text:
Cédric Pralet

Charles Lesire

Jean Jaubert

An Autonomous Mission Controller for Earth Observing Satellites

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Introduction

The mission of commercial Earth Observing Satellites (EOSs) consists in making observations of some areas at the Earth surface and in downloading collected data to ground reception stations. For most of these satellites, mission plans are first b uilt o n t he g round a t t he l evel o f the mission center, and then sent to the satellite by ground control stations. These plans contain sequences of time-tagged telecommands that must be executed while the satellite is orbiting around the Earth. Nowadays, the search for performance leads to the development of a new generation of commercial EOSs. As in the seminal NASA contributions on Deep Space 1 [START_REF] Muscetolla | Remote Agent: to boldly go where no AI system has gone before[END_REF] and Earth Observing 1 [START_REF] Chien | The EO-1 autonomous science agent[END_REF]), the objective is to get autonomous satellites that quickly adapt their behavior depending on the conditions encountered at execution time, instead of waiting for plans sent by the ground only a few times a day.

In this paper, we consider three situations in which adapting plans directly on board is relevant. First, many images realized by EOSs cannot be exploited due to the presence of clouds over observed areas. To improve on this point, we consider a scenario where the satellite regularly receives meteorological predictions from ground stations or from geostationary relay satellites. These predictions consume a low level of uplink bandwidth and can be received much more frequently than time-tagged plans. Second, due to on-board data compression, the exact volume of observation data is not known beforehand, especially due to the uncertainty about the presence of clouds on some parts of the images. Our goal is then to deliver data more quickly to the endusers by exploiting the real volumes of data files, instead of executing a timed-tagged download plan built on the ground based on conservative maximum volume assumptions for all images. Third, we consider scenarios in which urgent acquisition requests can be synthesized by the satellite following on-board detections, or received from the ground or from relay satellites using a low level of uplink bandwidth. The goal for the satellite is then to be reactive and to autonomously integrate the realization of these requests in the current plan, possibly by canceling low priority operations.

In this paper, we present techniques used for answering these needs for a new generation of autonomous EOSs. The main contribution is an instantiation of an architecture composed of a hierarchy of modules which use heterogeneous procedures to deliberate and which manage static memory allocation issues and action interruptibility in a clean way. We do not consider the functional layer of the satellite, realtime execution aspects, or fault detection, identification and recovery. Instead, we focus on the on-board deliberation capabilities and on the interaction with execution.

The paper is organized as follows. Sect. 2 recalls related works, Sect. 3 motivates our design choices, Sect. 4 describes the problem to solve, Sect. 5 gives the architecture of the EOS mission controller, Sect. 6 details the plan adaptation procedures, Sect. 7 details how planning and execution are interleaved, and Sect. 8 describes our first experiments.

Related Works

The development of autonomous mission controllers is not a new topic in the space domain. Almost all systems developed in this context use so-called timeline-based reasoning, which consists in using timelines for representing the evolution of relevant state attributes of the system and its environment, such as the states of instruments or the amount of resources available. Each timeline is composed of a sequence of tokens, which correspond to temporal intervals over which a state attribute takes a given value.

In the space domain, several operational autonomous mission controllers were already deployed: • the seminal Remote Agent [START_REF] Muscetolla | Remote Agent: to boldly go where no AI system has gone before[END_REF][START_REF] Jónsson | Planning in interplanetary space: Theory and practice[END_REF] which managed to take the full control of the NASA DS-1 probe launched in 1998; it used constraint-based reasoning and flaw resolution techniques for progressively building temporally flexible plans satisfying all constraints required between tokens;

• CASPER (Chien et al. 1999b;1999a;2014;[START_REF] Knight | CASPER: Space exploration through continuous planning[END_REF][START_REF] Estlin | Using continuous planning techniques to coordinate multiple rovers[END_REF], which was successfully used for NASA satellites EO-1 launched in 2000 and IPEX launched in 2013; for IPEX, CASPER reacted autonomously, during at least one year of operations, to the real on-board resource usages, to the real durations of activities, to the real data volumes, and to events detected on images; to do this, CASPER is called regularly (using a continuous planning strategy) and iteratively repairs conflicts on the current plan; it does not manipulate temporally flexible plans, but it contains repair procedures which can move activities; CASPER also exploits hierarchical decompositions of activities to perform short-term planning for low-level activities and long-term planning for high-level ones;

• the VAMOS experiment of the DLR BIROS satellite launched in 2016 [START_REF] Wörle | Ground assisted onboard planning autonomy with VAMOS[END_REF]; given a baseline ground plan represented as a set of successive timeline blocks, VAMOS is able to autonomously activate timeline extensions on-board depending on the amount of resources available at execution time and to react to event detection by quickly generating new timeline extensions from a catalog of predefined extensions; to make these operations very quickly, VAMOS uses decision rules based on resource thresholds precomputed on the ground;

• the three ESA PROBA satellites, launched in 2001[START_REF] Rabideau | Tracatable goal selection with oversubscribed resources[END_REF], and 2013; for instance, PROBA-1 is able to realize autonomous maneuvers for realizing observations on areas whose coordinates are provided by the ground, and PROBA-V uses on-board decision rules to activate the acquisition flow for imaging lands [START_REF] Ilsen | PROBA-V: The example of onboard and onground autonomy[END_REF]);

• the autonomous controllers used for the NASA Martian rovers; for these rovers, mission plans are built on the ground and on-board reasoning is used for autonomous navigation tasks, for opportunistic science in the middle of navigation tasks, and for coping with activities whose duration is longer than expected based on some clean up operations if the real cumulated duration of a block of activities is longer than a given margin [START_REF] Gaines | Productivity challenges for Mars rover operations[END_REF].

Besides these deployed systems, several other experimental autonomous controllers have been tested.

• As in the Remote Agent and IxTeT-eXeC [START_REF] Lemai | Interleaving temporal planning and execution in robotics domains[END_REF], some experimental controllers execute temporally flexible plans. This is the case for the GOAC architecture [START_REF] Fratini | APSI-based deliberation in goal oriented autonomous controllers[END_REF][START_REF] Cesta | Continuous planning and execution with timelines[END_REF]) and for the SanchoExpress on-board executive [START_REF] Victoria | Autonomous mission planning and execution for two collaborative mars rovers[END_REF]. Both of them manipulate plans defined as timelines where transition times between tokens are subject to minimum and maximum temporal distance constraints. Simple temporal network reasoning is then used to propagate the earliest possible start time of each transition and to detect potential conflicts. Other experimental controllers manipulate temporally flexible plans defined as partial order schedules [START_REF] Policella | Generating robust schedules through temporal flexibility[END_REF]): see [START_REF] Pralet | Satellite data download management with uncertainty about the generated volumes[END_REF] for an application to flexible download plans for EOSs and [START_REF] Chi | Embedding a scheduler in execution for a planetary rover[END_REF] for an application to the flexible execution of the Mars 2020 rover activities.

• As in CASPER, other prototypes use iterative plan repair, but with a specific effort to use predefined intelligent repair rules to decrease the computational effort. This is the case for MEXEC developed for the future Europa Clipper mission near Jupiter [START_REF] Verma | Autonomous science restart for the planned Europa mission with lightweight planning and execution[END_REF], and for the TVCR system studied for ExoMars [START_REF] Woods | On-board planning and scheduling for the ExoMars mission[END_REF]).

• As in VAMOS, other approaches combine ground planning and on-board reasoning by using, at the level of the flight software, a set of resource thresholds computed on the ground to decide whether additional activities can be activated online [START_REF] Maillard | Postponing decision-making to deal with resource uncertainty on Earth-observation satellites[END_REF]2016). In the space domain, only a few work has been realized on plans containing explicit conditional branches [START_REF] Washington | Plan execution, monitoring, and adaptation for planetary rovers[END_REF].

• Some other autonomous controllers follow a different approach, where execution is interleaved with planning based on a fast greedy search that has a reduced worstcase time complexity [START_REF] Khatib | Interleaved observation execution and rescheduling on Earth observing systems[END_REF][START_REF] Chien | Heuristic onboard pointing re-scheduling for an Earth observing spacecraft[END_REF][START_REF] Pouly | Autonomous mission planning in space : Mission benefits and real-time performances[END_REF][START_REF] Rabideau | Prototyping an onboard scheduler for the Mars 2020 rover[END_REF][START_REF] Pralet | A generic constraint-based local search library for the management of an electromagnetic surveillance space mission[END_REF][START_REF] Rabideau | Tracatable goal selection with oversubscribed resources[END_REF]. Such greedy searches manipulate consistent plans and use an iterative selection-insertion mechanism. At each step, the latter selects one candidate activity a and tries to insert a into the plan. If the insertion succeeds, a new current plan is obtained, otherwise a is rejected and the next activity is considered. The contributions that follow this approach differ in the way the next activity is selected and in the way insertions are made. For replanning in case of addition of a new goal, some of these approaches restart from an empty plan [START_REF] Chien | Heuristic onboard pointing re-scheduling for an Earth observing spacecraft[END_REF], while others use incremental processing, for instance by restarting from a plan where only the lowest priority activities are removed [START_REF] Rabideau | Tracatable goal selection with oversubscribed resources[END_REF].

In another direction, the definition of autonomous controllers in the space domain requires the definition of a robotic architecture composed of several modules. Some approaches use a three-tier architecture involving a deliberative layer, an executive layer, and a functional layer. Other approaches are inspired by the work on IDEA [START_REF] Muscettola | IDEA: Planning at the core of autonomous reactive agents[END_REF]T-REX (McGann et al. 2008), which allow for a more flexible interleaving between planning and execution. Basically, a T-REX agent controls a set of control loops called reactors. The latter manipulate timelines, and to progressively build a globally consistent plan they exchange goals defined as desired future timeline values. At each deliberation cycle, a T-REX agent tries to synchronize the view of the timelines among the reactors, dispatches goals between the reactors, and finally allocates some time to each reactor to deliberate. In the space domain, the T-REX approach was used for the APSI deliberative reactor of the GOAC architecture developed for ESA, where the APSI framework is used to deliberate [START_REF] Fratini | APSI-based deliberation in goal oriented autonomous controllers[END_REF][START_REF] Cesta | Continuous planning and execution with timelines[END_REF]. More recently, it was also used in ERGO [START_REF] Ocón | Using the ERGO framework for space robotics in a planetary and an orbital scenario[END_REF], where a PDDL planner is used by a mission reactor, and where the autonomy level can range from reactive to deliberative behaviors.

To deal with our autonomous EOS scenario, we developed a timeline-based mission controller whose main design choices are given below.

First, we use simple decision rules rather than black-box multi-criteria planning procedures. One reason for this is that the mission controller must bring some guarantees on how preferences of the end-users are taken into account. For instance, high priority requests must always be preferred to low priority ones, the geocentric pointing (pointing in the direction of the Earth center) must be preferred when there are sufficiently long periods without observation, and the devices (the mass memory, the acquisition instrument, and the emission antenna) must be switched off when possible but not too often for long-term reliability issues. Also, the mission controller is an embedded software which must not use dynamic memory allocation. This means that the used memory must be reserved at the initialization step, and not during the execution of the decision procedures. This is why we do not use black-box planners which do not offer such a guarantee.

Second, we use the T-REX approach that decomposes the mission manager into several reactors. This allows to have several smaller subproblems for which specific reasoning procedures can be used instead of a global problem which is harder to solve. This is particularly useful because EOSs have low computational capabilities (typically 100 times slower that a modern laptop), and the time available to make decisions is limited to avoid missing acquisition and download opportunities while the satellite is moving on its orbit. The T-REX approach also leads to a modular architecture where reactors can be more easily changed, reused, and validated. We also make some efforts to get incremental deliberation procedures that quickly deal with goal updates and avoid replanning from scratch.

Third, in our architecture, a reactor can manipulate flexible plans internally but we do not have a global simple temporal network representing the set of all feasible plans. One reason for this choice is that in the EOS scenario considered, postponing an activity is not just a matter of temporal constraints, essentially due to complex state constraints. One of them is related to the kinematic features of agile satellites, which use gyroscopic actuators to move around their gravity center along the three axes (roll, pitch, and yaw). Also, acquisition and download activities can be performed in parallel but there is a coupling between the pointing of the satellite used for observing and the pointing required for downloading data to a given ground station (download is not possible if the angle between the current satellite pointing and the satellite-station vector is too high). To take these state constraints into account, we fix the timings of acquisition activities when building the download plan.

Fourth, as in CASPER, we manipulate both long-term high-level plans (coarse acquisition and download activities) and short-term low-level plans (detailing when the devices must be switched on and off). To get an explicit relationship between high-level activities and low-level ones, we exploit hierarchical decompositions of goal activities.

Fifth, to perform planning and execution in parallel, we make a clear distinction between the activities whose execution is committed and the activities whose presence in the plan can still be changed if needed, and a clear distinction between the activities that can be interrupted and those which cannot, as in IxTeT-eXeC [START_REF] Lemai | Interleaving temporal planning and execution in robotics domains[END_REF].

Planning Problem Description

At each step, the autonomous controller must consider:

• a set of observation requests R; each request r ∈ R has a priority, a duration, and a set of possible realization time windows; each request r ∈ R also has an estimated data volume (exact volume if data has already been acquired and compressed) and a boolean cloud cover prediction for each possible realization window;

• the kinematic capabilities of the satellite; to simplify the presentation, we only consider maneuvers in terms of roll angles (pointing of the satellite to the right or to the left of its ground trace); we use a simple model where the minimum transition duration between two successive observation requests r 1 , r 2 is obtained from the difference between the roll angle RollEnd r1 obtained at the end of r 1 and the roll angle RollStart r2 required at the start of r 2 , divided by a mean rotation speed around the roll axis;1

• a set of ground reception stations S, with for each station s ∈ S a set of time windows during which downloading data is possible; observing and downloading is parallel is possible, but only if the pointing used for observing is not too far (in terms of angular distance along the roll axis) from the direction of the satellite-station vector;

• the features of the devices (the observation instrument, the mass memory, and the emission antenna), including the fixed durations required to switch on and off each device.

Fig. 1 shows, at two different steps of the execution, the kind of plans obtained from the autonomous EOS controller presented in this paper. In Fig. 1, the current execution time is represented by the red vertical dashed line, and the current start time of the planning horizon is represented by the blue vertical dashed line. Several timelines are used:

• pointing, which represents the evolution of the pointing of the satellite; possible tokens are MAN(ρ, ρ ) (maneuver from roll angle ρ to roll angle ρ , in magenta), GEO (geocentric pointing, in blue), and ACQ(ρ, ρ ) (pointing for realizing an acquisition whose start and end roll angles are ρ and ρ respectively, in red);

• memWrite, which represents the unique identifier of the file in which acquisition data are being written; possible tokens are WRITE(f) (when file number f is written, in red) and IDLE (when no file is written, in gray);

• memRead, which represents the unique identifier of the file from which downloaded data is being read; possible tokens are READ(f) (when file number f is read, in orange) and IDLE (when no file is read, in gray);

• instrState, memoryState, and antennaState, which represent the evolution of the state of each device; for these timelines, the possible tokens are ON A (ON state used for supporting acquisition and download activities, in green), ON M (ON state maintained between two activities, in green too; contrarily to ON A, the ON M token can be interrupted if needed), OFF (OFF state of the device, in gray), OFF TO ON (warming of the device, in yellow), and ON TO OFF (ON to OFF transition, in yellow too). Fig. 1 also shows the visibility windows available over three stations. Globally, each plan contains (1) a sequence of acquisitions interleaved with maneuvers and geocentric pointings, (2) download activities realized during station visibility windows, (3) operations over the devices to have the mass memory and the instrument ready during acquisitions, and to have the mass memory and the antenna ready during download activities. It is also possible to see that multiple planning horizons are used, with a long-term horizon for the global acquisition and download plans, and a short-term horizon for the detailed management of the devices. To build the plans presented before, the EOS autonomous controller uses the acyclic architecture provided in Fig. 2, which is composed of 10 reactors. To transform high-level goals into fine-grain plans, the reactors exchange goal requests (solid lines) and information on the system state (dashed lines). A reactor can also cancel a goal previously sent to another reactor.

At the highest level of the hierarchy, the Mission Reactor is responsible for managing the arrival of new observation requests. For each new request received, the Mission Reactor sends one acquisition goal to the Acquisition Reactor and one download goal to the Download Reactor.

At the lowest level, the Pointing Monitor, the Instrument Monitor, the Memory Monitor, and the Antenna Monitor are respectively responsible for managing the commands concerning the pointing of the satellite, the observation instrument, the mass memory, and the data emission antenna. These low-level reactors directly interact with the functional layer of the EOS. They receive time-tagged commands and they simply order these commands chronologically to send them to the devices when needed. The Acquisition Reactor is responsible for producing a high-level acquisition plan from the set of candidate acquisition goals it receives and from updated cloud cover predictions over the areas to be observed. It sends "ON goals" to the Memory and Instrument Reactors, to request the mass memory and the observation instrument to be switched on during observations. It also sends pointing commands to the Pointing Monitor, and write commands to the Memory Monitor (command to write the data flow generated by the observation instrument during a fixed time window).

The Download Reactor is responsible for producing a download plan from the set of candidate download goals it receives, from all inputs on the real data volume after compression, from the end dates of acquisitions (to ensure that for each request, data download is realized after data acquisition), and from the pointing of the satellite synthesized by the Acquisition Reactor. Such a pointing can indeed limit download opportunities over a given station. The Download Reactor sends ON goals to the Memory and Antenna Reactors, to request that the mass memory and the antenna must be switched on for downloading data.

The Instrument Reactor, the Memory Reactor, and the Antenna Reactor are respectively responsible for managing the ON/OFF state of the observation instrument, the mass memory, and the emission antenna. To achieve the ON goals received, they compute switch-on/switch-off commands that are then sent to the device monitors. These reactors are instantiations of a generic Device Reactor.

As in T-REX, each timeline is owned by a unique reactor. For example, as shown in Fig. 2, the memoryState timeline is owned by the Memory Reactor. The reactors interact through goal transmissions and read operations over external timelines (e.g., the Download Reactor listens to updates on the pointing managed by the Acquisition Reactor).

Goal Decompositions

The decomposition of high-level goals into subgoals is shown in Fig. 3. The decomposition also associates with each goal g the set of all possible tokens that might be useful over timelines to achieve g. All goals and their tokens are created at the initialization of the flight software, to avoid dynamic memory allocation. Fig. 3 shows the 6 types of goals manipulated:

• the request goal, which covers one acquisition goal and one download goal;

• the acquisition goal (acqGoal), which covers:

tokens IDLE and WRITE over the memWrite timeline; the first one is used to model an idle state of the data writing process between the end of the previous acquisition and the start of the acquisition associated with the goal; the second one is used to describe that data is written in a file during the acquisition; commands used to start and end the recording of the acquisition flow (cmdStartWrite and cmdEndWrite); -ON goals over the mass memory and the instrument (memOnGoal and instrOnGoal); pointing commands, including cmdManeuverToGeo used for reaching a geocentric pointing between the last acquisition realized and the acquisition considered (command used only if there is a sufficient time gap between the two acquisitions), cmdManeuverToAcq used for realizing a maneuver just before the acquisition considered, and cmdScanAcq used for scanning a ground area; four tokens are associated with the pointing timeline to describe the evolution of the pointing from these commands;

• the download goal (dlGoal), whose decomposition is similar to the decomposition of an acquisition goal; the main difference is that it does not involve elements related to the pointing of the satellite;

• the ON goals over the three kinds of devices (instrOn-Goal, memOnGoal, antennaOnGoal); each ON goal has fixed start and end times; it covers tokens and commands that can be used to enforce the goal (see the algorithms described in the following section). Even if it is not explicitly represented here, each goal has parameters which describe its features. There is also a relationship between the parameters of a goal and the parameters of the subgoals and tokens it covers. For instance, for an acqGoal realized over time slot [150,173], subgoal memOn-Goal has [150, 173] as a required time slot. Similarly, given an acquisition goal, if the roll angle at the start of the acquisition is 24 degrees, then the cmdManeuverToAcq command also has as a target the 24 degrees roll angle.

Data Structures Associated With Reactors

In the autonomous EOS controller, each goal type is handled by a unique reactor and each reactor handles a finite set of potential goals. For instance, there is a constant giving the maximum number of acquisition goals which can be handled by the system. If this number is exceeded, low priority goals can automatically be rejected. Also, for the sake of future incremental decision procedures, each goal has an update status: ADDED in case of an addition of the goal, REMOVED in case of a cancellation by the reactor which requested the goal, UPDATED in case of change in the parameters of the requested goal, and NONE otherwise.

Additionally, one token is used for each timeline to represent its initial state, and static data structures are used to represent the final evolution of timelines. As an illustration, the Acquisition Reactor can use a cmdManeuverToGeo command to realize a maneuver to the geocentric pointing at the end of the planning horizon, together with some associated tokens over the pointing timeline. The acquisition and download reactors can use IDLE tokens at the end of their planning horizon. Each device reactor can used a cmdSwitchOff command to switch the device off after the last activity, together with tokens over the device state timeline.

Plan Adaptation Procedures

To handle the set of reactors, the autonomous controller uses a planningStep() function which sequentially calls the plan adaptation procedures of each reactor, from high-level reactors to low-level reactors. From a generic point of view, it makes reactors deliberate in a topological order of the DAG whose arcs correspond to goal and timeline value transmissions between reactors (note that the Download Reactor is at a lower level than the Acquisition Reactor due to read operations over the pointing and acqEndTime timelines). We now detail the deliberation procedure used by each reactor. We exclude the MissionReactor which only forwards acquisition and download subgoals without making any decision. We also exclude the Instrument, Memory, Antenna, and Pointing Monitors which only maintain a chronological ordering of the goals they receive.

Acquisition Reactor: Greedy Hierarchical Adaptation

The Acquisition Reactor computes the sequence of acquisitions which must be successively realized by the satellite. It uses a generic temporal constraint manager [START_REF] Pralet | An incomplete constraint-based system for scheduling with renewable resources[END_REF] to automatically obtain earliest and latest start times of successive acquisitions, based on the realization window chosen for each of them and on the required roll angle transitions between acquisitions. Internally, the reactor handles temporally flexible plans, but the ON goals sent to low-level reactors are time-tagged (by the earliest start and end times of acquisitions).

Given the current plan, the Acquisition Reactor uses the following steps to adapt its internal plan and the sub-goals sent to lower level reactors (see Fig. 4 for an illustration):

1. read all acquisition goals updates (with status REMOVED, ADDED, or UPDATED); remove from the plan all goals whose status equals REMOVED or UPDATED, and add to the set of active goals all goals having the ADDED status; in Fig. 4, this step removes acquisition A from the plan due to the cloud cover prediction over A; 2. apply a greedy selection-insertion search: at each step, select an unplanned active goal that has no cloud cover and whose priority is the highest, and break ties by considering first the oldest activated goals; to insert the acquisition a associated with the goal:

• consider the next possible acquisition window w for a in the chronological order; to free some place for a, remove all acquisitions a of the plan which have a priority lower than a and which overlap w in the earliest start time plan (taking into account roll angle transitions); in Fig. 4, when the insertion of F is considered, this step removes observations B and C from the plan; • try to insert a into the plan at a position which offers the highest temporal flexibility in the realization of a, to favor future acquisition insertions; • if the insertion of a succeeds, then a new current plan is obtained; the acquisitions removed for inserting a can possibly be reinserted at future steps of the greedy search; in Fig. 4, this occurs for observation B, as shown in the final plan obtained, but not for C; • if the insertion of a fails, come back to the state of the plan before the test of the insertion of a in window w; try to insert a in the next window if one exists, or consider the next candidate acquisition for insertion;

3. in the plan, add intermediate geocentric pointings as soon as the distance between two successive acquisitions is greater than a given threshold, and come back to a geocentric pointing at the end of the planning horizon; add maneuvers to fill the pointing timeline; 4. from the earliest start time plan obtained, derive all updates on goals to be sent to the lower level reactors.

The incrementality of the previous procedure could be improved, for instance by avoiding the recomputation of all geocentric pointings each time a new plan is synthesized.

Download Reactor: Chronological Decision Rules

The Download Reactor restarts from an empty download plan when there is a change in the end time of an acquisition or in the data volume after compression. It also rebuilds a plan when a change in the pointing profile invalidates one download activity of the current plan. The Download Reactor deliberates following decision rules that fill the download plan in a chronological way, by considering at each step a download goal (dlGoal) associated with a highest priority request (greedy selection-insertion mechanism). The deliberation procedure is illustrated in Fig. 5 and works as follows. 1. Based on the pointing timeline obtained from the Acquisition Reactor, the set of available station visibility windows is reduced in order to get effective visibility windows during which downloading data is compatible with the pointing used for observing (angle between the satellite pointing and the satellite-station direction less than a given threshold). In Fig. 5, the visibility window of station 1 is split into two effective visibility windows. 2. To initialize the chronological construction of a plan, the current time t is set to the maximum between the start time of the first effective station window and the first date at which both the mass memory and the emission antenna can be in the ON state, given the initial state of the device state timelines. 3. At each step, the planning algorithm selects the highest priority download goal whose realization can start at time t and finish before the end of one effective station window available at t. Ties are broken by considering first the download goals associated with data whose acquisition time is the lowest (the oldest data).

(a) If one such download goal g exists, it is enqueued at the end of the download plan and the new current time is set to the end time of the realization of g. In Fig. 5, this decision rule first inserts the download dl(A) of acquisition A when the current time equals t3, and then the download dl(B) of acquisition B when the current time equals t4. The download of A is inserted first because A has a highest priority. The download of B is realized before the download of F because dl(F ) is not a candidate download yet when the current time equals t4, since the end time of acquisition F has not been reached yet.

(b) If no such download goal exists, the current time t is moved forward to the minimum between the next acquisition end time and the next start time of an effective download window. The first case occurs when the current time is changed from t6 to t7 in Fig. 5. 4. The algorithm stops when there is no more effective station window or download goal over the planning horizon. Device Reactors: Chronological Decision Rules A Device Reactor restarts from an empty plan when an ON goal is updated (added, removed, or moved). It then deliberates over a short-term horizon to produce a so-called ON/OFF plan for the device. The deliberation procedure is illustrated in Fig. 6 and uses the following steps.

1. The ON goals are ordered by increasing start times. Some of these goals come from the Acquisition Reactor, while others come from the Download Reactor, hence there can be a temporal overlapping between them. , used for instance when inserting goal g2 in Fig. 6).

Otherwise, the reactor decides whether the device must be temporarily switched off just after t and then switched on a short time before t 1 (option used for the insertion of goal g3 in Fig. 6), or whether it must be maintained on from t to t 1 (option used for the insertion of goal g4 in Fig. 6). The choice between the two options is realized by switching the device off when t 1 -t exceeds a predefined threshold. At any step, the tokens added on timelines are those which are statically associated with goals, as defined in Fig. 3. Note that in Fig. 6, goal g4 is located after the end of the planning horizon (vertical bars on the figure), but it must be taken into account to determine whether the device must be switched off between the end of g3 and the end of the planning horizon. 3. If the end time of the planning horizon is not reached, commands and tokens are added to switch the device off just after the last token of the device state timeline and to keep it off until the end of the planning horizon.

The incrementality of the previous procedure could be improved to avoid building ON/OFF plans from scratch each time an input ON goal changes. However, the operations realized already have a low worst-case time complexity. Note also that for building an ON/OFF plan, there is no need to use a complex constraint-based or PDDL-based planner. The dedicated procedure proposed is both intuitive for the endusers and fast. Moreover, it is generic since it is used for three devices, the only parameter to set being the duration of ON TO OFF and OFF TO ON transitions, and the threshold defining when a device must be temporarily switched off.

Goal Planning Failures Goal planning failure is not an issue for the reactors used. Indeed, even if the sets of acquisition and download goals requested by the Mission Reactor usually lead to over-constrained planning problems, having unplanned goals is not an issue for the Mission Reactor. Moreover, the Acquisition and Download Reactors integrate constraints that ensure that the ON goals they request will always be feasible by the Device Reactors.

In a more general context, when a reactor r fails in planning a goal g requested by another reactor r , reactor r receives a message expressing that the realization of g has not been planned. At the next deliberation cycle, r can decide to update its own plan accordingly. Such planning steps can be iterated to try to converge to a state where all requested goals are planned. Even if the total allocated deliberation time does not suffice to reach a globally consistent plan, the plans of low-level reactors still remain valid, and in the worst case the satellite will just plan some useless operations.

Management of the Execution

Goal Execution Status As in the APSI Deliberative Reactor [START_REF] Fratini | APSI-based deliberation in goal oriented autonomous controllers[END_REF][START_REF] Cesta | Continuous planning and execution with timelines[END_REF], each goal has an execution status which allows to determine whether it needs to be taken into account by the deliberation procedures. In our case, the execution status of an active goal takes value BUFFERED when the execution of the goal has not started yet, EXECUTING when the realization of the goal is ongoing, EXEC SUCCESS when the execution of the goal has succeeded, and EXEC FAIL when it has failed. In our current prototype, we do not consider execution failures for which an additional analysis module explaining the reasons of the failure would be needed, together with potential reconfiguration mechanisms.

At the moment, our autonomous EOS controller is not used on a real satellite or connected to a real processor used in the space domain. Instead, we just simulate the execution of all basic commands. As commands cmdStartWrite, cm-dEndWrite, cmdStartRead, and cmdEndRead are executed within a single execution cycle, they have a null execution duration and immediately get status EXEC SUCCESS when their execution is triggered. Command cmdScanAcq used for scanning an observation area gets status EXECUTING when it is activated, and status EXEC SUCCESS when the duration of the associated acquisition is elapsed. Similarly, all commands used for switching devices on and off get status EXECUTING when they are activated, and status EXEC SUCCESS once the fixed duration of the associated device state transition is elapsed. The same kind of simulation can be made for commands cmdManeuverToGeo and cmdManeuverToAcq.

The execution status of an acquisition goal becomes EXECUTING when the associated WRITE token starts, and EXEC SUCCESS when this token ends. This implies that for the deliberation process, the realization of an acquisition goal can always be changed until its execution starts, even if previous operations were performed such as switching on devices for the sake of this goal. This brings more flexibility to insert the realization of last-minute high priority requests. Similarly, the status of a download goal becomes EXECUTING when the associated READ token starts, and EXEC SUCCESS when this token ends. The status of an ON goal expressed on devices (handled by the Memory, Instrument, and Antenna Reactors) also takes value EXECUTING and EXEC SUCCESS respectively at the start and end times associated with this goal. Last, the execution status of a request becomes EXECUTING when the execution of the associated acquisition goal starts, and status EXEC SUCCESS when the execution of the associated download goal ends.

Interleaving Execution and Planning Let t denote the current time (the execution time). As in T-REX, if the deliberation process of a reactor r is triggered at time t, then this process considers a planning horizon starting at time t = t + λ r where λ r is called the latency of reactor r. Another deliberation process will be triggered at time t , to obtain deliberations over a rolling horizon. 2 At time t, the part of the plan located over time interval [t, t [ is committed. In our implementation, the execution is simulated at all execution cycles t ∈ [t, t [ to update the execution status of commands and goals.

The deliberation process removes all tokens ending strictly before t . One difficulty is then that for a timeline tl , time t might be placed in the middle of a non-interruptible token tk. Non interruptible tokens are MAN(ρ, ρ ) and ACQ(ρ, ρ ) for the pointing timeline, READ and WRITE for the memRead and memWrite timelines, and ON TO OFF, OFF TO ON, ON A for the device state timelines. In this case, the deliberation process makes a copy of tk and records it as the initial token for timeline tl for the new planning horizon. Otherwise, if token tk is interruptible, the reactor makes a copy of tk and records it as the initial token for timeline tl , but the end time of this token is set to t , the start time of the planning horizon. As in T-REX, each reactor r then builds a plan over temporal window [t , t + π r ],

2 Recent strategies defined for M2020 schedulers that mix fixed cadence and event-driven deliberations could be considered for improving the efficiency of the approach [START_REF] Chi | Embedding a scheduler in execution for a planetary rover[END_REF].

where π r is called the planning horizon of r (with π r ≥ λ r ). In the end, planning and execution are synchronized based on commit window [t, t [, on goal execution status, and on the initial state computed for each timeline at t .

Experiments

The implementation of our EOS autonomous controller is based on several generic features for representing timelines, tokens, goal decompositions, reactors having planning and execution functions, goal activation and deactivation, and commitments. We used the prototype developed both on hand-written scenarios to test particular configurations and on randomly generated scenarios that validate the behavior of the prototype on a wider range of situations.

Each scenario (hand-written or random) defines the number of acquisitions and their features (priority, duration, roll angles, initial cloud cover prediction, maximum data volume, acquisition windows), the number of ground stations and their features (zenith angle of the satellite, download windows), and the features of the devices (durations of the transitions between the ON and OFF states, and maximum time gap for leaving the device ON between two usages).

Each scenario also defines all events that will be received by the autonomous controller over the planning horizon, including (1) the arrival of new acquisition requests (a scenario specifies the time at which each request is received by the controller), (2) the arrival of new cloud cover predictions (a scenario specifies the time at which each prediction is received), (3) the real volume of data associated with each acquisition (this real volume information is received by the controller at the end of each acquisition realized). In random scenarios, the parameters of these events are randomized, as well as the features of candidate observations and ground reception stations.

During our first experiments, we were able to visualize the events received by the autonomous controller, the evolution of the current plan (same view as in Fig. 1), and the concurrent execution of actions. For scenarios involving 10 requests, 3 priority levels, and 3 stations, each deliberation of the full controller (i.e. over all reactors) requires at most 3 milliseconds to converge to a new current plan on a standard laptop (Intel i5, 1.2GHz, 4GBRAM).

Conclusion

This paper presented an autonomous mission controller built for a new generation of EOS. One of its main strength is its capacity to use efficient reasoning procedure at the level of each reactor of the architecture. We should now test the approach on scenarios involving satellites which are agile along the three axis, and on scenarios involving memory and energy limitations. One challenge is also to formally validate the behavior of the controller, by validating first the behavior of each individual reactor, and then the interactions between the reactors. In this direction, it would helpful to use a formal language for describing the reactor architecture and the goal decompositions. The last point would be to add new modules providing to each reactor the current state observed or estimated for the timelines it owns.

Figure 1 :

 1 Figure 1: Timelines used by the mission controller

  Figure 2: Reactor-based architecture

Figure 4 :

 4 Figure 4: Adaptation of the acquisition plan (prioritary acquisitions in red, non prioritary ones in green)

Figure 5 :

 5 Figure 5: Successive insertions of downloads in the download plan during a deliberation of the Download Reactor

Figure 6 :

 6 Figure 6: Plan built by a Device Reactor to satisfy ON goals over fixed time intervals (SW tokens correspond to ON TO OFF and OFF TO ON transitions)

  2. At each step, the next ON goal g over a given temporal window [t 1 , t 2 ] is considered. Let δ denote the duration required by an OFF TO ON transition. Two cases are analyzed to deliberate. (a) In the first case, the last token on the device state timeline takes value OFF or ON TO OFF and finishes at time t. If it is not possible to have the device in the ON state at t 1 (t 1 -t < δ), the ON goal is rejected. Otherwise, the device is kept off until time t 1 -δ, switched on at t 1 -δ, and used in the ON state over [t 1 , t 2 ] (insertion of one OFF token over [t, t 1 -δ], one OFF TO ON token over [t 1 -δ, t 1 ], and one ON A token over [t 1 , t 2 ]). In Fig.6, these steps are used for planning the realization of goal g1 (yellow). (b) In the second case, the last token on the device state timeline takes value ON A (active ON), ON M (maintain ON), or OFF TO ON. If t ≥ t 2 , no operation is needed. Otherwise, if t ≥ t 1 , a token is added to use the device in the ON state until time t 2 (insertion of an ON A token over [t, t 2 ]

The approach can be extended to deal with fully agile satellites which can move around the three axis (roll, pitch and yaw), with time-dependent effects in terms of minimum transition durations.


Cédric Sauder
email: sauder@lcts.u-bordeaux1.fr

Jacques Lamon
email: lamon@lcts.u-bordeaux1.frsauder@lcts.u-bordeaux1.fr

The tensile creep behavior of SiC-based fibers with low oxygen content

The creep behavior of Hi-Nicalon, Hi-Nicalon S and Tyranno SA3 fibers is investigated at temperatures up to 1700°C. Tensile tests were carried out on a high capability fiber testing apparatus in which the fiber is heated uniformly under vacuum. Analysis of initial microstructure and composition of fibers was performed using various techniques. All the fibers experienced a steady-state creep. Primary creep was found to be more or less significant depending on fiber microstructure. Steady-state creep was shown to result from grain boundary sliding. Activation energy and stress exponents were determined. Creep mechanisms are discussed on the basis of activation energy and stress exponent data. Finally, tertiary creep was observed at very high temperatures. Tertiary creep was related to volatilization of SiC. Results are discussed with respect to fiber microstructure.

1-Introduction

SiC/SiC composites are designed to be used at high temperatures in various systems including aerojet engines and stationary gas turbines for electrical power/steam cogeneration on the one hand. Furthermore, owing to the stability of SiC under neutron irradiation and to recent progress in the fabrication of stoechiometric fibers, it is considered that SiC/SiC composites are possible candidates for nuclear applications, such as, for instance, structural components facing the plasma in fusion reactor [START_REF] Muroga | Overwiew of materials research for fusion reactors[END_REF][START_REF] Hasegawa | Critical issues and current status of SiC / SiC composites for fusion[END_REF] , or control bars and fuel containers in the Generation IV nuclear power plants.

Structural performances of SiC/SiC composites depend on fiber reinforcement, and more particularly on sensitivity of mechanical properties of fibers to temperature and environment.

The present paper focuses on the creep behaviour of SiC-based fibers with a low oxygen content under inert atmosphere. These fibers are potential candidates to reinforcement of SiC/SiC composites for nuclear applications.

A lot of papers on the creep behaviour of ceramic fibers are available in the literature. Data have been produced on SiC-based fibers see for instance [START_REF] Yun | Tensile creep and stress-rupture behavior of polymer derived SiC fibers[END_REF][START_REF] Yun | Comparison of the tensile, creep, and rupture strength properties of stoichiometric SiC fibers[END_REF][START_REF] Hochet | Microstructural evolution of the latest generation of small diameter siC based fibres tested at high temperature[END_REF][START_REF] Bodet | Tensile creep behavior of a silicon carbidebased fiber with a low oxygen content[END_REF][START_REF] Chollon | Correlation between microstructure and mechanical behaviour at high temperatures of a SIC fibre with a low oxygen content (Hi-Nicalon)[END_REF][START_REF] Dicarlo | Microstructural factors affecting creep-rupture failure of ceramic fibers and composites[END_REF] . Authors used mainly uniaxial tensile loading conditions, or a qualitative technique such as BSR (Bending Stress Relaxation). But only some of these papers were interested in the creep mechanisms [START_REF] Yun | Comparison of the tensile, creep, and rupture strength properties of stoichiometric SiC fibers[END_REF][START_REF] Bodet | Tensile creep behavior of a silicon carbidebased fiber with a low oxygen content[END_REF][START_REF] Dicarlo | Microstructural factors affecting creep-rupture failure of ceramic fibers and composites[END_REF] .

Testing tiny objects such as small diameter ceramic fibers (diameter may be as small as 10 µm) at high temperatures for long times is not straightforward. Results and analyses may be biased as a result of testing conditions. Testing method thus warrants consideration in order to produce valuable results.

During most of the tensile creep tests reported in the literature, the fiber was not at a uniform temperature (cold gripping method). Furthermore, test duration rarely exceeds 48 hours, for practical reasons associated to the design of experimental set up.

The cold grip based technique presents a few important drawbacks. Fiber specimens are generally quite long (length averages 100 mm), and there is a significant temperature gradient.

Owing to temperature gradient, determination of creep strain from fiber deformation is not straightforward [START_REF] Kandil | Tensile creep of ceramics: the development of a testing facility[END_REF] . Heavy and tedious calibration operations are required. Then, the use of long specimens is not recommended because of fiber diameter variation. Specimen length must be selected with respect to wave length in diameter variation [START_REF] Davies | Effect of variable radius on the initial creep rate of ceramic fibres[END_REF] .

In the hot grip based technique, short specimens are used and the entire fiber can be at a uniform temperature. Some authors claim that fiber may degrade due to the cement used for gripping fiber ends. This difficulty can be overcome with recent products. Furthermore, results obtained using the hot grip based technique appeared to be consistent with other available data [START_REF] Yun | Tensile creep and stress-rupture behavior of polymer derived SiC fibers[END_REF] .

Thus, in the present paper, some effort was directed toward the testing method, in order to overcome the difficulties associated to the cold grip based technique, and to produce valuable creep data on the last generation of SiC-based fibers.

2-Fibers and experimental procedure

2.1-Description of fibers

Hi-Nicalon and Hi-Nicalon S (Nippon Carbon Co) and Tyranno SA3 (Ube Indstry ltd.) SiCbased fibers were investigated (Table 1). Two different batches of Tyranno SA3 fibers were tested (they are referred to as SA3 (1) and SA3 (2)). Sylramic fibers were not considered in this study because they contain boron, which makes them sensitive to significant degradation under neutron irradiation [START_REF] Newsome | The effect of neutron irradiation on silicon carbide fibers[END_REF] .

Quantitative analyses of fibers composition and structure were performed using X-Ray Diffraction, Raman Spectroscopy, Transmission Electron Microscopy (TEM), Electron Probe Microanalysis (EPMA) and fractography. Specimens for TEM were prepared following the method proposed by Berger and Bunsell 12 .

2.2-Creep tests

The fiber samples were taken from tows (gauge length 25 mm). Graphite grips were affixed to sample ends using carbon based cement C34 (from UCAR Co).

The creep tests were performed on a tensile device (figure 1) designed for testing carbon fibers at temperatures up to 3000°C [START_REF] Sauder | Thermomechanical properties of carbon fibers at high temperatures (up to 2000°C)[END_REF] . Heating is generated by electric current circulating through fiber, under secondary vacuum (residual pressure ∼ 10 -4 Pa). Under such environment, active oxidation is infinitively slow [START_REF] Shimoo | Thermal stability of Polycarbosilane-derived silicon carbide fibers under reduced pressures[END_REF] . Temperature of fiber was measured using a bichromatic pyrometer. Temperature profiles showed that temperature is uniform over more than 95% gauge length [START_REF] Sauder | Thermomechanical properties of carbon fibers at high temperatures (up to 2000°C)[END_REF] . Furthermore, it appeared that grips remained at a temperature close to room temperature during the tests (< 50°C). Thus, the loading frame compliance was not affected during the tests. Fiber deformations can be derived from grip displacement. Loading frame compliance was taken to be equal to that estimated at room temperature. Computations of temperature distributions for various thermal conductivities showed that the temperature gradient from the core to the surface of the fiber is less than 2°C at 1000°C [START_REF] Sauder | Thermomechanical properties of carbon fibers at high temperatures (up to 2000°C)[END_REF] .

Fiber was first kept stress free at the test temperature for 30 mn. Then the stress was applied.

This operation took less than 10 seconds. Diameter of each fiber was measured in-situ using a laser mounted on the testing apparatus. It is given by the average of several measurements along the gauge length. To ensure a good reproducibility of results, only those specimens with quite uniform diameters were tested. For these specimens, diameters measured along fiber differed from the average by less than 3%.

Fiber deformations were derived from grip displacement. Data were corrected to account for deformation of loading frame. The loading frame compliance was estimated using the conventional calibration technique based on tensile tests on fibers having various gauge lengths [START_REF]Advanced technical ceramics -Ceramic Composites. Methods of tests for reinforcement -Part 6 : Determination of tensile properties of filament at high temperature -European standard CENTC 184[END_REF] . As indicated above, since the grips remained at a temperature close to room temperature during the tests, the loading frame compliance estimated at room temperature was pertinent.

Most of the creep tests were interrupted before fiber failure, for analysis of crept fibers.

Stresses in the range 150-850 MPa were applied, whereas temperatures were in the 1150-1700°C range. Tests as long as 350 hours, were performed in order to identify the different creep stages.

3-Results and discussion

3.1-Structure and composition of fibers

Table 1 summarizes results of microstructural analyses. All the fibers contain a small amount of oxygen (0.2%). Higher oxygen contents were reported for Hi-Nicalon fibers [START_REF] Bodet | Tensile creep behavior of a silicon carbidebased fiber with a low oxygen content[END_REF]16 (0.6-0.9 w/o).

There is a larger amount of free carbon in the Hi-Nicalon fiber when comparing with Hi-Nicalon S. Hi-Nicalon S is stoechiometric, but results indicate an excess of carbon. Figures 2(a) and 2(b) show that element concentration is uniform in both fibers. However, a carbon rich phase was detected using EPMA. It was located in the surface, over a thickness < 100 nm.

Hi-Nicalon fiber microstructure is well documented [START_REF] Bodet | Tensile creep behavior of a silicon carbidebased fiber with a low oxygen content[END_REF][START_REF] Berger | Microstructure and thermo-mechanical stability of a low-oxygen Nicalon fibre[END_REF][START_REF] Hochet | Microstructural evolution of the latest generation of small-diameter SiC-based fibres tested at high temperatures[END_REF] . Thus, data from the literature can be reported here. Hi-Nicalon fibers consist of fine β-SiC grains, that may be faulted [START_REF] Hochet | Microstructural evolution of the latest generation of small-diameter SiC-based fibres tested at high temperatures[END_REF] . Grain size averaged 5 nm (table 1). The largest grains were 20 nm (table 1). The carbon phase (turbostratic carbon) consists of distorted stacks of 5-10 graphitic planes, 2 to 5 nm long.

Hi-Nicalon S is made up of clusters of SiC grains (figure 3). Grain size averages 20 nm (table 1). The biggest grains were 50 nm large. Carbon is located between the SiC grains (figure 4).

Grains boundaries do not appear clearly (figure 4).

Concentration in C and Si was not found uniform in the SA3 fibers (figure 2). There is a larger amount of free carbon present in the core. The SA3 (1) fiber contained a larger amount of free carbon when compared to more recent SA3 (2) (table 1). Elemental composition in SA3 ( 2) is closer to stoechiometry, suggesting that fibers of this second batch have been improved. A carbon rich phase was detected in the surface, over 300 nm in the SA3 (1) fibers and 100 nm in the SA3 (2) ones. Aluminum was identified (table 1). According to Ishikawa [START_REF] Ishikawa | A thermally conductive SiC-Polycristalline fiber and its fiber-bounded ceramic[END_REF] , Al aggregates at grain boundaries.

Grain size is much larger when comparing with Hi-Nicalon and Hi-Nicalon S fibers.

Difference in grain size can be noted from micrographs shown on figure 5. The size of β-SiC grains averaged 200 nm (table 1). The biggest grains were 400 nm large. Grains displayed stack faults (figure 3). This explains the discrepancy in grain sizes estimated using XRD and TEM (table 1). Grain size was bigger from the core to the surface of fibers. As opposed to Hi-Nicalon S fibers, grain boundaries are clearly marked (figure 4). Carbon shows a turbostratic structure. It is located between β-SiC grains (figure 4).

3.2-Creep behaviour

The typical creep curves that were obtained are shown on figure 6. Steady state creep was observed after a more or less long primary creep stage, depending on fiber : after about 140 h for Hi-Nicalon fibers at 1200°C, about 72 hours for SA3 (1) fiber at 1200°C, about 8 hours for SA3(2) fiber at 1250°C, and about 8 hours for Hi-Nicalon S at 1350°C. The creep results

reported by most authors were obtained during much shorter tests (< 48 hours). Thus, it may be anticipated that their tests were not sufficiently long, so that true secondary creep stage was probably not reached.

Figure 7 shows a typical creep curve obtained under incremental temperature steps. It can be noted that creep accelerated at temperatures > 1600°C (tertiary creep). Creep curves were fitted by the following well accepted equations of deformations in the primary and in the secondary stages. Tertiary creep is examined in a subsequent section :

ε e = o E σ (1)
ε p = σA [1 -exp (-pt)] (2)
ε s = Bσ n t (3) ε = ε e + ε p + ε s (4)
where subscripts, e, p and s refer respectively to elastic regime, primary and secondary creep.

σ is the stress on fiber, E o is initial fiber Young's modulus, t is time, A, B, n and p are constants.

Figure 6 shows that an excellent agreement was obtained for quite all the fibers. Note that Hi-Nicalon S and SA3 fibers are less sensitive to creep than Hi-Nicalon.

Based on microstructure analysis, the fibers can be considered to be a mixture of wrinkled carbon-layer packets and SiC grains. Possible controlling creep mechanism may involve grain boundary sliding, carbon diffusion, dewrinkling, deformation and sliding of carbon crystallites [START_REF] Bodet | Tensile creep behavior of a silicon carbidebased fiber with a low oxygen content[END_REF] .

3.3-Creep mechanisms -Primary creep

Primary creep can be attributed to viscoelastic deformation of carbon at grain boundaries.

Viscoelasticity of carbon has been discussed by Kelly [START_REF] Kelly | Physics of graphite[END_REF] and it has been observed by Sauder et al. [START_REF] Sauder | The tensile behavior of carbon fibers at high temperatures up to 2400°C[END_REF] on various carbon fibers at high temperatures. Because of the very weak interaction between layer planes, each basal plane can deform as a separate unit in two dimensions, which produces substantial basal plane shear [START_REF] Kelly | Physics of graphite[END_REF] . Furthermore, magnitude of viscoelastic response of carbon fibers under tension depends on orientation of graphitic planes [START_REF] Sauder | The tensile behavior of carbon fibers at high temperatures up to 2400°C[END_REF] . It increases with the fraction of graphitic planes with a large angle to loading direction (isotropic carbon). By contrast, it is limited in the anisotropic fibers, in which most of the graphitic planes are oriented parallel to loading direction. In SiC fibers, orientation of graphitic planes is influenced by grain boundary distribution. Thus, graphitic planes can take all orientations.

Furthermore, it was indicated earlier that the carbon present in these SiC fibers consists of stacks of a few graphitic planes. As a consequence, primary creep may involve deformation of carbon at grain boundaries and grain sliding due to basal plane shear.

It is worth mentioning that primary creep was more significant in those fibers that contained a large amount of carbon (Hi-Nicalon). This supports the above carbon deformation driven mechanism.

Although Hi-Nicalon and SA3 (1) fibers possessed the same fraction of carbon, Hi-Nicalon fiber showed larger sensitivity to creep. This discrepancy can be attributed to grain size, that is much smaller in Hi-Nicalon fiber. It can also be related to the structure of carbon which displayed a better organization in SA3 ( 1) fiber (smaller distance between two successive layers : d 002 ), as a result of higher processing temperature. Low d 002 implies a larger stiffness and smaller deformations.

Hi-Nicalon fiber contains a significant amount of low density SiC. This SiC phase is not stable, as a result of short duration of pyrolysis step during fiber processing [START_REF] Hochet | Microstructural evolution of the latest generation of small diameter siC based fibres tested at high temperature[END_REF] . Grain growth thus starts at 1200°C in Hi-Nicalon fiber. It causes creep rate decrease. This phenomenon may explain the imperfect fit of experimental creep curve by equations ( 1) -(4) (figure 6 (a)).

3.4-Secondary creep : mechanism

Stationary creep was investigated essentially on Hi-Nicalon S and Tyranno SA3 fibers, which displayed a reasonably short primary creep stage. Extensive investigation of Hi-Nicalon would have required long experiments, as indicated above.

Creep rate in the steady state is expressed by the following general relationship :

) exp( . RT Q d D n m g o - = σ φ ε D = D o exp(- RT Q ) ( 5
)
Where φ is a material constant, D is diffusivity, Q is the apparent activation energy, R is the universal gas constant, T is temperature in Kelvin, dg is the grain size, σ is the applied stress, and m and n are exponents. Different values of m and n correspond to different mechanisms.

Values of n and Q may be obtained experimentally and used to infer a rate-controlling mechanism for creep.

The creep rate depends on temperature through an Arrhenius exponential term (equation 5).

Figure 8 shows typical Arrhenius creep rate plots obtained for the SA3 (2) fiber. Activation energy was determined by fitting equation (5) to creep rates determined at various temperatures.

The largest apparent activation energy was determined for Hi-Nicalon S fibers (table 2).

Lower similar values were obtained for both SA3 (1) and SA3 (2) fibers. Knowing that the main difference between both SA3 fibers lies in the amount of free carbon, this result indicates that secondary creep was not influenced by the amount of carbon.

Determination of stress exponent by fitting equations (5) to creep rates determined at different stresses (figure 9), yields stress exponents of 2.5 for all the fibers. It is worth mentioning that plots of strain rates determined under various temperatures and applied stresses (figures 8-10), and creep parameters reported in table 2 do not exhibit a noticeable discrepancy, which demonstrates the pertinence of experimental work. Diffusional creep in polycrystalline SiC occurs by diffusion of carbon [START_REF] Francis | Creep of Polycrystalline silicon carbide[END_REF] or silicon [START_REF] Krishnamashari | Interpretation of high-temperature creep of SiC by deformation mapping techniques[END_REF] at grain boundaries [START_REF] Francis | Creep of Polycrystalline silicon carbide[END_REF][START_REF] Krishnamashari | Interpretation of high-temperature creep of SiC by deformation mapping techniques[END_REF] or within grains [START_REF] Morscher | Bend stress relaxation and tensile primary creep of a polycrystalline α-SiC fiber[END_REF] or by diffusion of impurities at grain boundaries [START_REF] Grathwohl | Creep of Hot-pressed and sintered SiC with different sintering additives[END_REF] . There is a very limited amount of data on diffusion of carbon and silicon elements in SiC. There is no consensus about diffusion rate. Depending on author, diffusion rate of carbon would be 100 times faster than that of silicium 26,[START_REF] Eveno | Diffusion of 13 C and 29 Si implanted ions in SiC[END_REF] , or it would be slower 28 . Activation energies for diffusion of carbon and silicium within grains in β-SiC made via Chemical Vapor Deposition have been estimated to be 840 KJ mol -1 29 and 910 KJ mol -1 30 respectively. It is worth reminding that creep of polycrystalline SiC cannot be controlled by dislocation motions at temperatures < 1700°C [START_REF] Kossowsky | Cyclic fatigue of Hot-pressed Si 3 N 4[END_REF][START_REF] Farnsworth | Deformation behavior of dense polycrystalline SiC[END_REF] . For Nicalon SiC fibers tested in CO, n ≈ 1. Activation energy was found to be consistent with activation energies of thermally activated viscous flow of glasses at high temperatures [START_REF] Bodet | Microstructure stability and creep behavior of Si-C-O (nicalon) fibers in carbon monoxide and argon environments[END_REF] .

n exponents between 2 and 3 that have been determined for low oxygen content SiC fibers [START_REF] Yun | Comparison of the tensile, creep, and rupture strength properties of stoichiometric SiC fibers[END_REF][START_REF] Dicarlo | Microstructural factors affecting creep-rupture failure of ceramic fibers and composites[END_REF][START_REF] Piant | Comportement mécanique à haute temperature des fibres SiC de dernière generation[END_REF] correspond to grain boundary sliding in the absence of glassy phase [START_REF] Langdon | Grain Boundary Deformation Process[END_REF] .

Creep of the fibers of this study (n ≈ 2.5) may be attributed to grain boundary sliding, without grain elongation and glassy phase (Rachinger mechanism). In polycrystalline ceramics, accommodation results from diffusion and fold formation at triple junctions [START_REF] Langdon | Grain Boundary Deformation Process[END_REF] . In SiC fibers, it probably involves carbon deformation.

Apparent activation energy determined on Hi-Nicalon S (770 KJ mol -1 , table 2) is consistent with that corresponding to diffusion of carbon or silicon within grains [28][START_REF] Hon | Self-diffusion of 14 C in Polycristalline β-SiC[END_REF][START_REF] Hon | Self-diffusion of 30 Si in Polycristalline β-SiC[END_REF] . Diffusion within grains can be related to feature of microstructure. As it was mentioned in section 2.3.1, grain boundaries were not clearly defined. It may be thought that they cannot be preferred ways for diffusion.

Activation energy determined for SA3 fibers (table 2) is close to that corresponding to diffusion of Al at grain boundaries in polycrystalline SiC [START_REF] Tajima | Grain boundary segregation in aluminium-doped silicon carbide[END_REF][39][40] . This suggests the contribution of diffusion of Al at grain boundaries. It is also close to half pf that one corresponding to diffusion of C or Si within grains for Hi-Nicalon S (table 2). So the contribution of diffusion of C or Si at grain boundaries cannot be discarded. the third stage and cross section of fibers was examined using scanning electron microscopy.

Figures 11 and12 show the typical microstructure of fibers that was observed. It consists of two distinct parts : the core and an annular region. The microstructure of the core was unaffected whereas Auger analysis showed that the annular region was made of pure carbon.

Furthermore, the diameter of fiber was unchanged. These results suggest that silicon volatilized and that this phenomenon advanced from the surface towards the core. Data in the literature support this assumption. Thus, figure 13 shows that SiC decomposes at temperatures above 1400°C when pressure is identical to that one in the chamber (10 -4 Pa). Furthermore, authors have shown that gaseous Si (g) is produced preponderantly under these conditions 41- 48 . Experimental conditions were favourable to silicon volatilization. Thermodynamic equilibrium could not be reached and pressure of gaseous Si(g) remained above equilibrium value in the chamber : i) pressure in the chamber (10 -4 Pa) is smaller than that of Si (g) at temperatures above 1400°C, according to figure 13. As a consequence, gaseous species can be eliminated.

ii) Chamber wall was covered with a deposit after the tests, indicating that gaseous products condensed.

The above phenomenon cannot be attributed to active oxidation from residual oxygen. Active oxidation would have a more serious effect. Under such vacuum conditions, oxidation products (SiO (g) and CO (g)) would be continuously eliminated, so that the fiber would be completely destroyed. Authors who observed degradation of SiC fibers at high temperature under argon [START_REF] Chollon | Fibres céramiques à base de carbure de silicium et à faible taux d'oxygène[END_REF] , attributed this phenomenon to active oxidation. But they did not go into a deep investigation to ascertain their interpretation.

The creep rate acceleration would result from a change in the stress state in the SiC fiber, caused by the annular degradation of fiber. During Si volatilization, stiff SiC is replaced by a porous carbon material that is much more compliant. As a consequence, the load is carried preponderantly by the SiC core. As annular degradation proceeds, there is an increase in stress, according to the following equation :

σ (t) = 2 2 )) ( ( t e R R c c o - σ (6)
where σ o is the applied stress, R c is the fiber diameter and e(t) is the thickness of annular carbon layer.

In a first step, a simple linear time dependence was selected for e(t) :

e(t) = kt (7)
The degradation rate was estimated from the thickness of annular layer determined from micrographs of fibers after interrupted creep tests. K = 2.10 -12 m.s -1 was estimated for the Hi-Nicalon S fiber.

Stress relation (6) was introduced into equations ( 3) and (4). Figure 14 shows the creep curve that was predicted for Hi-Nicalon S. A good agreement with experimental results was obtained, which supports the analysis. Nevertheless, a slight discrepancy can be noticed, which may result from approximations in annular degradation law and in load sharing.

Contribution of annular carbon layer was neglected. Refinement, if necessary, would introduce a more complex annular degradation law and contribution of carbon layer in load sharing.

3.6-TEM analysis of crept fibers

TEM analysis was performed on SA3 (2) fibers tested at 1600°C and Hi-Nicalon S fibers tested at 1500°C. Creep tests were interrupted when total deformation of fiber reached 6%.

The following features were observed :

(i) carbon was highly preponderant in the superficial region (thickness was close to 500 nm) (ii) cavities were not detected at triple junctions. As indicated above it may be thought that accommodation is made possible because of carbon anisotropy (iii) in Hi-Nicalon S fibers (core), grains were larger when compared with as-received fibers (figure 15)

(iv) in SA3 fibers (core), grains were smaller when compared with as-received fibers (figure 15).

Grain growth in Hi-Nicalon S fibers after treatment at 1400°C has been reported in the literature [START_REF] Sha | Effect of heat treatment on the tensile strength and creep resistance of advanced SiC fibers[END_REF] . This phenomenon may be similar to that observed on Hi-Nicalon fibers. It suggests that the finishing treatment aimed at the elimination of carbon was not carried out at a sufficiently high temperature. Grain shrinkage in SA3 fibers is intriguing. It seems logical to look for a connection with Si volatilization. Further investigation is required.

4-

Conclusion

The tensile creep behaviour of SiC fibers with a low oxygen content was investigated up to very high temperatures. Tests of long duration were carried out on a high performance testing device. The three stages of creep were evidenced.

Primary creep was particularly long in the Hi-Nicalon fibers. It lasted more than 144 hours.

Primary creep was attributed to viscoelastic deformation of carbon at grain boundaries.

Primary creep is enhanced by the amount of free carbon. Hi-Nicalon fiber experienced much larger deformations than Hi-Nicalon S and SA3 fibers. Furthermore, shorter primary creep stage was observed on both latter fibers.

Determination of creep constants including stress exponent (n ≈ 2.5) and apparent activation energy suggests the following mechanisms of secondary creep :

grain boundary sliding without grain elongation and glassy phases (Rachinger type).

Accommodation was due to compliance of carbon.

-Diffusion of Al, C or Si at grain boundaries in SA3 fiber -Diffusion of carbon or silicium within grain in Hi-Nicalon S fiber.

But diffusion of impurities was not established, due to the paucity of data in the literature on diffusion of impurities within SiC polycrystals.

Tertiary creep was shown to be due to an increase in stress as the load bearing fiber area is reduced by volatilization of Si. Some microstructural changes were detected by TEM analysis such as grain growth in Hi-Nicalon S fibers and grain shrinkage in SA3 fibers. The former can be related to some extent to that one observed on Hi-Nicalon fiber, whereas the latter may be associated to Si volatilization. .

Figure 9 : Logarithmic plot of strain rate versus applied stress for SA3 (2) fiber. Test stop for SEM observation

n

  =1 has been determined for polycrystalline SiC ceramics. Creep results from diffusional processes either at grain boundaries (Coble creep n = 3) or within grains (Nabarro Herring creep n = 2). High activation energy corresponds to Nabarro Herring creep. Creep rate is very sensitive to grain size (equation 5) : m = 2 or 3. Identical trends have been reported for both αand β-SiC.

Figure 10 compares

 10 Figure 10 compares creep rates for Hi-Nicalon S and SA3 (2) fibers under 850 MPa. It

Figure 1 :Figure 2 :

 12 Figure 1 :Schematic diagram of the high temperature fibre testing apparatus.

Figure 3 :

 3 Figure 3 : Microstructure and electron diffraction pattern of (a) Tyranno SA3(2) and (b) Hi-Nicalon S fibre.

Figure 4 :Figure 5 :Figure 6 :

 456 Figure 4 : Lattice fringe images showing the presence of turbostratic Carbon at SiC grain boundary for (a) Hi-Nicalon S and (b) Tyranno SA3(2) fibre.

Figure 7 :

 7 Figure 7 :Creep of SA3(2) fiber under a stress of 150MPa and in the 1350-1700°C temperature range.

Figure 8 :

 8 Figure 8 : Steady state creep rate versus reciprocal temperature for SA3(2) fiber.

Figure 10 :

 10 Figure 10 : Steady state creep rate versus reciprocal temperature for SA3(2) and Hi-Nicalon S fibers under a stress of 850MPa.

Figure 11 :

 11 Figure 11 : Creep test at 1450°C and under a stress of 500MPa for Hi-Nicalon S fiber, and SEM micrographs of cross section after test interruption.

Figure 12 :

 12 Figure 12 : SEM micrographs of SA3(2) cross section after creep test presented of figure 7.

Figure 14 :

 14 Figure 14 :Comparison of experiment and prediction of creep behavior at 1450°C and under a stress of 500MPa for Hi-Nicalon S fiber.

Table 1 .

 1 Properties of SiC fibers investigated in the present study

	Suppliers	Nippon Carbon Co., Japon	Ube industries ltd, Japon
	Type of fiber	Hi-Nicalon	Hi-Nicalon S Tyranno SA3 (1) Tyranno SA3 (2)
	Lot n°	225103	320203	M-0110071	M-0304041
	Diameter (µm)	14 16	13 16	7.5	7.2
	Density (g.cm -3 )	2.74 16	3.0 16	3.0	3.1
	Tensile strength (GPa) 2.8 16	2.5 16	2.8 16	2.8
	Tensile modulus (GPa) 290	375	325	380
	Grains size (nm)
	XRD	5-10	20	60-70	60-70
	TEM	5-10	10-50	50-400	50-400
	Chemical composition
	(wt./at.%)
	Si	62.1/41.3	68.4/48.1	66.6/46.0 (edge) 60.3/39.5 (core)	69.1/49 (edge) 66.1/45.6 (core)
	C	37.7/58.5	31.3/51.5	33/53.6 (edge) 39.2/60.1 (core)	30.5/50.7 (edge) 33.5/54.1 (core)
	O	0.2/0.2	0.3/0.3	0.2/0.2	0.1/0.1
	Al	-	-	0.3/0.2	0.3/0.2
	C/Si (at. %)	1.41	1.07	1.16 (edge) 1.52 (core)	1.03 (edge) 1.19 (core)

Table 2 .

 2 Steady state creep parameters

	Fibers	Temperature Range (°C)	Activation energy	n
			Q (kJ.mol -1 )
	SA3(1)	1150-1500	370 (360-370)	2,5 (2,35-2,6)
	SA3(2)	1150-1500	370 (360-370)	2,5 (2,3-2,6)
	Hi-Nicalon S	1300-1500	770 (750-770)	2,6 (2,4-2,9)

Acknowledgements

This work was supported by CNRS and CEA and was accomplished as part of the CPR ISMIR research program. The authors would like to thank J.M. Goyheneche, X. Bourrat and B. Marini (CEA) for valuable discussions. They are grateful to Dr. T. Ishikawa for the support of Tyranno SA3 samples and Nippon Carbon for the supply of Hi-Nicalon S fiber.