Frank Papenmeier
email: frank.papenmeier@uni-tuebingen.de

Meike Uhrig
email: meike.uhrig@uni-tuebingen.de

Alexandra Kirsch
email: alexandra.kirsch@uni-tuebingen.de

Human Understanding of Robot Motion: The Role of Velocity and Orientation

Keywords: human-aware robot navigation, experimental paradigm, acceptance measures

A general problem in human-robot interaction is how to test the quality of single robot behavior, in order to develop robust and human-acceptable skills. The most typical approach are user tests with subjective measures (questionnaires). We propose a new experimental paradigm that combines subjective measures with an objective behavioral measure, namely viewing times of images viewed as self-paced slide show. We applied this paradigm to human-aware robot navigation. With three experiments, we studied the influence of two aspects of humans' understanding of robot motion: velocity profiles and the robot's orientation. A decreasing velocity profile impaired observers' comprehension of observed motion, and robot orientations diverting from the robot's motion vector caused reduced perceived autonomy ratings. We conclude that the viewing time paradigm is a promising tool for studying humanaware robot behavior and that the design of humanaware robot navigation needs to consider both the velocity and the orientation of robots.

Motivation

Human-aware navigation is a basic prerequisite for mobile robots operating in human living and working environments. The term implies that simply reaching a goal location is not enough, the expectations of potential users must also be considered. Kruse et al. [14] identify three main goals for human-aware navigation: comfort, naturalness and sociability. Comfort and sociability play a role in direct interaction, whereas naturalness is also needed in situations where a robot can be observed by a person, even without direct contact.

In this paper, we study the naturalness of robot motion. We introduce a new experimental paradigm and apply it to two aspects of robot motion, namely velocity and orientation. We study isolated robot movement, i.e. without direct interaction with a person. In such a context, a common approach is the use of video material [START_REF] Woods | Comparing human robot interaction scenarios using live and video based methods: towards a novel methodological approach[END_REF] and to measure naturalness 1 with questionnaires [START_REF] Lichtenthäler | Influence of legibility on perceived safety in a virtual human-robot path crossing task[END_REF][START_REF] Woods | Comparing human robot interaction scenarios using live and video based methods: towards a novel methodological approach[END_REF], such as the Godspeed V questionnaire [START_REF] Bartneck | Measurement instruments for the anthropomorphism, animacy, likeability, perceived intelligence, and perceived safety of robots[END_REF].

As an alternative to using questionnaires, Lu and Smart [START_REF] Lu | Towards more efficient navigation for robots and humans[END_REF] offered an interesting implicit measure of naturalness: the efficiency of humans moving in the same environment as the robot. The idea is that if the robot moves naturally, the person will feel comfortable and move normally, whereas unnatural robot movement will make people be more cautious and slow down. But this approach requires a fully implemented navigation with perception on a real robot, the effort to organise participants, and the difficulty of guaranteeing their safety. Additionally, the robot must work so robustly that it shows exactly the same behavior for every participant. Differences in lighting or small variations in timing can lead to very different user perceptions of the same robot.

If more general properties underlying human understanding of robot motion could be identified, a generalization to a wide range of robots and human-aware robot navigation scenarios might be possible. Kim and Pineau [START_REF] Kim | Socially adaptive path planning in human environments using inverse reinforcement learning[END_REF] tested their adaptive path planning algorithm with objective metics such as "closest distance to the pedestrian, avoidance distance to the pedestrian, and average time to reach the goal." But the first two only apply for scenarios with human presence, whereas the third is a standard measure for navigation, but without human-awareness. Kirsch [START_REF] Kirsch | Heuristic decision-making for human-aware navigation in domestic environments[END_REF] evaluated the naturalness of robot motion by considering the direction of the robot relative to the movement direction, thus measuring the portion of time the robot moves side-or backwards. But the only justification for this measurement is the informal observation that people usually move in a forward direction. It is possible that side-or backwards movements are acceptable from a robot, even though people would not move like this themselves.

The application of general properties of robot motion to human-aware navigation requires the systematic study of human perception and understanding of motion properties instead of the definition of such motion properties based on intuition only. However, studying human understanding of such properties using subjective measures based on questionnaires alone is not enough, because questionnaires are prone to biased responses. Thus, we introduce the viewing time paradigm and its application to the study of human-aware behavior in the following section. This paper makes two contributions:

1. the introduction of a new experimental paradigm for measuring human understanding of human-aware robot behavior.

the presentation of experimental results on observers'

understanding and rating of two features of robot motion: velocity profiles and robot orientation relative to the movement direction.

The paper is organized as follows: Section 2 introduces the viewing time paradigm that combines an objective measure of human understanding of robot behavior with subjective measures and provides a blueprint for an experimental setup. Section 3 uses this setup to study the effect of two properties of robot motion on human understanding and assessment of robot motion: Experiment 1 examines the effect of different velocity profiles and Experiment 2 examines the role of robot orientation relative to the movement direction. Experiment 3 studies both properties together. We conclude with a general discussion of the results, the limitations of the current work and future extensions of it.

Viewing Time Paradigm for Human-aware Robot Behavior

Objective measurements of human understanding of robot motion are necessary in order to fully evaluate both human-aware robot behavior in general and the naturalness of robot motion in particular. We propose a new method of measuring the naturalness of robot motion without requiring direct human-robot interaction. Our approach is based on psychological research on human event perception. This research studies the cognitive processes involved when viewing goal-directed actions.

According to research on event perception, human observers watching goal-directed actions comprehend these actions based on the construction of event models in working memory [START_REF] Zacks | Event perception: A mind-brain perspective[END_REF][START_REF] Zwaan | The construction of situation models in narrative comprehension: An event-indexing model[END_REF]. Event models are descriptions of the perceived scene and allow for predictions about upcoming events [START_REF] Zacks | Event perception: A mind-brain perspective[END_REF]. Thus, they guide perception. Whenever the deviation between observers' predictions based on the event model and the present sensory input exceeds an error detection threshold, event models in working memory are updated based on the current sensory information. Event model updating is resource intensive and requires time. Thus, in analogy to reading times used to measure event model updating during discourse comprehension [START_REF] Curiel | Spatial and character situation model updating[END_REF][START_REF] Just | A theory of reading: From eye fixations to comprehension[END_REF][START_REF] Zwaan | Dimensions of situation model construction in narrative comprehension[END_REF], viewing times serve as a measure of event model updating during the comprehension of visual narratives and picture stories [START_REF] Cohn | Prediction, events, and the advantage of Agents: The processing of semantic roles in visual narrative[END_REF][START_REF] Hard | The shape of action[END_REF][START_REF] Magliano | Filling in the gaps: Memory implications for inferring missing content in graphic narratives[END_REF][START_REF] Magliano | The relative roles of visuospatial and linguistic working memory systems in generating inferences during visual narrative comprehension[END_REF]. Viewing times were applied to dynamic scenes by recent research [START_REF] Hard | The shape of action[END_REF][START_REF] Papenmeier | Action goal changes caused by agents and patients both induce the updating of event models 23[END_REF]. That is, movies were split into multiple images and participants viewed those images as self-paced slide shows. This allows for the measurement of viewing times per image. Images associated with event boundaries [START_REF] Hard | The shape of action[END_REF] or goal changes [START_REF] Papenmeier | Action goal changes caused by agents and patients both induce the updating of event models 23[END_REF] cause reliable increases in viewing times. Thus, viewing times are a promising measure for investigating the dynamic process of event model updating during dynamic scenes, including the process of observers' comprehension of perceived actions.

We introduce the viewing time paradigm to the study of human-aware robot behavior by applying it to the study of the naturalness of robot motion. Natural motion is highly predictable based on observers' prior knowledge. Thus, the more natural robot motion is, the better observers' predictions derived from their event models in working memory should fit their observations and the less event model updating should occur. Deviations from natural motion should require event model updating resulting in increased viewing times. This methodology does not require fully implemented exemplars and direct interactions with humans but can be applied to video material. This allows for the study of broad and general factors influencing the naturalness of robot motion.

The following provides a blueprint of an experimental setup using the viewing time paradigm.

Apparatus and stimuli

The robot behavior to be measured must be recorded and prepared as a sequence of images. One option is a video recording of a scene and an extraction of equidistant frames, the other option (which we used in this work) is a script that produces the situations in a simulator and records screenshots of those situations. The first option is best applied to real-life recordings of human-aware robot behavior. The second option is preferable in controlled experiments interested in perfect positioning of robots, such as when robot motion should exactly follow a pre-defined velocity profile (cf. Experiment 1).

No special equipment is required for the presentation of the images during the experiment. It is important to ensure, however, that the used screen and input device provide accurate timings in order to reduce the variance in the recorded viewing times and to ensure that viewing times are a valid measure of the time participants used for processing the respective images.

Procedure Participants are instructed that they will see several image sequences as self-paced slide show. They can proceed through each slide show with a predefined button, such as the space bar. Between respective images, a black screen of 200 ms is included. Because viewing times for the first image of a scene are usually increased [START_REF] Cohn | Prediction, events, and the advantage of Agents: The processing of semantic roles in visual narrative[END_REF], it can be advisable to include a preview of the scene. This is especially true if one is also interested in the viewing times during the first images of a sequence. In our experiments, for example, we added a semi-transparent layer showing a countdown from 3 to 1 on the first image and prepended this countdown as additional images to the image sequence. Following all frames of an image sequence, a last image showing the word "End" is shown. Following each image sequence, subjective ratings can be recorded. We used only one subjective rating (perceived autonomy), but more elaborate questionnaires are possible. Before each trial, a fixation cross is shown and participants are instructed that they are only allowed to make breaks whenever a fixation cross is shown.

Dependent measures

Viewing time is defined as the time between image onset and button press for each image in the sequence. Thus, this paradigm provides viewing times as a continuous measure of processing effort for each individual image. Depending on the analysis of interest, viewing times for individual images may be compared across experimental conditions or viewing times can be aggregated across images before comparing them across conditions. In addition to the viewing time measure, the paradigm can be used to collect subjective ratings following each image sequence.

Experiments

We applied the viewing time paradigm to the study of two features of robot motion: velocity changes (Experiments 1 and 3) and robot orientation (Experiments 2 and 3). In addition to viewing times as objective measure of the naturalness of robot motion, we also measured perceived autonomy as a subjective measure. We first explain the general method used in both experiments.

Apparatus and Stimuli

We presented image sequences showing a robot performing the same goal-driven action in each trial: moving from a starting position to a marked goal position that was 5 m away within the virtual simulation space (see Figure 1). The stimuli for the image sequences were created with the 3D simulator Morse [START_REF] Lemaignan | Human-robot interaction in the MORSE simulator[END_REF] with a simulated PR2 robot. A script positioned the robot at the locations shown in Figure 3 and took screenshots. The images were presented with a size of approximatly 24 x 10.5 degrees of visual angle on the screen and participants had an unrestricted viewing distance of 60 cm to the screen.

The perception of movement may depend on the camera position it is presented from [START_REF] Bordwell | Exceptionally exact perceptions: On staging in depth[END_REF][START_REF] Bordwell | Film art: An introduction[END_REF][START_REF] Kraft | The psychological reality of cinematographic principles. camera angle and cutting[END_REF]. We always used a direct sideways view (see Figure 1), following cinematographic conventions [START_REF] Bordwell | The continuity system[END_REF]23] at a virtual camera distance of 6 m, but varied the height of the camera (see Figure 2):

at the height of the robot's head (1.33 m above the ground). This perspective most closely resembles a natural perspective. -10 • rotated upwards, giving the spectator a view from slightly above. This camera perspective is usually used to make a character look inferior or helpless. It also simulates the view of a very tall person. -10 • rotated downwards. This perspective magnifies the character, making it look more potent or even dangerous. This perspective also simulates the view of a very small person, like a child.

We used the different camera positions to test whether the view towards the robot influences our measurements. It also serves as a variation in presenting the different situations, making participants evaluate the same situation several times without tiring.

We cropped all pictures to cinemascope format of 21:9 (a standard used for cinema movies) so that the robot's head was at 2/3 the picture height measured from the bottom, placing it at the "optical center" [START_REF] Hickethier | Film und Fernsehanalyse[END_REF].

Additionally, we presented image sequences both in a standard and horizontally mirrored version. This allowed us to evaluate whether our measures are affected by the robot either moving in a left-to-right or rightto-left direction.

Procedure We followed the procedure described in Section 2. Following each image sequence, participants rated the robot's autonomy on a scale from "pilot-operated" (1) to "self-propelled" (7). constant: x(t) = 0.5t increasing:

Experiment 1: Velocity Profiles

x(t) = 0.05t 2 decreasing: x(t) = t -0.05t 2 sinusoidal: 0.5t -0.4 cos( 3π T t + π 2 )
Fig. 3 Positions of robot along time for all four velocity conditions used in Experiment 1.

Stimuli and Design

In this experiment, we varied the velocity profiles of the robot while leaving robot orientation constant (robot faced in the direction of motion in all conditions). Importantly, robot navigation was equally efficient in all conditions because the robot always needed 10 seconds to reach the target which was 5 m away wihtin the virtual simulation environment.

Figure 4 shows the four velocity profiles, Figure 3 shows how each of the velocity profiles moves the robot along the 5 m trajectory. The virtual time between each frame is one second.

1. constant: The robot moves with a constant velocity of 0.5m/s. 2. increasing: The velocity increases linearly from 0.0m/s to 1.0m/s with a constant acceleration of 0.1m/s 2 . 3. decreasing: The velocity decreases linearly from 1.0m/s to 0.0m/s with a constant acceleration of -0.1m/s 2 . 4. sinusoidal: The velocity is determined by the formula v(t) = 0.4 sin(1.5 2π T t + π 2 ) with T being the total travel time of 10 seconds It is important to note that we constructed the velocity profiles in Experiment 1 in a way that the robot had the same mean velocity between frames 4 and 5. Thus, the robot moved the same distance between frames 4 and 5 in all conditions. Any changes in viewing times in frame 5 can thus be attributed to our manipulation and cannot be the result of varying apparent motion across conditions. The design of this experiment was a 4 (velocity: constant, increasing, decreasing, sinusoidal) x 3 (viewing angle: below, head, above) x 2 (motion direction: left-to-right, right-to-left) within-subjects design with four repetitions per conditions. The repetitions were distributed across four blocks and trials were presented in randomized order within each block. Thus, participants performed a total of 96 trials.

Results

For all ANOVA effects with violations of the sphericity assumption as indicated by a significant Mauchly's test, we applied the Greenhouse-Geisser correction.

Viewing Times We treated all responses with viewing times larger than 2 s as outliers and removed those responses from the data set. This resulted in the removal of 203 responses (0.7 % of data) across all participants.

In a first step, we analyzed mean viewing times aggregated across all frames using a repeated measures ANOVA with the factors velocity, viewing angle, and motion direction. This revealed a significant main effect of velocity, F (3, 87) = 38.59, p < .001, η 2 p = .57 (see Figure 5, top). Further evaluating this velocity effect with paired t-tests (p-values holm-corrected for multiple comparisons) revealed that robots with decreasing velocity were viewed longer than robots moving according to the other three velocity profiles, all ps < .001. Furthermore, sinusoidal velocity profiles were viewed longer than constant velocity, p = .008. There was no significant difference of viewing times between sinusoidal velocity and increasing velocity, p = .112, as well as between constant velocity and increasing velocity, p = .793. The other main effects and interactions of the ANOVA were not significant, all F s ≤ 2.22, ps ≥ .089, η 2 p s ≤ .07.

In a second step, we analyzed viewing times of frame 5 only. Frame 5 was constructed such that travelled distance between frames 4 and 5 was constant across all velocity conditions. Thus, any effects on viewing times observed in frame 5 cannot be attributed to varying motion occuring between successive frames. We analyzed viewing times using a repeated measures ANOVA with the factors velocity, viewing angle, and motion direction. This replicated the main findings of our previous analysis. We observed a significant main effect of velocity, F (3, 87) = 8.49, p < .001, η 2 p = .23 (see Figure 5, bottom). Further evaluating this velocity effect with paired t-tests (p-values holm-corrected for multiple comparisons) revealed that robots with decreasing velocity were viewed longer than robots moving according to the other three velocity profiles, all ps ≤ .004. The other three velocity conditions did not differ significantly from one another, all ps = 1.000. The other main effects and interactions of the ANOVA were not significant, all F s ≤ 1.63, ps ≥ .143, η 2 p s ≤ .05. Whereas sinusoidal velocity caused increased viewing times as compared with constant velocity in our first analysis (viewing times aggregated across all frames), this was not the case in our second analysis (viewing times at frame 5). Because the sinusoidal velocity profile consists of both, sections of increasing velocity and sections of decreasing velocity, these contradictory findings could be resolved if only the sections with decreasing velocity caused increased viewing times. We analyzed the difference in viewing times between the sinusoidal velocity condition and constant velocity condition across all frames (see Figure 6). For each frame, we conducted a t-test compairing the viewing times difference score against zero. This revealed that viewing times in the sinusoidal condition were significantly increased as compared with the constant condition in frames 2, 3, 7, 8, and 9 only, all ps ≤ .009 In all other frames, the difference in viewing times was not significantly different from zero, all ps ≥ .153. That is, only the sections with decreasing velocity of the sinusoidal condition (cf. Figure 4) caused increased viewing times as compared with the constant velocity condition but not the sections with increasing velocity. This finding mimics our overall finding that robots moving at a constantly decreasing velocity but not robots moving at a constantly increasing velocity caused increased viewing times as compared with the constant velocity condition. Because velocity was increasing in frame 5, no effects of sinusoidal velocity occured. Further, sinusoidal velocity contains only some sections of decreasing velocity. Therefore, there was a slight increase in viewing times for the sinusoidal condition in our first analysis that was smaller than in the decreasing velocity condition that consits of decreasing velocity throughout.

Perceived Autonomy

We analyzed the perceived autonomy rating using a repeated measures ANOVA with the factors velocity, viewing angle, and motion direction. Participants' rating of the perceived autonomy of the robot did not differ significantly across conditions. That is, there was no significant main effect of velocity, F (2.19, 63.62) = 2.05, p = .133, η 2 p = .07 (see Figure 7). Further, neither the main effects of viewing angle, F (1.51, 43.75) = 0.47, p = .573, η 2 p = .02, nor motion direction, F (1, 29) = 0.22, p = .643, η 2 p = .01, nor any of the interactions reached significance, all F s ≤ 1.28, ps ≥ .286, η 2 p s ≤ .04.

Discussion

With Experiment 1, we studied whether velocity changes influence observers' understanding of robot motion. We observed a reliable increase in viewing times caused by decreasing velocity. Because increased viewing times indicate situation model updating during the perception of goal-directed actions [START_REF] Cohn | Prediction, events, and the advantage of Agents: The processing of semantic roles in visual narrative[END_REF][START_REF] Papenmeier | Action goal changes caused by agents and patients both induce the updating of event models 23[END_REF], this finding indicates that observers' comprehension of robot motion was impaired by decreasing velocity. Whereas sinusoidal motion also caused a slight increase in viewing times, this was only true for those frames of the sinusoidal motion pattern that showed decreasing velocity. Thus, we conclude that decreasing velocity impairs the comprehension of robot motion.

In contrast to viewing times, the perceived autonomy ratings did not differ across conditions. That is, even though participants had a harder time in comprehending robot motion with decreasing velocity, the perceived autonomy of the robot was not affected. Therefore, one can consider viewing times and perceived autonomy as two measures that measure distinct aspects of the naturalness of robot motion, namely viewers' ability of comprehending and predicting robot motion as well as viewers' judgements of robots moving in a natural and autonomous way.

Neither the viewing angle of the camera nor the direction of robot motion had any effect in our exper-iment. Although the deviations in camera angle were small, this provides first tentative evidence that decreasing robot motion might be a general factor impairing observers' comprehension of robot motion. Stimuli and Design In this experiment, we varied the orientation of the robot while leaving robot motion constant (the robot moved with a constant velocity profile in all conditions). The robot moved along a linear trajectory and faced one of the four cardinal directions: forward, left, right, and backward (orientation relative to the motion vector). In each orientation condition, the robot started with the respective orientation and kept the orientation throughout the whole trial and motion. The condition with forward orientation is identical to the condition with constant velocity in Experiment 1.

The design of this experiment was a 4 (orientation: forward, left, right, backward) x 3 (viewing angle: below, head, above) x 2 (motion direction: left-to-right, right-to-left) within-subjects design with four repetitions per conditions. The repetitions were distributed across four blocks and trials were presented in randomized order within each block. Thus, participants performed a total of 96 trials.

Results

For all ANOVA effects with violations of the sphericity assumption as indicated by a significant Mauchly's test, we applied the Greenhouse-Geisser correction.

Viewing Times As in Experiment 1, we treated all responses with viewing times larger than 2 s as outliers and removed those responses from the data set. This resulted in the removal of 189 responses (0.7 % of data) across all participants.

We performed two repeated measures ANOVAs with the factors orientation, viewing angle, and motion direction. The dependent measure of the first ANOVA was viewing time aggregated across all frames (see Figure 8, top) and the dependent measure of the second ANOVA was viewing time at frame 5 (see Figure 8, bottom). Across both ANOVAs, we observed neither any significant mean effect, all F s ≤ 2.21, ps ≥ .119, η 2 p s ≤ .07, nor any significant interaction, all F s ≤ 2.22, ps ≥ .058, η 2 p s ≤ .07.

Perceived Autonomy

We analyzed the perceived autonomy ratings using a repeated measures ANOVA with the factors orientation, viewing angle, and motion direction. This revealed a significant main effect of orientation, F (2.20, 63.70) = 16.44, p < .001, η 2 p = .36 (see Figure 9). Further evaluating this orientation effect with paired t-tests (p-values holm-corrected for multiple comparisons) revealed that participants rated the perceived autonomy of robots facing in motion direction (forward condition) higher than robots facing the other three orientations, all ps < .001. The perceived autonomy ratings for the backward, left, and right orientation conditions did not differ significantly from one another, all ps ≥ .663. The other main effects and interactions of the ANOVA were not significant, all F s ≤ 2.02, ps ≥ .065, η 2 p s ≤ .07.

Discussion

With Experiment 2, we investigated the effect of robot orientation on observers' undestanding of robot motion.

In contrast to the direct manipulation of motion parameters in Experiment 1, our robot orientation manipulation in Experiment 2 left motion parameters unaffected. Instead, we manipulated the congruence between the robot's motion direction and its orientation.

Our viewing times analysis showed that the comprehension of robot motion was not affected by the orientation of the robot relative to its motion direction. It is important to note, however, that robot orientation was fixed through each motion sequence in our stimuli, thus not creating any additional motion signal. Research on visual attention showed that conflicting motion information of an object relative to its motion direction impairs attention [START_REF] Meyerhoff | Object-based integration of motion information during attentive tracking[END_REF][START_REF] St | Conflicting motion information impairs multiple object tracking[END_REF]. Therefore, future research should investigate whether changes in robot orientation creating a separate motion signal, such as the indepedent rotation of the torso during robot motion, might impair observers' understanding of robot motion.

Robot orientation affected observers' perceived autonomy rating. Robots moving in the direction of their heading were rated as being more autonomous than robots being oriented either orthogonal to their movement direction or facing backward. This result shows that even if comprehension of the underlying motion pattern is unaffected by the orientation manipulation, the subjective assessment of the robot motion is not. Because the aim of human-aware robot navigation is not only the match between observers' predicted motion patterns and actual robot motion but also the correct assessment of robot motion, such as being autonomous in our case, robot orientation should also be considered when designing human-aware robots.

As in Experiment 1, we neither found any influences of the viewing angle of the camera nor of the motion direction of the robot.

Experiment 3

The results of Experiments 1 and 2 suggest that velocity profiles and robot orientation have distinct effects on human understanding and subjective assessment of robot motion. Whereas velocity profiles affected viewing times but not perceived autonomy in Experiment 1, robot orientation affected perceived autonomy but not viewing times in Experiment 2. A potential argument against this conclusion is that we did not manipulate velocity and orientation together within one experiment, thus preventing us from testing for interactions between the two factors. Thus, it remains possible that velocity effects might be different, for example, when the robot is oriented backward instead of forward. Therefore, we conducted Experiment 3, in which we manipulated both velocity profiles (constant, increasing, decreasing) and robot orientation (forward, backward) within one experiment.

Method

Participants Twenty-two new students (16 female, age M = 22.45 years, SD = 4.10 years) from the University of Tübingen participated in this experiment in exchange of course credit or monetary compensation. We gained informed consent from the participants.

Stimuli and Design Stimuli and procedure were the same as in Experiments 1 and 2 with the exception that we manipulated both the velocity profile (constant, increasing, decreasing) and robot orientation (forward, backward) in this experiment. Participants performed 144 trials.

Results

For all ANOVA effects with violations of the sphericity assumption as indicated by a significant Mauchly's test, we applied the Greenhouse-Geisser correction. Due to a technical problem, we lost the perceived autonomy rating of one participant in one trial. Therefore, we removed this participant from the data set prior to the analysis.

Viewing Times As in Experiments 1 and 2, we treated all responses with viewing times larger than 2 s as outliers and removed those responses from the data set. This resulted in the removal of 120 responses (0.4 % of data) across all participants.

We performed two repeated measures ANOVAs with the factors velocity and orientation. The dependent measure of the first ANOVA was viewing time aggregated across all frames (see Figure 10, top) and the dependent measure of the second ANOVA was viewing time at frame 5 (see Figure 10, bottom). These analyses replicated the results from our Experiments 1 and 2. We observed a significant main effect of velocity on viewing times in both ANOVAs, F (1.42, 28.32) = 48.46, p < .001, η 2 p = .71 and F (1.42, 28.50) = 20.66, p < .001, η 2 p = .51, respectively. Importantly, these effects did not change with robot orientation as there was no significant interaction between velocity and orientation in both ANOVAs, both F s < 1. Furthermore, the main effect of orientation on viewing times was not significant in both ANOVAs, both F s < 1. Further evaluating the significant velocity effect with paired t-tests (p-values holm-corrected for multiple comparisons) revealed that viewing times in the decreasing velocity condition were longer than in the other two velocity conditions for both analyses, all ps < .001. In contrast to Experiment 1, viewing times for the increasing velocity condition were slightly lower than for the constant velocity condition when aggregating across all frames, p = .017. However, this finding was qualified by the analysis of frame 5 in which viewing times did not differ significantly between the increasing velocity condition and constant velocity condition, p = .099.

Perceived Autonomy

We analyzed the perceived autonomy ratings using a repeated measures ANOVA with the factors velocity and orientation (see Figure 11). This analysis replicated the results from our Experiments 1 and 2. While there was a significant main effect of orientation, F (1, 20) = 9.68, p = .006, η 2 p = .33, velocity did not significantly affect the perceived autonomy ratings, F (2, 40) = 2.18, p = .127, η 2 p = .10. Importantly, also the interaction of orientation and velocity was not significant, F (2, 40) = 1.13, p = .335, η 2 p = .05, indicating that the effect of orientation on perceived autonomy ratings was not influenced by the velocity profile underlying the respective robot motion. Replicating our results of Experiment 2, autonomy ratings were higher for robots oriented in the direction of their motion than for robots oriented backward.

Discussion

In this experiment, we manipulated velocity profiles and robot orientation within one experiment. This experiment replicated the results of our Experiments 1 and 2. That is, decreasing velocity caused increased viewing times but left perceived autonomy unaffected, whereas forward robot orientation caused higher perceived autonomy ratings but left viewing times unaffected. Critically, there were no interactions between velocity and orientation in all analyses. This provides further evidence that velocity profiles and robot orientation are two properties of robot motion with distinct effects on human understanding and subjective assessment of human-aware robot navigation.

General Discussion

The successful design of human-aware robots requires that human observers can easily understand the robots' behavior. Based on psychological research on goal-directed actions, we introduced the viewing time paradigm to the study of human-aware robot behavior and applied this paradigm to human-aware robot navigation. This involves the partitioning of movies into multiple static images. Observers view those images as self-paced slide show and viewing times for each image are measured. Violations of observers' predictions about upcoming events and thus difficulties in the comprehension of observed robot behavior cause increased viewing times of respective images. Furthermore, subjective measures of perceived robot properties can be measured following each slide show. We applied this method to the study of two properties potentially influencing the naturalness robot motion: velocity and robot orientation.

Decreasing velocity caused pronounced increases in viewing times in Experiments 1 and 3. Thus, decreasing velocity impaired the comprehension of robot motion. Also sinusoidal velocity caused a slight increase in viewing times as compared with constant velocity. This is in line with previous research showing that observers are worse in tracking objects moving with sinusoidal velocity than objects moving with constant velocity [START_REF] Meyerhoff | Not FLEXible enough: Exploring the temporal dynamics of attentional reallocations with the multiple object tracking paradigm[END_REF]. However, our analysis revealed that only those sections of the sinusoidal velocity profile that contained decreasing velocity but not increasing velocity impaired comprehension. Thus, we conclude that human understanding of robot motion containing portions of decreasing velocity is impaired.

Whereas robot orientation relative to the robot's motion vector did not influence viewing times in Experiments 2 and 3, robot orientation affected observers' rating of the perceived autonomy of the robot. Observers rated robots aligned with their motion direction as being more autonomous than robots oriented orthogonal to their motion direction or facing backward. Thus, whereas observers' comprehension of robot motion was not affected by robot orientation in our experiments, subjective ratings were.

Implications for Human-Aware Robot Navigation

Based on our results, the design of human-aware robot navigation should consider both velocity profiles and orientation. Observers' understanding and assessment of robot motion is best when robots are facing into their direction of motion and when their velocity profile contains minimal portions of decreasing velocity. Robots will always have to decrease their velocity to reach a goal point, but navigation algorithms often produce jerky motions. For example when robots pass a door, they often alternately accelerate and decelerate to find a way through.

To quantify the quality of a motion trajectory with respect to the velocity profile, we suggest the following evaluation function: with the starting time t 0 and end time t

1 calculate γ = t1 t=t0 neg(acc(t)) • acc(t)
where acc(t) is the acceleration at time t, and the function neg(x) = 1 for x < 0 and neg(x) = 0 for x ≥ 0. For the trajectories we used in our experiments, we get γ constant = γ increasing = 0, γ decreasing = -0.9, γ sinusoidal = -0.635.

The function γ punishes trajectories with decreasing velocities. But comparing the values with Figure 5 shows that the evaluation of the sinusoidal velocity profile is closer to that of the decreasing profile, whereas our data indicates that it should be closer to that of the constant and increasing profiles. A simple quadratic function can better model our observations:

η = -2γ 2 -γ
For the trajectories of our experiments we get η constant = η increasing = 0, η decreasing = -0.72, η sinusoidal = -0.165. Further studies will have to confirm or detail the form and parameters of this function, as well as necessary scalings, possibly with respect to the trajectory length.

For quantifying side-and backwards movement, Kirsch [START_REF] Kirsch | Heuristic decision-making for human-aware navigation in domestic environments[END_REF] suggested to count the number of timesteps in which the robot moved sidewards (|v y | > |v x |) or backwards (v x < 0). This agrees with the observations of Experiment 2, but it is not the only possible interpretation. We do not know what exactly should be considered as a sidewards movement. The 90 degree angle we used in Experiment 2 is rather extreme, possibly smaller deviations from the movement direction could have the same effect on perceived autonomy. Our experiment suggests that the amount of deviation from the movement direction is unimportant, but this should be verified in further research.

Limitations and Future Work

Whereas the robot moved with the same velocity profile throughout each trial in our experiments, real-world robot navigation consists of varying velocities across time. Therefore, future research should examine more complex velocity profiles. In particular, this applies to two aspects of velocity changes. First, the context might affect the impact of decreasing velocity on human understanding of robot motion. For example, it might be easier to comprehend decreasing velocity profiles if the robot reduced its velocity only once it almost reached its goal. Second, changes in velocity by themselves might affect human understanding of observed robot motion. For example, abrupt changes between increasing and decreasing velocity (or vice versa) might impair comprehension because perceptual prediction based on one velocity profile do not match to robot motion observed based on the new velocity profile thus requiring event model updating [START_REF] Zacks | Event perception: A mind-brain perspective[END_REF].

We used a straight navigation path in our experiments. This allowed for the systematic and controlled study of how robot velocity profiles affect human understanding of robot motion. A side effect of using a single straight navigation path is that the direction towards the goal of the navigation task was identical to the motion direction of the robot. By dissociating the orientation of robot motion and the location of the navigation goal (i.e., by introducing an obstacle into the environment), future research should investigate whether the effect of robot orientation on perceived autonomy found in our experiments is the result of the deviation between robot orientation and motion vector as suggested by our experiments. As an alternative, it could be possible that robots that are looking into the direction of their navigational goal and not robots that are looking into the direction of motion are perceived as autonomous. However, when navigational goal and motion direction are dissociated, robots orientated toward their navigation goal will constantly change their orientation during motion, thus creating two motion signals (motion direction and torso rotation). Such a conflicting motion signal by itself might impair observers' ability in tracking [START_REF] Meyerhoff | Object-based integration of motion information during attentive tracking[END_REF][START_REF] St | Conflicting motion information impairs multiple object tracking[END_REF] and thus understanding the robot motion. This must be considered by future research trying to disentangle this research question.

Robot motion in our experiments perfectly followed the designed velocity profiles. That is, we placed the robot at its respective locations instead of using a realistic robot motion controller. This served as a good starting point for establishing the viewing time paradigm to research on robot motion. It is important to note, however, that the viewing time paradigm is not restricted to such artificial motion patterns. Quite the opposite, it has been applied to realistic and real-world movie content in psychological research [START_REF] Hard | The shape of action[END_REF]. Importantly, viewing times are a sensitive measure that allows to determine the temporal locations of event model updating [START_REF] Hard | The shape of action[END_REF][START_REF] Papenmeier | Action goal changes caused by agents and patients both induce the updating of event models 23[END_REF]. That is, viewing times increase in those frames where processing associated with the comprehension of the visual scene occurs. This was also the case in our Experiment 1, in which we observed increased viewing times in the sinusoidal velocity profile as compared with the constant control condition only for frames that showed decreasing velocity. Therefore, it seems promising to apply the viewing time paradigm also to instances of robot navigation with a realistic robot motion controller in order to differentiate between instances where observers have an easy or a hard time in comprehending the observed robot motion.

Conclusion

We introduced the viewing time paradigm to the study of human-aware robot behavior. With three experiments, we demonstrated its usefulness in investigating two influential factors on human understanding of robot motion, namely velocity and robot orientation. Based on our results, we conclude that robot navigation should avoid phases of decreasing velocity, such as during jerky movements, and that the orientation of robots should be aligned with their motion direction in order to maximize human understanding and their assessment of the underlying robot motion.

Fig. 1 Fig. 2

 12 Fig. 1 Illustration showing a stimulus image with a robot oriented in motion direction as used in our experiments. The robot moves from the starting point to the ending point along a straight path.

3. 1 . 1

 11 MethodParticipants Thirty students (27 female, age M = 20.07 years, SD = 1.66 years) from the University of Tübingen participated in this experiment in exchange of course credit. We gained informed consent from the participants.

Fig. 4

 4 Fig. 4 Velocity across time for all four velocity profiles used in Experiment 1.

Fig. 5

 5 Fig. 5 Experiment 1: Viewing times per frame. Top: Viewing times aggregated across all frames. Bottom: Viewing times at frame 5. Robots moving with decreasing velocity caused longer viewing times than the other three velocity conditions. The sinusdoidal velocity profile caused slightly increased viewing times only when aggregated across all frames. Error bars indicate 95% within-subject confidence intervals [1].

Fig. 6

 6 Fig. 6 Experiment 1: Difference in viewing times between sinusoidal and constant velocity conditions across frames. Error bars indicate 95% confidence intervals.

Fig. 7

 7 Fig. 7 Experiment 1: Perceived autonomy ratings did not differ significantly across velocity conditions. Error bars indicate 95% within-subject confidence intervals [1].

3. 2

 2 Experiment 2: Robot Orientation 3.2.1 Method Participants Thirty new students (24 female, age M = 20.87 years, SD = 2.45 years) from the University of Tübingen participated in this experiment in exchange of course credit. We gained informed consent from the participants.

Fig. 8

 8 Fig. 8 Experiment 2: Viewing times per frame. Top: Viewing times aggregated across all frames. Bottom: Viewing times at frame 5. Robot orientation did not affect viewing times. Error bars indicate 95% within-subject confidence intervals [1].

Fig. 9

 9 Fig.9Experiment 2: Perceived autonomy rating across robot orientation conditions. The perceived autonomy of robots facing in motion direction was rated higher than for all other orientation conditions. Ratings for the left, right, and back orientation conditions did not differ significantly from one another. Error bars indicate 95% within-subject confidence intervals[START_REF] Baguley | Calculating and graphing within-subject confidence intervals for ANOVA[END_REF].

Fig. 10

 10 Fig. 10 Experiment 3: Viewing times per frame. Top: Viewing times aggregated across all frames. Bottom: Viewing times at frame 5. Decreasing velocity caused increased viewing times irrespective of robot orientation. Error bars indicate 95% within-subject confidence intervals [1].

Fig. 11

 11 Fig. 11 Experiment 3: Perceived autonomy ratings for robots oriented forward were higher than for robots oriented backward irrespective the velocity profile underlying robot motion. Error bars indicate 95% within-subject confidence intervals [1].

"Related adjectives are "predictable", "understandable", "readable" or "legible"."[14]

Author Note

We thank Eleni Sianni and Lisa Krösche for their help in conducting the experiments. We provide all data collected in the experiments as open data at the following location: https://osf.io/r4vwk/?view only= 4f4617644265439c83b6920093c3628c

Compliance with Ethical Standards

Conflict of Interest: The authors declare that they have no conflict of interest.


Jérôme Magnant

Laurence Maillé

René Pailler

Jean-Christophe Ichard

Alain Guette

Francis Rebillat

Eric Philippe

Carbon fiber /reaction-bonded carbide matrix for composite materials -Manufacture and characterization

Keywords: A. Sintering, B. Composites, C. Mechanical properties, Reaction Bonded Silicon or Boron Carbide

The processing of self-healing Ceramic Matrix Composites by a short time and low cost process was studied. This process is based on the deposition of fiber dual interphases by chemical vapor infiltration and on the densification of the matrix by reactive melt infiltration of silicon. To prevent fibers (Ex-PAN carbon fibers) from oxidation in service, a self-healing matrix made of reaction bonded silicon carbide and reaction bonded boron carbide was used. Boron carbide is introduced inside the fiber preform from ceramic suspension whereas silicon carbide is formed by the reaction of liquid silicon with a porous carbon xerogel in the preform. The ceramic matrix composites obtained are near net shape, have a bending stress at failure at room temperature around 300 MPa and have shown their ability to self-healing in oxidizing conditions.

INTRODUCTION

Non-oxide Ceramic Matrix Composites (CMCs), i.e. mainly those consisting of a SiC or Si 3 N 4 based matrix reinforced with either carbon or SiC fibers, have the potential for being used as structural materials at temperatures up to 1500°C, in different fields including advanced engines, gas turbines for power/steam co-generation, heat exchangers, heat treatment and materials growth furnaces, as well as nuclear reactors of the future. [START_REF] Naslain | SiC-matrix composites: Nonbrittle ceramics for thermo-structural application[END_REF][START_REF] Jones | Radiation resistant ceramic matrix composites[END_REF] CMC are processed according to : (i) the gas phase route (CVI: Chemical Vapor Infiltration), [START_REF] Naslain | The CVI-process: State of the art and perspective[END_REF] (ii) the liquid phase routes either from polymers (PIP: Polymer Impregnation and Pyrolysis), [START_REF] Interrante | Fabrication of SiC matrix composites using a liquid polycarbosilane as the matrix source[END_REF][START_REF] Takeda | Strength of a Hi-Nicalon/siliconcarbide-matrix composite fabricated by the multiple polymer infiltration-pyrolysis process[END_REF] or molten elements reacting with ceramic charges in the preforms or with the atmosphere purity, well controlled composition and microstructure and can be employed in different step of CMC manufacturing (interphases, coatings and matrix infiltration). Furthermore, CVI is a very flexible process: a large number of preforms of different shapes and sizes can be treated simultaneously yielding near-net shape parts. However, it is a costly and a relatively slow technique since it has to be performed at low deposition rate in order to avoid a too rapid sealing of the pore entrance by the deposit and it yields composites with some residual porosity (≈ 10-15%), hence displaying a low thermal conductivity and a poor hermeticity with respect to gas and fluid liquids. The PIP process is, as the CVI, a low temperature process but it is a lengthy technique since several time-consuming PI-P sequences are necessary to achieve an acceptable densification. It yields composites with a significant residual porosity and implies considerable handling. In the MI process or RMI process when the impregnation is reactive (also called Liquid Silicon Infiltration process, LSI) a porous fiber preform is first consolidated with a carbon deposit (either by CVI, PIP or Slurry Infiltration) and next is impregnated with liquid silicon (or a liquid silicon alloy) which climbs by capillary forces in the pore network. Silicon then reacts with the consolidation carbon to yield, in a short time, a composite with a SiC+Si matrix and almost no open residual porosity and hence an excellent hermeticity with respect to gas and liquid fluids as well as a high thermal conductivity. The manufacturing costs of ceramic composites are mainly affected by the processing time, the fiber costs and the machining effort. The hybrid process based on I-CVI and MI is the process that displays, from our viewpoint, the best potential to man-power complex shape CMC pieces in term of time, cost and volume production. Firstly, The I-CVI is the method of choice for the deposition of mechanical fuse and diffusion barrier interphases since it yields deposits of relatively uniform composition, structure and thickness, even in preforms of complex fiber architecture. Secondly, MI is used to fill the residual open porosity of composites prepared by I-CVI to increase both the thermal conductivity and hermeticity. Carbon fibers are used in CMC because of their unique high-temperature mechanical properties and their low cost, despite the fact that carbon fibers undergo active oxidation at very low temperature (≈350°C -450°C). Carbon fibers based CMC have a microcracked matrix due to the coefficient of thermal expansion mismatch between the carbon fiber (very low and even negative along the axis and positive and relatively high radially) and the ceramic matrix. Theses microcracks are pathways for the in-depth oxygen diffusion towards the oxidation prone fibers. Solutions developed to utilize CMC in oxidizing atmosphere are the utilization of the far more expensive SiC fibers [START_REF] Filipuzzi | Oxidation Mechanisms and Kinetics of 1D-SiC/C/SiC Composite Materials: I, An Experimental Approach[END_REF] or, for Cfiber reinforced ceramic matrix the utilization of Environmental Barrier Coating (EBC), [START_REF] Goujard | On the chemical vapor deposition of Si/ B/C-Based coatings in various conditions of supersaturation[END_REF][START_REF] Lee | Environmental barrier coatings for silicon-based ceramics[END_REF][START_REF] Ullmann | Yttrium-silicates for oxidation protection of C/C-SiC composites[END_REF] and/or selfhealing interphases and matrix. [START_REF] Naslain | Synthesis of highly tailored ceramic matrix composites by pressure-pulsed CVI[END_REF][START_REF] Lamouroux | A multilayer ceramic matrix for oxidation resistant carbon fibers-reinforced CMCs[END_REF] The concept of self-healing materials is based on the introduction of elements inside the materials forming fluid oxide phases in a wide range of temperature that can fill the cracks, rendering the whole materials self-healing. Self-healing mechanisms are mainly achieved by introduction of boron species efficient at relatively low temperature (500-1000°C) and silica-rich phases efficient at high temperature (1000-1500°C) (equations 1 to 4). [START_REF] Lamouroux | A multilayer ceramic matrix for oxidation resistant carbon fibers-reinforced CMCs[END_REF] SiC (s) + 2 O 2(g) = SiO 2(s) + CO 2(g)

(1)

SiC (s) + 3/2 O 2(g) = SiO 2(s,l) + CO (g) (2)
B 4 C (s) + 4 O 2(g) = 2 B 2 O 3(s,l) + CO 2(g) (3) B 4 C (s) + 7/2 O 2(g) = 2 B 2 O 3(s,l) + CO (g) (4)
Self-healing interphases and self-healing matrices have been successfully deposited inside fiber preforms by I-CVI process. [START_REF] Naslain | Synthesis of highly tailored ceramic matrix composites by pressure-pulsed CVI[END_REF][START_REF] Lamouroux | A multilayer ceramic matrix for oxidation resistant carbon fibers-reinforced CMCs[END_REF] The need for low cost CMC required the development of short time and costeffective processes. In this paper a hybrid process was studied to develop a fully dense matrix which is able to slow down oxygen diffusion towards the oxidation prone carbon fibers by healing the cracks. This process consists in (i) depositing a pyrocarbon mechanical fuse and a SiC diffusion barrier on carbonfibers by CVI, (ii) introducing boron carbide and alumina powders into the fiber-preform by slurry infiltration, (iii) forming a porous carbon xerogel network between the powder particles by a sol-gel process and, next, (iv) consolidating the fiber-preform by reactive melt infiltration of silicon which bonds alumina and boron carbide particles and react with the porous carbon to form silicon carbide (equation 5).

Si (l) + C (s) = SiC (s) (5)
The self-healing matrix fabricated is then made of reaction bonded boron carbide (RBBC), reaction bonded silicon carbide (RBSC), residual free silicon and alumina phases.

In this study, aluminium element is introduced in the matrix to reduce the volatilisation of boron species at high temperature in the presence of water vapor. [START_REF] Grente | Amélioration de la résistance à la corrosion à haute temperature de composites à matrice céramique élaborés par voie gazeuse[END_REF] The processing and properties of reaction bonded silicon carbide, reaction bonded boron carbide and composites processed by liquid silicon infiltration have been reported by several authors. [24][START_REF] Forrest | The fabrication and properties of self-bonded silicon carbide, Special Ceramics[END_REF][26][START_REF] Luthra | Toughened Silcomp composites-Process and preliminary properties[END_REF][START_REF] Pan | The infiltration of cobalt silicides into silicon carbide preforms[END_REF][START_REF] Chiang | Reaction-formed silicon carbide[END_REF][START_REF] Esfehanian | Development of a high temperature Cf/XSi2-SiC (X = Mo, Ti) composite via reactive melt infiltration[END_REF][START_REF] Zhu | High temperature mechanical properties of SiC-Mo 5 (Si,Al) 3 C composites[END_REF][START_REF] Sangsuwan | Reactive infiltration of silicon melt through microporous amorphous carbon preforms[END_REF][START_REF] Speicher | Optimized morphological design for silicon infiltrated microporous carbon preforms[END_REF][START_REF] Greil | Biomorphic cellular silicon carbide ceramics from wood: 1processing and microstructure[END_REF][START_REF] Hayun | Microstructural evolution during the infiltration of boron carbide with molten silicon[END_REF][START_REF] Mallick | Development of multi-phase B-Si-C ceramic composite by reaction sintering[END_REF] One of the main challenges in processing reaction-bonded silicon carbide is that the porosity of carbon to be infiltrated must be low enough to minimize free silicon content, but high enough to avoid the shocking-off phenomena i.e. the stop of silicon impregnation due to the full filling of the porosity by the formed silicon carbide phase. The minimum amount of porosity required to avoid shocking off phenomena depends of the density of the carbon and can be calculated by the formula [1], [START_REF] Singh | Effect of carbon preform pore volume and infiltrants on the composition of reaction formed silicon carbide materials[END_REF] where V i , M i and d i are respectively the volume fraction, the molar weight and the density of the species i.

SiC c c c SiC SiC d M d V M V     [1]
In the case of carbon xerogel the density was measured and its value is around 1.65. By assuming that the volume fraction of SiC is maximum (V SiC =1), V C calculated equal 58% and, as a result the porosity has to be higher than 42% to avoid shocking-off phenomena. The carbon phase is usually obtained by the pyrolysis of phenolic resin or pitch. The pyrolysis of pitch leads to the covering of the pore surfaces whereas the pyrolysis of resin usually leads to pieces of cokes which cannot be totally transformed into SiC by reaction with silicon. Porous carbon can be obtained from furfurylique resin and foaming agent as patented by Hucke. [START_REF] Hucke | Composite bodies comprising a continuous framework and an impregnated metallic material and methods of their production[END_REF] In this work, porous carbon is formed by a sol-gel process from resorcinol and formaldehyde to form a RF xerogel. [START_REF] Matos | The effect of surfactants on the porosity of carbon xerogels[END_REF] This method was chosen for its ability to easily tailor the porosity of the carbon xerogel by adjusting the synthesis parameters (amount of reactants, nature and amount of catalyst, gelification, drying and pyrolysis parameters). The microstructure is based on a continuous silicon carbide networks to allow good strength at high temperature and to limit matrix creep. The aims of this paper are, firstly, to present and discuss the different steps of the hybrid process developed as well as some chemical, physical and mechanical properties of the fabricated CMC and, secondly to compare the mechanical properties of the CMC processed by our short time, scalable, cost-effective hybrid process developed with the ones processed by the costly but high effective CVI process.

EXPERIMENTAL PROCESS

Fiber preforms and dual interphases of PyC/SiC

The main characteristics of Ex-PAN carbon fibers are given in Table 1. It is well known that fiber/matrix bonding is a key factor controlling performances of ceramic matrix composites [START_REF] Naslain | The design of the fibre-matrix interfacial zone in ceramic matrix composites[END_REF][START_REF] Després | Mechanical properties of C/SiC composites as explained from their interfacial features[END_REF][START_REF] Boccaccini | Use of electrophoretic deposition in the processing of fibre reinforced ceramic and glass matrix composites: a review[END_REF] . In order to arrest and deflect the microcracks of the matrix and to insure a load transfer function, a pyrocarbon interphase (PyC i ) was deposited by CVI on the fiber surface from propane (according to equation 7a).

C 3 H 8(g)  3C (s) + 4 H 2(g) (7a)
To minimize possible chemical reactions of carbon fibers with silicon melt during the fabrication, a SiC coating was deposited on the PyC interphases by CVI according to equation 7b.

CH 3 SiCl 3(g)  SiC (s) + 3 HCl (g) (7b) H2(g)

Slurry preparation

Commercial boron carbide (grade F15, HC Starck) and alumina (Alfa Aesar) powders were used and their size distributions are reported in Figure 1. Mixed boron carbide+alumina aqueous suspensions were prepared using electrosteric dispersion mechanism by the addition of polyethylenimine dispersant (PEI, Sigma-Aldrich). Suspension compositions are given in Table 2.

Introduction of the ceramic particles into the fiber preforms

Different techniques can be used to introduce ceramic particles inside fiber preforms from colloidal suspensions: Electrophorese Impregnation (EPI), [START_REF] Eustathopoulos | Wettability at high temperatures[END_REF] submicronic powder aspiration 44 and slurry infusion under vacuum. This last method was chosen in this work for its ability to be easily transposed at plantlevel to impregnate preforms with complex shape. The impregnated preforms were then dried during 48h at 25°C.

Formation of porous carbon inside the preform

Xerogels with different synthesis parameters were studied to find the most appropriate one for the impregnation by liquid silicon and the conversion in silicon carbide. The molar resorcinol / formaldehyde ratio (R/F) was fixed to 1/2, the solid content (R%) was varied from 20 to 40 % and the catalyst (sodium carbonate) content was given by the molar resorcinol / catalyst ratio (R/C) and varied in the range [2000, 5000]. Resorcinol was added to formaldehyde and the mixture was stirred for 15 min. Sodium carbonate was dissolved in deionised water to form a separate solution. The two solutions were then mixed and stirred during 24 hours, introduced in the fiber preform and left 1 hours under vacuum, then a gelification period in a closed system at 65°C during 48 hours happened followed by a drying period at 85°C during 48 hours and a pyrolysis step in argon atmosphere at 950°C.

Fiber-preforms densification by Silicon Melt Infiltration (MI)

The experimental arrangement used to realize infiltration of silicon inside the fiber preform is schematically shown in Figure 2. The utilization of a carbon-weaving between the fiber-preform and silicon aims to avoid machining of the composite after the elaboration. The zirconium lump is used to obtain a low partial pressure of oxygen during the thermal treatment (at equilibrium between Zr and ZrO 2 , p O2 = 10 -24 atm) in order to avoid oxidation of the surface of the melt and to promote wetting. The melt infiltration was realized under vacuum during 30 min at a temperature slightly above the melting point of silicon. Indeed, to avoid to trap some gaseous species inside the material, it is necessary that the flow of silicon raising by capillarity inside the material be low enough. 45 A low flow can be achieved by a low σ/η ratio where σ and η are respectively the interfacial tension and the viscosity of the melt (Figure 3). 46 Thus, the melt infiltration was conducted at 1420°C.

Characterization

The microstructures were characterized by scanning electron microscopy and energy-dispersive X-ray spectroscopy on polished and HF-HNO 3 chemical-etched surfaces (Quanta 400 FEG, FEI; EDAX).

RESULTS AND DISCUSSION

Introduction of the ceramic powders and formation of the porous carbon network into the fiber preforms

After the under-vacuum slurry infusion step, the inter-tows porosity of the preform is filled homogenously by the mineral charges, as can be seen from Figure 4. Xerogel with different porosity were prepared and impregnated by melted silicon (Figure 5). It clearly appears from Figure 5 that the dimension, the interconnectivity and the content of free silicon can be tailored by properly choosing the porosity of the initial carbon xerogel. When the porosity of the xerogel is below 42%, shocking off phenomena occur. The value calculated is in agreement with this fact. Figure 6 shows that the pore size of the porous carbon can also be tailored by adjusting the processing parameters of the xerogel. A microstructure of a carbon xerogel is seen in Figure 7 where the carbon and the porosity networks clearly appear.

Fiber-preforms densification by Silicon Melt Infiltration (MI)

Complete infiltration of silicon inside the fiber preform occurs only if a preliminary thermal treatment just below the melt temperature of silicon takes place. During this thermal treatment, species are desorbed from the powders and the silicon carbide coating is desoxydized (equations 8 to 10). Furthemore, silicon vapor can condensate on the preform surface which will promote its further wetting by the molten silicon.

Si (g) + SiO 2(s) = 2 SiO (g) (8)
SiC (s) + 2 SiO 2(s) = 3 SiO (g) + CO (g) (9) SiO 2(s) = SiO (g) + ½ O 2(g) (10) The formation of carbon xerogel inside the preform leads to a continuous network of silicon carbide according to equation ( 5), which is not the case without introduction of carbon inside the preform prior to silicon impregnation (Figure 8). The formation of silicon carbide decreases the free silicon content in the materials and hence enhances the mechanical behavior in temperature. Silicon carbide in the composite prepared without carbon xerogel is formed by a dissolution-precipitation mechanism. [START_REF] Hayun | Microstructural evolution during the infiltration of boron carbide with molten silicon[END_REF] The porosity distribution of the fiber preform at the different state of its process is presented in Figure 9 and the microstructure of the composites in Figure 10. The pore size inside the tow of the fiber preform is between 0.1 to 10 µm whereas the inter-tows porosity size is between 10 to 300 µm. The boron carbide and alumina powders are present inside the inter-tows matrix but not in the intra-tow matrix. This is due to a too low pore size entrance for the powders. After the powder introduction, the pore size of the preform is mainly around 0.08 µm and is filled by carbon xerogel after its introduction and its pyrolysis.

The dense matrix is made of boron carbide, silicon carbide, free silicon, alumina and it fills homogenously the inter-tows porosity of the fiber-preform. The intra-tow porosity is filled by silicon. No fiber degradation was observed, nor decohesion between the fibers and the matrix. The matrix is in a microcracked state after elaboration due to the coefficient of thermal expansion mismatch between the carbon fibers and the matrix phases. The sealing of these cracks by the self-healing phases in oxidizing conditions was studied.

Self-healing behavior

Figure 10b reveals the morphology of a polished section of the composite exposed 13h at 700°C in air.

The healing of the matrix cracks can be clearly observed (encircled on Figure 11). At 700°C the sealing of the cracks is due to the formation of B 2 O 3 liquid phase and is favorable to impede the in-depth oxygen diffusion towards the oxidation prone fibers. For oxidation treatment at 600°C during 15 hours the cracks are not fully sealed due to incomplete formation of B 2 O 3 (Figure 10a). Indeed, at 600°C, its formation rate remains slow and respectively its volatilization rate significantly high due the reaction of B 2 O 3 with moisture in air (P H2O ≈ 1 kPa). 48 For temperature of 1100°C, the cracks are sealed by an amorphous protective and stable Si-B-O-Al phase. Indeed this sealing phase is chemically stable in a purely corrosive environment (H 2 O/Ar) at 600°C (Figure 12).

Mechanical behavior

The mechanical behavior of the composites studied at room temperature is given in Figure 13. The composites elaborated show a high bending stress at failure (≈ 300 MPa). At room temperature, there is no significant difference observed between the composite processed with or without carbon xerogel. This can be explained by the facts that the fibers are mainly responsible of the ultimate stress of the composite.

As a result, the tensile mechanical properties at room temperature which will come after were determined on composites processed without formation of carbon-xerogel. The mechanical behavior in temperature of the composite processed with and without carbon xerogel formation will be given in a further paper.

From the tensile curves (Figure 14), at the beginning of the tensile loading, no linear elastic behavior is observed which is due to the microcracked state of the composite after processing (Figure 10). Damage initiation in ceramic-matrix composites is often a critical step in their mechanical behavior. The crack propagation has to be controlled in order to avoid catastrophic rupture. The fact that the composite is already damaged at the end of the processing stage may be considered as a sign that the material is able to withstand further damage. Such a composite exhibits a higher mechanical reliability than undamaged materials. The loading-unloading cycles indicate an intensification of the hysteresis loops with strain accumulation which is related to an increase of the friction area. The small drop in composite stiffness characterized by the tangent modulus, attests the progressive feature of the damage. The residual strain accumulation after unloading is related to the thermal stress relaxation coming from the processing stage.

The composite surface rupture shows multiple crack deviations at the interfaces with the extraction (pullout) of the fibers (Figure 15). Such morphology of fracture surface implies a high energy dissipated by friction at the interfaces.

The stress at failure of our composites have to be compared with the stress at failure of our reference composites which are a C f /SiC composite and a C f /Si-B-C composite with a multilayered self-healing Si-B-C matrix processed by Chemical Vapor Infiltration. It clearly appears on the figure 15 that the mechanical behaviour at room temperature of the composite fabricated by the hybrid process is similar to the one of our reference composites processed by CVI. The next step of our works will be, first, to determine how the formation of a silicon carbide network by the reaction between silicon and carbon xerogel positively influence the mechanical properties in temperatures and, second, to determine the lifetime of the composites processed by our hybrid process under oxidizing conditions and to compare it with the lifetime of carbon fiber reinforced self-healing Si-B-C ceramic matrix processed by CVI. [START_REF] Lamouroux | A multilayer ceramic matrix for oxidation resistant carbon fibers-reinforced CMCs[END_REF] This will be addressed in a further paper.

CONCLUSION

Ceramic matrix composites with a self-healing matrix were successfully processed by a low cost, shorttime, near-net-shape and scalable process based on the reactive melt infiltration of silicon into a fiber preform containing boron carbide+alumina powders and a porous carbon xerogel. The microstructure of the matrix was optimised by properly choosing the porosity of the carbon xerogel to minimize the content of free silicon, to optimize its distribution and to avoid the phenomena named shocking-off. The shocking-off phenomena corresponds to the fact that the infiltration by silicon in the liquid state is stopped, due to the increase in volume of the formed silicon carbide which occupies too much space and fills up the porosity. The good impregnation of liquid silicon into the preform was possible only if this one was heat-treated at a temperature just below the melting point of silicon. This was attributed to the desorption of gaseous species from the powders and to the desoxidation of silicon carbide coating. The self-healing matrix fabricated is made of reaction-bonded silicon carbide, reaction-bonded boron carbide, and residual free silicon. The ceramic matrix composite processed has a high bending stress at failure (≈300 MPa) and has shown its ability to self-healing in oxidizing conditions.

List of figure and table captions

  Porosity was determined by Hg-porosimetry (Micromeritics, AutoPore IV). Crystalline phases were determined from powders by X-ray diffraction patterns obtained in a θ-θ Bragg-Brentano configuration (D8 advance, Bruker). Mechanical properties at room temperature were determined by bending tests and tensile tests. Three point bending tests were performed on 45x12x2.5 mm 3 parallelepiped samples with a crosshead speed of 0.5 mm/min and a span of 30 mm (Model 5569, Instrom Corp). Tensile tests were based on unloading-reloading cycles at several levels of strain in order to follow (i) changes in the damage with change in the longitudinal elastic modulus and (ii) the intensity of the work of friction occurring at the interfaces which is related to the hysteresis loops.

Figure 1 :Figure 2 :Figure 3 :Figure 4 :

 1234 Figure 1: Particle size distribution of the powders Figure 2: Experimental arrangement used to realize the infiltration of silicon inside the fiber-preforms. (1) fiberpreform; (2) carbon weaving; (3) silicon lumps; (4) zirconium lump; (5) BN-covered carbon crucibleFigure 3: Evolution of σ/η ratio vs temperature for silicon melt (according to Kimura et al. 47 ) Figure 4: Micrographs of fiber preforms (a) before impregnation by the ceramic powders and (b) after impregnation. B 4 C+Al 2 O 3 powders correspond to light grey contrast between the tows in (b).

Figure 5 :

 5 Figure 5: Optical microstructure of reaction bonded silicon carbide fabricated from carbon xerogels whose porosity before silicon impregnation is (a) 78%, (b) 62%, and (c) 36%. Silicon corresponds to the light grey contrast and silicon carbide to the dark grey contrast.

Figure 6 :

 6 Figure 6: Pore size distribution of different porous carbon xerogels.

Figure 7 :

 7 Figure 7: SEM microstructure of a porous carbon xerogel.

Figure 8 :

 8 Figure 8: Microstructure of the matrix of the composite after liquid silicon infiltration (a) without addition of carbon xerogel, (b) with carbon xerogel. Samples etched in HF/HNO 3 solution to remove free silicon. Boron carbide corresponds to the dark grey contrast, silicon carbide to the white in (a) and light grey contrast in (b).

Figure 9 :

 9 Figure 9: Porosity distribution in the fiber preform at the different states of its process: (a) before the introduction of the powders, (b) after the introduction of the powders, (c) after the formation of carbon xerogel, and, (d) after impregnation by silicon melt.

Figure 10 :

 10 Figure 10: SEM micrographs of C f / B 4 C-SiC-Si-Al 2 O 3 composite processed with carbon xerogel, (a) low, (b) medium, (c) large magnification. Boron carbide corresponds to the dark grey contrast, silicon carbide to the light grey contrast and silicon to the white contrast.

Figure 11 :

 11 Figure 11: SEM back-scattered micrographs of C f / B 4 C-SiC-Si-Al 2 O 3 composite processed with carbon xerogel after oxidation under air at (a) 600°C-15h, (b) 700°C-13h, and (c) 1100°C-30min.

Figure 12 :

 12 Figure 12: SEM back-scattered micrograph of C f / B 4 C-SiC-Al 2 O 3 -Si composite processed with carbon xerogel after oxidation under air at 1100°C-30min and a thermal treatment at 600°C during 70 hours under H 2 O/Ar (P H2O =10 kPa) to study the stability of the oxide self-healing phase under wet atmosphere.

Figure 13 :

 13 Figure 13: Bending stress at RT of the C f /B 4 C-SiC-Si-Al 2 O 3 composites processed with and without carbon xerogel.

Figure 14 :

 14 Figure 14: Tensile stress at RT of the C f /B 4 C-SiC-Si-Al 2 O 3 composites fabricated by the hybrid process without carbon xerogel and of our reference composites processed by CVI.

Figure 15 :

 15 Figure 15: SEM image of the surface rupture of the CMC showing the fiber debonding from the matrix

14 Figure 2 Figure 3

 1423 Figure 1

Figure

  Figure 4

4

 4 Figure 4

  Figure 5

Figure 8 a b Figure 9 Figure 10

 8910 Figure 8

Figure 11 0

 11 Figure 11

Figure 13

 13 Figure 13

  Figure 14

Table 1 :

 1 Main characteristics of the carbon-fibers used in this study.

Table 2 :

 2 Description of the composition of the suspension.

Acknowledgements

This work was supported by DGA (French Direction Générale pour l'Armement) and SAFRAN-Snecma Propulsion Solide through a grant. The authors acknowledge S. Bertrand (SAFRAN-Snecma Propulsion Solide) for material supply.