturally integrate a human user as a specific agent. According to this view, the MASKS environment [START_REF] Schroeder | A Multi-Agent System to Facilitate Knowledge Discovery: An Application to Bioinformatics[END_REF] introduces agent interactions based on cooperative behaviors to facilitate knowledge discovery. Agents, that encapsulated machine learning algorithms, respectively evaluate and may merge their generated rules. In [START_REF] Bottoni | Collaborative Indexing and Retrieval by Annotation: the Case of Artistic Artifacts[END_REF], a MAS is used to collaboratively annotate artistic artifacts. The system opens a share space to enable experts to insert their own annotations and learn mutually from each other.

Interactive knowledge construction literature indicates that human/machine interaction enables knowledge discovery both for the machine and the human. Whilst the human helps to focus the machine learning process to the discovery of useful chunk of knowledge, the machine helps to focus the human learning process to a deep exploration of the data at hand.

The Methodological Concepts

Signal Interpretation. We consider interpretation as a complex process involving complementary exploration, description and annotation tasks, which are operated by a collection of autonomous agents (including humans), working to progressively refine the interpretation [START_REF] Bottoni | Collaborative Indexing and Retrieval by Annotation: the Case of Artistic Artifacts[END_REF]. The role of the exploration task is to focus the attention, at each abstraction level, on relevant information, in terms of time series segments, event classes or typical event relations. In our system, several steps are necessary before reaching the upper notion of scenario: 1) Segmentation, 2) Symbolic time series and 3) Scenario construction. The description and annotation steps are situated in a dynamic context which includes the agent past experience and additional information on data. The description task aims to build numerical and symbolical models of the information under interest, possibly by fusion. Finally, the annotation task role is to attach symbolic labels to newly provided raw data using the constructed models.

Human-Machine Collaboration. We propose to approach the interpretation of time series data as performed by two cooperating agents -a man and a machine -operating across three successive abstraction levels (segments, symbolic time series and scenarios). These agents share a common environment (e.g. annotations, time series data, segments ...) and mutually interact via annotations to progressively refine their own interpretation. In the absence of consistent a priori knowledge and considering the difficulty of this processing, an active partnership between man and machine is sought. It does not come down to a fixed request-answer interaction scheme in which each actor is meant to compensate for the lack of knowledge of its partner, and therefore supposed to share its world of meaning. This partnership is rather meant to allow a co-construction of annotations, in which the interpretation of facts is not defined beforehand by one of the actors, but co-constructed in the course of their interaction. According to this principle, each partner is in turn given the possibility to observe and interpret annotations provided by its partner, and/or to propose annotations judged as appropriate according to a given interpretation context. In such framework, each partner is meant to "play" in its own world of meaning, thus preserving its autonomy, with no prevalence of one on the other. In consequence, there is a possibility of learning and discovery for both partners. To be noticed is the fact that any information -be it a case example or a conceptual interpretationis provided within its context of appearance, so that interaction develops in a situated way.

A Multi-Agent System for Time Series Interpretation

Central to our design, is the distinction between three main tasks, namely segmentation (localization of relevant segments), classification (symbolic labeling of the segments), and scenario construction (computation of inter-symbol relationships). Dedicated agents are conceived to support these various tasks; they make use of specific models, which drive the way to explore and describe, via annotations, the information at hand (forward application). These models are autonomously computed (backward application), based on knowledge discovery methods, and according to previously computed annotations, which may be provided by an external user, or by other agents. Interaction and feedback loops occur all along the interpretation process to ensure its progressive refinement.

To be noticed is the fact that all these processes, as the human agent himself, run in parallel and may interact at any time, thanks to the annotation process which results in modification propagated within the information at hand, and thus altering but not disrupting the interpretation process.

Scenarios construction

Segment.

Classif.

System Design

A global view of the system architecture is presented in Figure 1. A triadic organization is proposed as a conceptual framework to support the needed inter-agent interactions and feedback loops. A triad is made of two processing entities working in reciprocal interaction that constitutes a more abstract processing whole. Each abstraction level is organized into a triad, giving rise to new annotation elements to be processed at a higher abstraction level (upper triad). Conversely, each upper level triad may launch lower-level triadic agents (feedback loop). Time series data are processed within the segmentation and classification triads, which mutually interact (links 1 and 2, Figure 1) within the symbolic translation triad to build symbolic time series. Symbolic time series are processed within the scenario construction triad. The symbolic translation and scenario construction triads mutually interact within the system triad (links 3 and 4). Scenarios are the final outcome to the system triad (link 5). When entering a feedback loop (link 4, 4s and 4c), the constructed scenarios may conversely be used to propagate modifications to the symbolic time series, and from this triad to the lower level classification and segmentation agents.

Agentification

Classification Agents. For the sake of simplification, we first of all describe the system style of working in front of univariate time series. The general control cycle of a classification agent is (i) to collect segments (ii) to compute segment descriptors (iii) to classify them and (iv) to build segment class models. The segments to analyze may be pointed out by a human, or delimited by the segmentation agents. At system start, some initial annotations or models are provided to some agent, to launch the whole interpretation process. Each segment is described by a feature vector (typically 20 sampled values and the length of the segment), which are classified. A weighted Euclidean distance is used to compare them. The k-mean algorithm has been selected because of its capacity to work under our specific constraints: lack of a priori knowledge (in particular no a priori knowledge of the number of classes to observe), and dynamicity (evolution of the class characterization along the interpretation in progress). We use an extended version of the algorithm, in which different distances (i.e. adaptive weights in the Euclidean computation) are selected and computed, depending on the class under interest. For each class, the mean vector and the distances weights constitute the model of the segments of this class, attached to a symbolic name with no proper semantic.

The next issue to consider is then how to match this symbolic name with an intelligible denomination for the clinician (e.g. asynchrony events). This is performed by means of triadic man-machine interaction, according to which any modification (e.g. annotation) performed by any agent is merely a perturbation of the information under interpretation. According to this view, the system interpretation may be shifted toward human interpretation in a transparent way.

Segmentation Agents.

For each class of segments constructed by the classification agent, a new segmentation agent is created, and provided with the corresponding segment model. Consequently, the number of segmentation agents changes in the course of the interpretation. Each segmentation agent performs a pattern matching algorithm : It calculates the distance between the agent's segment model and a sliding window of variable length, that delineates a segment, moving on the time series. Then, the segments closest to the model are selected. A non-overlapping constraint is used to eliminate further segment hypotheses. Distances are computed in the model parameter space (the previously described vectorial description of a segment), rather than in the time series space, to cope with differences of pattern size. The segmentation of a time series is the concatenation of the segments constructed by all these agents.

Here again, annotations are exchanged between the machine and the human via the interface. Segments are shown to the human through the system visualization interface. Such visualization allows focusing the human attention in two ways: whilst annotated signal elements point out "recognizable" events, and submit them to further examination, non annotated events conversely either reveal a lack of knowledge, or suggest further exploration of the data.

To be noticed is the fact that any result, newly obtained at the segmentation level, is transmitted forward to the classification agent, which may in turn drive a further launching of segmentation agents. This process continues until some stabilization is being reached, which is controlled by human interventions.

Symbolic Translation Triad.

The role of the symbolic translation triadic agent is to translate numerical time series into symbolic time series. It collects to this end the segments and models of segments computed by the segmentation and classification agents. For each segment (S), the triadic agent creates a timestamped symbol with the date and duration of S and the symbolic name (N ) of the most accurate models of segments. Concatenated time-stamped symbols for a given time series constitute the symbolic time series of a patient record. The whole process results in concatenated time-stamped symbols which characterize the patient record at the symbolic level.

For multivariate time series, one classification agent is dedicated to each type of time series (Flow, Paw, ...), and defines the corresponding segmentation agents. The symbolic time series merges time-stamped symbols from all types of time series. Scenario Agents. The scenario construction is considered as the process of finding temporal relations between symbols. This process is driven by the assumption of some symbols, selected by the clinician, that are to be "explained" through their causal links to some ancestor "events" (symbols). The task of the scenario agent, associated to a symbol E, is to collect the symbols preceding each occurrence of E in a temporal window with a fixed length. Each set of such symbols is then considered as an example for the learning process at hand. From these examples, the agent finally constructs the time-stamped pattern, i.e. the scenario that "explains" E. To this end, we use an extended version of the A Priori algorithm [START_REF] Dousson | Discovering Chronicles with Numerical Time Constraints from Alarm Logs for Monitoring Dynamic Systems[END_REF], which builds the biggest frequent time-stamped pattern. The resulting scenario may of course be submitted to the user, which may result in modifications in the proposed pattern, or collecting other example patterns to support or contradict the current interpretation. In a complementary feedback loop (link 4 in Figure 1), the proposed scenario may be considered as a model to drive further analysis. Any deviation from the current model is considered as a potential for improvement of the annotation process. The system will then focus its attention on the corresponding deviation locations.

Patient-Ventilator Asynchronies Exploration Results

Rationale

Patients suffering from respiratory disorders and hospitalized in Intensive Care Units are mechanically supported with assist-control ventilation. An adequate synchronization between patient and ventilator is then required to improve patient's comfort and optimize work of breathing. A recent study [START_REF] Thille | Patient-Ventilator Asynchrony During Assisted Mechanical Ventilation[END_REF] shows that 24% of 60 patients mechanically ventilated exhibited an asynchrony index higher than 10% of respiratory efforts. Ineffective triggering, i.e. when patient's efforts do not result in ventilator triggering, was the major cause (85%) of asynchrony. Asynchrony was associated with a longer duration of mechanical ventilation. Therefore, it is important to identify factors increasing the incidence of asynchrony. Some major asynchronies can be detected by an experienced clinician. This remains a difficult extra workload and no physiological models exist yet to allow for their automatic detection. In order to detect, from the physiological data, specific patterns, regularities or sequences of events (scenarios), associated to the occurrence of asynchrony, we provided a clinician with our system to annotate and explore respiratory time series. They were constituted of flow and airway pressure (Paw) signals continuously recorded during 30 minutes and sampled at 200 Hz (see [START_REF] Thille | Patient-Ventilator Asynchrony During Assisted Mechanical Ventilation[END_REF] for details).

Time Series Data Exploration Case Study

We first of all illustrate the capacity of our system to build annotations in an autonomous way, thereby assisting the clinician in the elaboration of new interpretation models; we illustrate in a second step its capacity to validate previously constructed models, assisting the clinician in the model-driven investigation of unknown data. Alternating successive steps of model construction/model validation would finally allow the clinician to build a progressively refined interpretation of data, together with more robust models.

Models Construction and Automatic Asynchrony Detection. Three patient's records were fully interpreted via our system. Using the system interface, the clinician by a visual inspection, annotated some inefficient triggering (see Figure 2a) on a specific part of the signal. Then, the clinician launched the processing step i.e. the execution of the classification agents, the segmentation agents and finally the symbolic translation triadic agent. Based on the initial partial annotation by the expert, the system symbolically labeled the complete time series (see Figure 2b). On the Figure 2, all asynchronies considered as similar to those annotated by the clinician as ineffective triggering, were retrieved (dark-gray boxes). The three complete time series were automatically annotated based on clinician's annotations that represented about 30% of the total asynchronie events. The mean sensitivity and the mean specificity were respectively egal to 0.64 and 0.93. Finally, the system constructed scenarios that bring new information about asynchrony occurrence conditions. For this purpose, Paw and Flow signals were automatically explored in a temporal windows (fixed to 10s i.e. approximatively three periods) around asynchrony events. Our system detected that asynchrony on the Flow signal was associated in 90% of cases with asynchrony on the Paw signal and that they were preceeded by another asynchrony in 90% of cases. This extracted knowledge was then used to automatically detect deviant patterns, such as a single asynchrony (may be artefactual) or mismatch between flow and paw asynchronies. New annotations (artefacts, trends) should be inserted by the clinician to finalize the validation and enrich these first results.

Models Comparison and Extraction of New Patterns. Our system may also support the clinician in the model-driven investigation of unknown data, to validate the genericity of a previously constructed model. To illustrate this point, we used seven new data sets. For three of these data sets, the "ineffective triggering" model that was previously built from one patient data set, appeared clearly not relevant. However, for the four remaining data sets, the model revealed adapted and the clinician was able to identify new patterns: two ineffective triggering in the same period pattern (see Figure 3) and double triggering patterns. Extensive data exploration should be realized to confirm these preliminary results.

Discussion and Perspectives

We have presented an original approach to support clinicians in the difficult task of multivariate time series data interpretation. Our approach is centered on the collaboration between a clinician and an autonomous system, both embedded in a learning cycle. We advocate for the design of computerized tools that really support the clinician in his/her decision making process, rather than provide him/her with final results. The presented system participates to this medical computerized tools design evolution [START_REF] Zupan | Knowledge Based Data Analysis and Interpretation[END_REF]. We are aware of the computing complexity of the processes we have presented. But we assume that data interpretation is a prospective task with no critical time constraints.

The undergoing experiments on patient ventilator asynchrony exploration strongly support the interest of our approach. We expect that the global system implementation in progress, including the feedback from scenario construction, will improve the detection of known events and consequently its sensitivity. Several extensions of the present implementation may be envisaged. The fusion of several physiological parameters would enable the construction of more elaborate asynchrony models, as well as taking into account contextual information such as pathology, treatments or the mode of ventilation used. The objective is to integrate contextual information on patient as a interpretation element and maybe enable clinician to construct typical scenarios for groups of patients. Finally, the preliminary experiments on scenario learning indicate that a more sophisticated time representation should be introduced (such as interval relations for example). Further experimentations in close collaboration with clinicians will allow us to fully evaluate the real impact of such as interactive approach for knowledge discovery and knowledge formalization.

Fig. 1 .

 1 Fig. 1. MAS entities organization according to recursive triads. The classification triad is expanded to show the man-machine interaction.

Fig. 2 .Fig. 3 .

 23 Fig. 2. Model construction (Flow signals). 2a (left): Two annotations (gray horizontal bar) are inserted on the flow signal by the clinician to indicate asynchrony periods. 2b (right): Annotation completion by the system: dark-gray boxes indicate retrieved asynchronies periods. Medium-gray boxes indicate retrieved non-asynchronies periods.

Acknowledgments. We thank Dr. Thille and Pr. Brochard from H. Mondor Hospital (Créteil, Fr) for providing the clinical data and for comments.