Vincent Weistroffer

Alexis Paljic

Philippe Fuchs

Olivier Hugues

Jean-Paul Chodacki

Pascal Ligot

Alexandre Morais

Assessing the Acceptability of Human-Robot Co-Presence on Assembly Lines: A Comparison Between Actual Situations and their Virtual Reality Counterparts

This paper focuses on the acceptability of humanrobot collaboration in industrial environments. A use case was designed in which an operator and a robot had to work sideby-side on automotive assembly lines, with different levels of co-presence. This use case was implemented both in a physical and in a virtual situation using virtual reality. A user study was conducted with operators from the automotive industry. The operators were asked to assess the acceptability to work side-by-side with the robot through questionnaires, and physiological measures (heart rate and skin conductance) were taken during the user study. The results showed that working close to the robot imposed more constraints on the operators and required them to adapt to the robot. Moreover, an increase in skin conductance level was observed after working close to the robot. Although no significant difference was found in the questionnaires results between the physical and virtual situations, the increase in physiological measures was significant only in the physical situation. This suggests that virtual reality may be a good tool to assess the acceptability of human-robot collaboration and draw preliminary results through questionnaires, but that physical experiments are still necessary to a complete study, especially when dealing with physiological measures.

I. INTRODUCTION

Robots are becoming more and more present in our everyday lives. Robots are now able to guide people inside museums, some can communicate and play with children, or even be used as therapeutic companions in hospitals. Those new applications for robots show that situations where humans and robots interact with each other are becoming more and more important. An even stronger level of interaction is reached when humans and robots have to collaborate on a specific task, especially in industrial environments such as assembly lines: humans and robots may have different roles and complementary skills. In this context, new kinds of robots have appeared that are able to work side-by-side with people without harming them. Although the functionalities of those new collaborative configurations have been well studied in the literature, no concrete studies have appeared to evaluate how the collaboration with robots is perceived and accepted by workers, at least in industrial environments. That is why this paper will not present any considerations about robot functionalities (robot control, movement planning), but will rather focus on operators' behavior towards human-robot configurations: a specific use case was designed to assess the acceptability of human-robot co-presence on assembly lines.

The second issue addressed in this paper is the relevance of the use of virtual reality to study the acceptability of human-robot collaboration. For practical and economic reasons, some studies on the acceptability of human-robot interaction have used images or videos of robots as stimuli to the users. Their impressions could then be analyzed to design an acceptable physical robot. Other studies have used virtual reality scenarios to incorporate more interaction with the robots in the simulation. However, the impressions of people towards images, videos or simulations of robots may be different from their experience in real situations with physical robots. This paper tries to shed some light on those considerations by comparing people's reactions when collaborating with an industrial robot both in a physical situation and its virtual reality counterpart.

II. RELATED WORK

A. Human-Robot Collaboration

Human-robot interaction is a wide field in which researchers study how people interact with robots, especially in a social manner [START_REF] Fong | A survey of socially interactive robots[END_REF]. Those robots can be used as domestic assistants at home [START_REF] Parlitz | Careo-bot 3 -rationale for human-robot interaction design[END_REF], guides in museums [START_REF] Thrun | Minerva: a second-generation museum tour-guide robot[END_REF], companions for children [START_REF] Dautenhahn | A quantitative technique for analysing robot-human interactions[END_REF] or for the elderly [START_REF] Shibata | Cross-cultural studies on subjective evaluation of a seal robot[END_REF] in hospitals. Humanrobot collaboration implies more interaction between people and robots: they have to work together on a common task in order to reach a common goal [START_REF] Bauer | Human-robot collaboration: a survey[END_REF]. Such a collaboration betwen a human and a robot has already been studied with social robots, for example with Leonardo [START_REF] Breazeal | Tutelage and collaboration for humanoid robots[END_REF] for a buttonpressing task or the mobile robot helper [START_REF] Kosuge | Mobile robot helper[END_REF] to handle an object with a human. More complex scenarios, more related to the industry, have arisen, such as solving a construction task collaboratively with a human (JAST robot [START_REF] Foster | The JAST collaborative human-robot dialogue system[END_REF]) or helping a human co-worker to collect parts and put them into bins [START_REF] Hinds | Whose job is it anyway? a study of human-robot interaction in a collaborative task[END_REF].

In industrial environments, human-robot collaboration has taken increasing importance: industrial robots can provide complementary skills to human co-workers and assist them in difficult, tiring and hazardous tasks. Such robots have to work alongside humans in a safe way without harming them. New industrial robots have been designed to comply with those needs, such as the Universal Robot UR5 1 , the Kuka LWR [START_REF] Haddadin | Towards the robotic co-worker[END_REF], the Kuka MRK 2 or the recent Baxter robot [START_REF] Fitzgerald | Developing Baxter[END_REF] from Rethink Robotics. The applications of those robot assistants in the industry are diverse: fetching and carrying objects, like the rob@work [START_REF] Helms | rob@work: Robot assistant in industrial environments[END_REF], or assisting humans with handling and assembling parts, like the PowerMate [START_REF] Schraft | Powermate : A safe and intuitive robot assistant for handling and assembly tasks[END_REF].

B. Acceptability of Human-Robot Collaboration

Although those new kinds of robots already exist in industrial environments and a large part of the literature has been spent on their functionalities, especially by making them physically safe for human-robot interaction and collaboration [START_REF] Haddadin | Safety evaluation of physical human-robot interaction via crash-testing[END_REF], little has been done to study how those robots are perceived and accepted in the work environment of people.

In the field of social robotics, the question of the acceptability to interact with robots has been well studied. De Graaf and Ben Allouch [START_REF] De Graaf | Exploring influencing variables for the acceptance of social robots[END_REF] recently provided an interesting exploration of the influencing variables for the acceptance of social robots. One of the most studied factor in humanrobot interaction is probably robot appearance and especially anthropomorphism. Mori's Uncanny Valley [START_REF] Mori | The uncanny valley[END_REF] asserts that a robot's anthropomorphism tends to increase its familiarity among people, until a certain point is reached where strange details, almost human-looking, may actually repel people. A large number of studies on robot appearance were conducted to confirm or discredit this effect [START_REF] Goetz | Matching robot appearance and behavior to tasks to improve human-robot cooperation[END_REF] [START_REF] Kanda | Analysis of humanoid appearances in human-robot interaction[END_REF]. Another factor influencing the acceptability to interact with robots is the nature of their movements: several studies tried to discern what were the best robot movement profiles to interact with people [START_REF] Kulić | Affective state estimation for human-robot interaction[END_REF] [21] [START_REF] Weistroffer | A methodology to assess the acceptability of human-robot collaboration using virtual reality[END_REF]. The acceptability of human-robot collaboration may also be influenced by user characteristics, such as age, gender or culture.

In the field of industrial robotics, factors such as robot appearance and movements may still have an influence on the acceptability of human-robot collaboration. Hinds et al. [START_REF] Hinds | Whose job is it anyway? a study of human-robot interaction in a collaborative task[END_REF] focused on professional service robots and the influence of a robotic coworker's appearance and role on a simple partscollecting task. Zanchettin et al. [START_REF] Zanchettin | Acceptability of robotic manipulators in shared working environments through human-like redundancy resolution[END_REF] studied the influence of a robotic manipulator's movements while sharing a working environment with a human. Weistroffer et al. [START_REF] Weistroffer | A methodology to assess the acceptability of human-robot collaboration using virtual reality[END_REF] compared different industrial robot arms and movement profiles while exchanging parts with a human. Karwowski and Rahimi [START_REF] Karwowski | Worker selection of safe speed and idle condition in simulated monitoring of two industrial robots[END_REF] studied the influence of robot size and robot speed on the operators' willingness to enter a robot's working area.

However, additional factors probably have to be taken into account when collaborating with industrial robots, such as time distribution and space distribution between the human and the robot [START_REF] Schraft | Powermate : A safe and intuitive robot assistant for handling and assembly tasks[END_REF]. Indeed, robot appearance and movements are likely to assume less importance as people are generally focused on their own task, even when working alongside robots. Time distribution and space distribution are actually little studied as factors in the acceptability of human-robot collaboration. In this paper, a specific industrial use case 1 http://www.universal-robots.com 2 http://www.mrk-systeme.de was designed to evaluate the influence of human-robot copresence on the acceptability to work with robots.

C. Virtual Reality

The study of human-robot interaction uses either actual scenarios, in which people interact directly with robots, or pre-recorded scenarios, in which people are shown different images or videos of robots. When dealing with human-robot collaboration, a high level of interaction is required in the scenarios: images and videos are not sufficient to account for this need. That is why virtual reality has been used in some cases to place people in virtual environments and to make them interact with virtual robots. For example, De Santis et al. [START_REF] Santis | A virtual-reality-based evaluation environment for wheelchair-mounted manipulators[END_REF] used virtual reality to study the usability of robotic arms mounted on a wheelchair. Nonaka et al. [START_REF] Nonaka | Evaluation of human sense of security for coexisting robots using virtual reality. 1st report: evaluation of pick and place motion of humanoid robots[END_REF] used virtual situations to evaluate the influence of robot movements on people's perception. Weistroffer et al. [START_REF] Weistroffer | A methodology to assess the acceptability of human-robot collaboration using virtual reality[END_REF] used virtual industrial robots to study the influence of their appearance and movements on people's acceptability to collaborate with them.

However, little is known about the relevance to use virtual reality situations as counterparts of real physical situations: people are likely to behave differently in front of virtual robots (probably feeling less threat). The question here is how strongly can we rely on virtual reality simulations results to be reproducible in equivalent physical situations. Inoue et al. [START_REF] Inoue | Comparison of human psychology for real and virtual mobile manipulators[END_REF] compared human-robot interaction tasks (handling objects and moving close to humans) using the same physical and virtual situations and showed that human psychological states were the same with the virtual and physical robots. However, the users were mainly passive in front of the robots (there was no physical interaction and collaboration with the robots) and their physiological states were only measured through subjective questionnaires. Those limitations probably call for deeper analysis about the relevance to use virtual reality, especially when physical contact is possible between humans and robots and when physiological measures are used to assess people's affective state.

D. Study Objectives

This paper focuses on two specific issues: evaluating the acceptability of human-robot co-presence in industrial environments, and assessing the relevance to use virtual reality experiments in this evaluation. In this context, a specific use case was set up, largely inspired by industrial assembly lines, in which an operator and a robot had to work side-by-side on a car door. This use case was implemented both in a physical environment (with an actual robot and actual assembly tasks) and in a virtual environment. A user study was conducted in order to compare users' reactions.

III. TASK DESCRIPTION

A. Current Assembly Task

In the context of human-robot collaboration in an industrial environment, the situation we decided to study is a car door assembly. One of the necessary operations during this assembly is the setting of the sealing sheet. The current task in car plants requires the operators to put a sealing sheet on the door, to ensure it is well positioned and to permanently stick it to the door. This last operation requires the operators to take a metallic pattern (the shape of the sheet) above their heads, to put it on the sheet and to roll the glue lines of the sheet with a caster at the edges of the pattern (see Fig. 1). This task can be tiring for the operators since they have to look for the pattern above their heads (uneasy position) and they have to manipulate the caster (uneasy movements of the wrist). Work quality is also at stake here since this operation is not correctly reproducible. That is why a new assembly task was considered, with a robot performing the caster-rolling task on the sheet while the operator is free to perform operations next to the robot.

B. New Assembly Task

In this new assembly task, the operator and the robot are placed next to each other: the operator first places the sheet on the door and the robot then has to roll the caster around the edges of the sheet to fix it permanently (see Fig. 2). This configuration occurs while the doors are in movement on assembly lines. To optimize assembly time and be as close as possible to a real situation, the operator also has to perform additional operations on the door while the robot is working: assembling adhesive shutters, plastic clips, the window scraper, a body of cables and the door joint. The order of those operations was fixed considering the movement direction of the doors on the assembly lines (from left to right when facing the doors) and the configuration with the robot. It is shown in Fig. 3.

Such a use case has already been shown by BMW [27] with a Universal UR10 robot, but little information is available about it: it seems the robot performed its task alone without any interaction with humans. In our situation, we wanted the operator and the robot to be co-workers and to work side-by-side, enabling them to interact and to touch each other, for example when the operator was late in his work. This situation was representative of human-robot copresence (rather than collaboration): the operator and the robot had to share the same physical space.

C. Human-Robot Configuration

Since one of our aims was to study the acceptability of human-robot co-presence on assembly lines, one necessary factor was the distance between the operator and the robot. In that context, two conditions of human-robot co-presence were chosen: one where the operator works far away from the robot (P f ) and the other where the operator works close to the robot (P c ). The size of the working areas was the same for both conditions (1.8m) but they were located at different distances from the robot: for P f , it began at 3.9m from the robot, and for P c it began at 3m (see Fig. 5). The operator could begin to work on the door once it was fully inside the working area and had to stop when the door completely left the area (even if all the tasks were not completed). The operators were given start and stop notifications by the coordinators.

D. Robot's Behavior

The robot that was chosen for the task was a Kuka KR5SI: this is a Kuka KR5 ARC HW allowing safe interaction with humans thanks to the integration of additional sensors by the company MRK-Systeme 3 . Indeed, the robot was supplemented with damping safety pads around its initial structure, in which were located proximity capacitive sensors and tactile sensors to detect any collision. The robot could detect the proximity of an operator at a distance of around 10cm from its outer surface. Whenever such a detection happened, a sound signal was triggered and the robot stopped its current activity (the assembly line went on); the sound signal vanished and the robot resumed its task once the human presence went farther from the robot. If a strong hit occured on the safety pads, an emergency stop was triggered: the robot stopped as well as the assembly line.

For the robot to be aware of the assembly line progress, a laser sensor was placed above and behind the robot to detect 3 http://www.mrk-systeme.de the arrival of a specific door. Moreover, to detect the position of the edges of the sealing sheet on the door, another laser sensor was placed inside the robot head. The robot head was also equipped with a caster to perform its operation on the door. Since the topic of this paper is not about robot functionalities, this will not be described any further.

E. Virtual Environment

The virtual environment was a faithful reproduction of the physical one (see Fig. 4). Exact 3D models of the actual assembly line, including the doors, the robot and the assembly parts, were used at real scale in the virtual environment. The virtual assembly parts could be taken by approaching one's virtual hands from them and could be assembled on the door by moving them to their correct locations (highlighted in red). The operators could use both hands to manipulate assembly parts: one hand was sufficient for small parts, while two hands were required for the sealing sheet and the window scraper.

The virtual scenario was implemented within the Virtools VR software 4 . The virtual environment was projected inside a 3-side CAVE using active stereoscopy: the front and the floor screens were 4 meters wide, and an additional screen on the right enabled the operators to observe the robot next to them (see Fig. 6). The movements of the users were tracked thanks to ARTrack cameras: 3D trackers were positioned on their head, their hands and each side of their back. The hand trackers enabled the operators to manipulate the virtual assembly parts, while all the trackers were used for proximity detection with the virtual robot. If such a detection occured (10cm), the same sound signal than in the physical environment was triggered.

IV. USER STUDY

A. Aims of the Study

The aims of this study were twofold: evaluating the acceptability of human-robot co-presence on assembly lines, and assessing the relevance to use virtual reality in this evaluation. In this context, a within-subject study was performed with operators from car assembly lines. Two independent variables were taken into account: the situation S of the test (physical S p or virtual S v ) and the co-presence P with the robot (far P f or close P c ).

B. Protocol

For each subject, the test lasted a whole day: one half-day for the physical situation and the other half-day for the virtual situation. Half of the users began with the physical situation (morning) and ended with the virtual situation (afternoon), while the other half did the opposite. For each half-day, the order of conditions P f and P c was randomised.

At the beginning of each half-day, the operators were given a document with information about the operations to perform on the doors (either physical or virtual). They were given as much time as they wanted to learn the operations and train on a single door (a physical one for S p and a virtual one for S v ): for this static training step, the doors were not moving and the robot was off. Once the operators were ready, some time was given to show how the robot was performing its task and was behaving next to humans. After this description, the test began: for each condition, the operators had to complete four cycles of doors (one cycle being a four-door procession). The two first cycles were mainly used for training purposes while the two last ones were used for actual data acquisition.

Questionnaires were given and physiological measures were taken at different moments of the test: they are described in Section IV-C. An overview of the whole protocol is shown in Table I, while Table II shows the protocol for a single condition.

C. Measures

To compare each condition and assess the acceptability of human-robot collaboration from the operators' point of view, several data were collected. As was proposed by Weistroffer et al. [START_REF] Weistroffer | A methodology to assess the acceptability of human-robot collaboration using virtual reality[END_REF], a set of questionnaires was used to gather the users' subjective impressions, and physiological measures were taken to assess their affective state. Performance data were also collected during the tasks.

1) Questionnaires: Bartneck et al. [START_REF] Bartneck | Measurement instruments for the anthropomorphism, animacy, likeability, perceived intelligence, and perceived safety of robots[END_REF] provided an interesting survey of questionnaires related to human-robot interaction and proposed their own standard ones, mainly focused on social robots. We took inspiration from them and wrote our own questionnaires to be more representative of the industrial context and of the considerations of the study: we added questions related to safety, utility, efficiency and acceptability, and questions about human-robot co-presence, related to the distance to the robot.

The users were given a questionnaire Q p after each condition (see Table II): it consisted in 6-point Likert scales to assess their subjective impressions about the activity and co-presence with the robot. They were also given a more global questionnaire Q s at the end of each half-day (see Table I), to assess their level of comfort with the operations and the use of the system. The whole day eventually ended with open questions: the operators could give any remarks about the robot, the co-presence configuration or the test itself.

2) Physiological Measures: Kulić and Croft [START_REF] Kulić | Affective state estimation for human-robot interaction[END_REF] were the first ones to use physiological measures to assess the affective states of users interacting with robots. For their experiments, they used heart rate, skin conductance and facial muscle contraction as indicators of the users' affective state while observing robot movements.

our study, we measured heart rate and skin conductance thanks to a physiological monitoring system from Biopac Systems5 with a Bionomadix PPG (Photoplethysmogram) and EDA (Electrodermal Activity) amplifier. PPG signal provided information on the subject's pulse rate (PR), while EDA signal measured the skin conductance level (SCL). It was not possible to record the operators physiological measures while working: the measures were taken on the fingertips and the signals were disturbed by hand movement and object prehension, making the analysis impossible. Therefore, the measures were taken at specific moments of the test while the operators were sitting for about 3 minutes (see Table II): at the beginning of each condition (φ 0 ) and right after completing each cycle (φ 1 , φ 2 , φ 3 , φ 4 ).

For the off-line analysis, for each measure, the mean PR and the mean SCL were computed over one minute (during the rest period for φ 0 , and following rightaway the activity for φ 1 , φ 2 , φ 3 , φ 4 ). This resulted in 20 indicators per user (5 measures × 4 conditions) both for PR and SCL. For each user, the minimum m and maximum M values were found among all the indicators and each indicator was then normalized between m and M (giving a value between 0 and 1). This normalization enabled the comparison of physiological results between users.

3) Performance Data: To complement the results obtained through questionnaires and physiological measures, we also gathered performance data from the activity on the doors. We were interested in the number of non-completed operations, the number of proximity detections by the robot (sound signal) and the task duration (from the first part assembled on the door, to the last one or to the exit of the door from the operator's area). Those data were collected for each door. In the physical situation, they were gathered off-line thanks to video recordings of the tests. In the virtual situation, those data were automatically saved through the software (additional data were also gathered).

D. Population

For this user study, the population was chosen from a set of operators working on assembly lines in the car industry. Eight operators participated in this user study (the two first ones were mainly used to adjust the test settings and were not taken into account in the results): one woman and seven men, with an average age of 40. It was really important to have participants who were from the industrial field to get relevant results. It was however not possible to get as large a number of participants as we wanted, mainly due to the availabality of operators and time constraints (the test lasted a whole day). Experiments are still conducted in order to increase the population size.

V. RESULTS

A. Performance Data

The performance data consisted in the number of noncompleted operations, the number of proximity detections with the robot and the task duration. They were all computed for each door. Fig. 7 shows the average over all the doors and all the users. On the whole, the operators did not have difficulties in completing their operations, both in the physical and virtual situations. They were however less used to virtual operations than physical ones: that is why the number of non-completed operations was higher in S v (more than two) than in S p (less than one). One possible explanation is the lack of haptic feedback for S v . Moreover, the average task time was lower in S v than in S p : even if the operators were not used to it, the virtual operations took less time to perform than physical ones.

Number of Non-Completed OperaƟons

When working in the virtual situation, the operators behaved differently and were less aware of the virtual robot presence next to them: either because they could not sense it haptically, or because they could not see it in their peripheral vision (because of the frame of the stereoscopic glasses), or even because they could not properly hear the robot movements next to them (only the proximity sound signal was simulated). The operators often became conscious of the virtual robot proximity only once they heard the sound signal, thus explaining the higher number of proximity detections in S v P c compared to S p P c .

Finally, the reduced awareness of the robot presence in S v probably made the operators more relaxed, and this relaxation was all the more important since the operators were far from the robot (S v P f ). Being more relaxed, the operators spent more time on their operations and became late: indeed, the number of non-completed operations and the task duration were significantly higher for S v P f than for S v P c . A Wilcoxon test was performed for the number of noncompleted operations (W=854, p<0.001), while an ANOVA was performed for the task duration (F=18, p<0.001).

B. Questionnaires

1) Co-Presence Questionnaire Q p : The results of the copresence questionnaire Q p are shown in Fig. 8 (for each question, the average answer over all the users is taken). Wilcoxon tests were performed to assess significant differences in the results. The distance with the robot was well-adapted The speed of the robot was well-adapted

The robot was competent

The robot was efficient

The robot was useful

The interacƟon with the robot was pleasant The collaboraƟon was acceptable Yes No Fig. 8. Results of the Q p questionnaire On the whole, the co-presence with the robot was found more acceptable (last question) in the far condition than in the close condition, both in the physical and virtual environments, even if no significant difference was shown. Three main reasons appear to explain this trend.

First, the distance to the robot was found more adapted in the far condition in both situations: Wilcoxon tests showed a significant difference between S p P f and S p P c (W=51.5, p=0.04), and between S v P f and S v P c (W=56.5, p=0.007).

Secondly, the operators found that the robot constrained their work more in the close condition than in the far condition: Wilcoxon tests showed a significant difference between S p P f and S p P c (W=12.5, p=0.04), and between S v P f and S v P c (W=8, p=0.006).

Finally, the operators had to adapt to the robot more in the close condition than in the far one: Wilcoxon tests showed a significant difference only between S v P f and S v P c (W=7, p=0.007). Some significant differences appeared between the physical and virtual situations: for the far condition, the robot induced less constraints and less necessity to adapt in the virtual situation than in the physical one (W=50, p=0.004; W=58, p=0.005; respectively). This is again explained by the fact that, in the virtual situation, the operators were less aware of the presence of the robot.

No significant difference was found with the other questions.

2) Situation Questionnaire Q s : The results of the situation questionnaire Q s are shown in Fig. 9. Wilcoxon tests were performed to assess significant differences in the results. You were at ease with the operaƟons The robot was an asset for work success

The robot was an asset for your health

The robot was useful You were feeling safe

The collaboraƟon was efficient You were as efficient as you wanted

The robot was efficient

The collaboraƟon was acceptable

The robot aspect was safe Fig. 9. Results of the Q s questionnaire

On the whole, no significant difference was found in the questionnaire between the physical and virtual situations. However, it can be noted that the operators were feeling more at ease and efficient with the operations in the physical situation: this is understandable since they were not especially used to virtual reality settings.

C. Physiological Measures

The physiological measures consisted in the users' average pulse rate (PR) and skin conductance level (SCL) right after the activity. For each condition, four measures were taken into the normalized φ 1 , φ 2 , φ 3 , φ 4 . The results are shown in Fig. 10 (for each condition, the average over φ 1 , φ 2 , φ 3 , φ 4 and over all the users was taken). Two-way ANOVAs were performed to assess significant differences in the results, situation (physical or virtual) and distance to the robot (far or close) being the independent variables. Both for pulse rate and skin conductance level, a significant influence of the situation was found (F=3.28, p=0.08 for PR; F=5.54, p=0.03 for SCL). Those differences between situations are certainly inherent to the fact that the two situations occured at different moments of the day (two halfdays). The influence of the distance to the robot (between P f and P c ) is more important in the analysis.

No significant influence of the distance to the robot was found for the average pulse rate. However, the average pulse rate seems higher after working close to the robot compared to far from it, especially in the physical situation. This correlates with the questionnaires results: by working closer to the robot, the operators were more constrained in their work, had to adapt to the robot and had to speed their activity, thus inducing an increase in pulse rate. This trend was less relevant in the virtual situation.

A significant influence of the interaction between situation and distance to the robot was found for the average skin conductance level (F=8, p=0.009). Indeed, in the physical situation, the average SCL was significantly higher after working close to the robot than far from it (F=4.6, p=0.04), while there was no significant difference in the virtual situation. In the physical situation, the operators were more stressed when working close to the robot, although they did not mention it in the questionnaires. This stress occured because the robot was a constraint and the operator had to adapt to it in order to finish in time. However, this trend did not appear in the virtual situation: the operators were less aware of the robot presence, they probably felt less threat from the virtual robot and considered their activities less seriously.

On the whole, working close to the robot seems to have made the operators speed their activities, thus inducing an increase in their pulse rate and in their level of stress. This trend however did not appear in the virtual situation.

VI. CONCLUSION

This paper focused on the acceptability of human-robot collaboration in industrial environments. A use case was implemented in which an operator and a robot had to work in co-presence on automotive assembly lines. A user study was conducted to assess the acceptability of human-robot copresence at different distances to the robot. This user study included a physical situation and its virtual counterpart to evaluate the relevance to use virtual reality in the study of acceptability.

Both in the physical and virtual situations, the co-presence seemed more acceptable when working far from the robot. Indeed, the questionnaires results showed that the distance was less adapted in the close condition because the robot was perceived as a constraint and the operators had to adapt their work to the robot. This correlates with the results on physiological measures, which showed an increase in skin conductance level after working close to the robot compared to far from it (only in the physical situation). However, working far from the robot may also decrease the operator's efficiency (as shown in the virtual situation), since the operators seemed to have more time to complete the operations. These results show that questionnaires and physiological measures are good indicators in the overall study of the acceptability of human-robot collaboration.

At first glance, virtual reality seems to be a relevant tool to study the acceptability of human-robot collaboration: the situation (physical or virtual) did not have any influence on the questionnaires results, except concerning the efficiency of the operators (less used to virtual reality systems). However, the tendency of physiological measures to increase after working close to the robot, visible in the physical situation, did not appear in the virtual one. This is probably due to a diminished feeling of presence in the virtual environment: the operators were less aware of the virtual robot presence, either haptically or visually, and were feeling more relaxed.

Although the non-reproducibility in the physiological results emphasizes the necessity to perform experiments in physical situations, these results show that virtual reality may be an interesting tool in the study of the acceptability of human-robot collaboration. The questionnaires results were globally the same in the physical and virtual situations: in future use cases, questionnaires results obtained through virtual situations could be used to draw interesting preliminary conclusions on acceptability before the design of actual physical situations. Virtual situations also have the possibility to easily test additional hypothesis that may not be feasible in physical ones. In our use case, we believe that having the operator and the robot work side-by-side, especially in the virtual situation, diverted the operators' awareness of the robot presence: the operators focused more on their task than on the robot. In the future, we intend to perform additional studies to overcome this situation, with use cases in which an operator and a robot face each other and have to cooperate with each other by exchanging assembly parts (human-robot co-action). We still plan to conduct user studies both in physical and virtual situations to further evaluate the relevance to use virtual reality in the study of the acceptability of human-robot collaboration.

Fig. 1 .

 1 Fig. 1. Current task on assembly lines

Fig. 2 .

 2 Fig. 2. New assembly task with human-robot co-presence

Fig. 4 .

 4 Fig. 4. The physical (left) and virtual (right) environments

Fig. 5 .

 5 Fig. 5. The two configurations of human-robot co-presence: far and close

Fig. 6 .

 6 Fig. 6. A user in the physical environment and inside the CAVE

Fig. 7 .

 7 Fig. 7. Users' performance data

Fig. 10 .

 10 Fig. 10. Results of the physiological measures

http://www.3ds.com/products-services/3dvia/ 3dvia-virtools/

http://www.biopac.com

ACKNOWLEDGMENT

The authors wish to thank the operators who gave their time to participate in the study. This research benefited from the support of the Chair 'PSA Peugeot Citroën -Robotics and Virtual Reality', led by MINES ParisTech and supported by PEUGEOT S.A. The partners of the Chair cannot be held accountable for the content of this paper, which engages the authors' responsibility only.


Raul Magni Berton

Elderhood and compliance: how Aging Dictators affect civil wars

In democracies, civil wars are less likely to occur. According to the minimal approach to democracy, the reason is that opposition parties can reasonably expect to win the next elections. They therefore prefer to wait than to rebel. In dictatorships, waiting until the dictator dies is generally much more costly. This waiting period, however, is considerably shortened when the dictator is old. Therefore, the risk of domestic conflict should decrease along with the age of leaders. Based on 149 countries from 1946 to 2001, our empirical analysis shows that the leader's age decreases the likelihood of civil war in dictatorships, but not in democratic regimes. More precisely, this is true in weakly institutionalized dictatorships, but not in authoritarian regime types which provide institutional ways of controlling and replacing the incumbent.

Introduction

In primitive and agrarian societies, elderhood has often been associated with high status [START_REF] James | Hierarchy in simple ''egalitarian'' societies[END_REF][START_REF] Posner | Aging and old age[END_REF]. In many tribes, the chief was chosen among the oldest men [START_REF] Simmons | The role of the aged in primitive society[END_REF][START_REF] Read | Leadership and Consensus in a New Guinea Society[END_REF][START_REF] Spencer | The Samburu; A Study of Gerontocracy in a Nomadic Tribe[END_REF] and this is classically explained by two main groups of factors, based either on social ties which are acquired with age or on personal characteristics, such as wisdom or knowledge [START_REF] Werner | Gerontocracy among the Mekranoti of central Brazil[END_REF]). However, these explanations fail to explain why, in modern democracies, gerontocracy declines. Moreover, recent studies show that aging dictators produce less economic growth, because their time horizon decreases (Jong-A-Pina and Mierau 2011). This should not provide incentives for groups to choose old chiefs.

In this article, we put forward that gerontocracy is a way to foster civil peace. In re-elective political systems, citizens submitted to an unwanted ruler tend not to revolt because they are aware that an institutional mechanism exists to get rid of the leader. This is the main claim of the minimal approach to democracy [START_REF] Przeworski | Minimalist conception of democracy: A defense[END_REF]: revolts are likely to occur when there is no other ways to change the leadership within a reasonable lapse of time. When political systems do not provide such an institutional mechanism, the change in leader can be expected to occur only through the leader's death or through a revolution. In such a situation, being ruled by an old leader allows dissatisfied people to expect a change reasonably soon and, for these reasons, deters them from revolting.

The case of the Vatican is instructive. Though the pope is elected, there are no mechanisms but his death to dismiss him. As a consequence, since 1503, the average age of popes on the day of their election has been 64. In particular, the two last popes were over 75 at their election, which reflects the increase in life expectancy. No re-elective democracy is so gerontocratic. For example, since 1789, the US presidents have been elected, on average, at 55. Electing old popes produces a limitation in incumbency (the average length of pontificate is 10 years), which approaches that of a re-elective democracy.

This hypothesis means that old leaders are preferred by people not for their social or personal characteristics, but precisely because they are likely to step down from power after a few years. The basic assumption is that risk-averse people minimize the possible loss and make the choice which excludes the worst scenario happening -this is known as the minimax strategy. Since future leaders may be appreciated or hated, the minimax strategy consists in shortening the length of their reign.

Several empirical consequences can be derived from this hypothesis. For example, introducing reelective systems should decrease the mean age of the leaders1 . Or, again, every peaceful mechanism implemented to allow a change in leadership should produce social peace. Also, in democracies, non removable offices are likely to be held by old people.

The main testable consequence of this hypothesis, however, is that, in political regimes which are deprived of an institutional way of dismissing the leader, the risk of civil war decreases with the age of the dictator. This comes directly from the suggested relationship between expected time of reign and opponents' likelihood of revolt. This is the empirical expectation tested in this article.

In the next section, we develop this hypothesis more specifically. Section 3 is dedicated to presenting our data, our methodology and other causes of revolt we control for. Section 4 displays our results, before concluding.

Leader's age, civil conflict onset and regime type

While leaders are increasingly considered as one of the main units of analysis in international relations, current research almost exclusively focuses on the impact of leaders' features on their own behavior [START_REF] Jones | Do Leaders Matter? National Leadership and Growth Since World War IF[END_REF]Olken 2005, DeRue et al. 2011), including studies centered on the age of dictators (Walter and Scheibe 2013). In this respect, this article differs from the literature on age and leadership since, following our hypothesis, leaders' age has an impact on the behavior of people who are ruled by those leaders, rather than on the leaders' own behavior. This difference probably explains why, while the relationship between age of dictators and international wars has been largely studied, nothing is yet known about age and civil wars. Indeed, unlike international wars which are initiated by leaders, civil wars are often triggered by an organized part of civil society 2 . The personal characteristics of leaders indubitably influence their activity -in international conflicts, for example -but they also influence the activity of their environment, like civil wars.

What happens in international crises, however, provides interesting clues for understanding civil wars.

Recent literature finds that aging leaders are more likely to be involved in militarized disputes than young leaders [START_REF] Michael | Leader age, regime type and violence[END_REF][START_REF] Potter | Does experience matter? American presidential experience, age, and international conflict[END_REF][START_REF] Daehee | Testing the Biden Hypotheses: Leader tenure, age, and international conflict[END_REF]. These findings have two consequences for this study. First, they disprove the hypothesis that old leaders are perceived as weaker. Spisak (2012) confirms, with experimental evidence, that older-looking leaders are significantly preferred during war. Therefore, aging dictators should experience fewer civil wars because of their authority. Second, according to [START_REF] Chiozza | Leaders and International Conflict[END_REF], leaders who anticipate a forcible removal from office, e.g. through civil war (Chiozza and Goemans 2004), have an incentive to initiate international conflict. Therefore, if aging leaders tend to trigger international wars, we should argue, contrary to our prediction, that they feel more threatened by domestic unrest than younger leaders. Interestingly, however, there are some exceptions to the rule. [START_REF] Michael | Leader age, regime type and violence[END_REF] find that in personalist regimes, the general effect reverses: as age increases, the risk of conflict declines in comparison to other types of regimes.

According to our general hypothesis, the older the leader, the lower the risk that a civil conflict breaks out. However, this relationship depends on political regime type: We expect political institutions, and especially those that rule access to, and exit from, office, to mediate the effect of age on civil conflict.

The most straightforward implication is that regimes which have regular, competitive elections, like 2 Although it might be difficult to identify the initiator of a conflict with accuracy, most studies on political institutions and civil war at least implicitly rely on the assumption that civil conflicts are initiated by dissatisfied opposition groups (see e.g. [START_REF] Hegre | Toward a democratic civil peace? Democracy, political change, and civil war, 1816-1992[END_REF][START_REF] Fearon | Ethnicity, insurgency, and civil war[END_REF][START_REF] Regan | Changing lanes or stuck in the middle: Why are anocracies more prone to civil war?[END_REF][START_REF] Fjelde | Generals, dictators, and kings: Authoritarian regimes and civil conflict, 1973-2004[END_REF], and not the incumbent. democracies, cancel out the impact of age on civil wars because they provide other mechanisms to get rid of the leader.

H1: In democracies the age of the leader does not impact the risk of civil war.

Yet, there are other potential exceptions to our general expectation, even for non-democratic regimes.

More specifically, we expect the leader's age to be strongly related to occurrence of civil war when the regime is poorly institutionalized, displays a strong tendency toward personalization of power, is not based on a clear time horizon, and does not rely on transparent rules about the access to and succession in power. Yet, recent research has shown that this is not necessarily the case for every non-democratic regime, and points toward the high institutional diversity of contemporary dictatorships. Numerous classifications of dictatorships are now available, the most prominent of which (e.g. Geddes 1999a; [START_REF] Hadenius | Pathways from authoritarianism[END_REF][START_REF] Cheibub | Democracy and Dictatorship Revisited[END_REF] are based on the nature of the ruling institution, the mode of succession and alternation, the way the leader accesses and exits office, and the allocation of power within the ruling elite. Among the most commonly identified subtypes are military dictatorships (Geddes 1999a;[START_REF] Hadenius | Pathways from authoritarianism[END_REF][START_REF] Cheibub | Democracy and Dictatorship Revisited[END_REF], party regimes (Geddes 1999a;[START_REF] Hadenius | Pathways from authoritarianism[END_REF][START_REF] Magaloni | Credible power-sharing and the longevity of authoritarian rule[END_REF][START_REF] Magaloni | Political order and one-party rule[END_REF], and monarchies [START_REF] Hadenius | Pathways from authoritarianism[END_REF][START_REF] Cheibub | Democracy and Dictatorship Revisited[END_REF][START_REF] Geddes | Authoritarian regimes: A new dataset[END_REF]. Because of the specificities of those three regime types, we do not expect them to display the same relationship between the leader's age and the risk of civil conflict outbreak.

The typical military dictatorship displays three features that are likely to affect the relationship between the leader's age and the risk of conflict. First, military dictatorships are often of temporary nature (Geddes 1999a;[START_REF] Hadenius | Pathways from authoritarianism[END_REF], which shortens the waiting time until the next change of leadership. Second, most of them rely on rules for sharing and rotating political power and thus provide institutional mechanisms to get rid of the leader (Geddes 1999b, 10). Alternation in power within the military junta can also happen in a more informal way: As Geddes puts it, "coups in military regimes are usually leadership changes, the analogue of votes of no confidence in parliamentary systems" (Geddes 1999b, 23). Third, and most importantly, military leaders typically rule as a junta (Cheibub et al. 2010, 85), which means that the ruling entity is the military itself, not a single man (see also Geddes 1999a, 121). According to Geddes, military dictatorships often seek to prevent the personalization of the rule by choosing an officer known for legalism and low charisma to lead the junta (Geddes 1999b, 10). Furthermore, military leaders seem to face lower incentive to consolidate their personal power than party cadres or members of the ruling clique in civilian dictatorships. Only a small minority of them originally joined the military to attain political power. Most of them are primarily motivated by the military's corporate interests, absolutely want to avoid threatening the cohesion of the military, suffer a lower cost if they lose their office than elites in civilian dictatorships, and are strongly dependent on the other officers to maintain themselves in power and consolidate their rule. Hadenius and Teorell (2007, 151) confirm that military dictatorships tend to exhibit a lesser degree of concentration of power than most other types of autocracy. In short, in military regimes, the individual characteristics of the leader are likely to be less relevant in explaining the occurrence of civil war.

H2: In military dictatorships, the age of the leader does not impact the risk of civil war.

Likewise, we do not expect the leader's age to affect civil war in party dictatorships either. First, past studies on single-party regimes mostly agree on the fact that the party -not the dictator -is the actual ruling entity, or at least exerts some influence on policies and access to political offices (Geddes 1999a(Geddes , 1999b;;[START_REF] Hadenius | Pathways from authoritarianism[END_REF][START_REF] Magaloni | Credible power-sharing and the longevity of authoritarian rule[END_REF]. Second, party regimes -contrary to other civilian regimes -usually display succession and alternation mechanisms (Geddes 1999a). Thus, they share two common features with military dictatorships: they are more institutionalized than the average dictatorship and the leader is controlled by a strong organization. Therefore, we also expect party regimes to alter the relationship between age and conflict.

H3: In single-party regimes, the age of the leader does not impact the risk of civil war.

Monarchies are also a special case, since one of their defining features is hereditary succession. For the opposition, even if the monarch is old, there is little incentive to wait until his death in the hope of attaining political power because he will be replaced by a member of the ruling family: There is no mechanism of alternation through death in those cases. Thus, from the opposition's perspective, the incentive to rebel is stable over time and is not affected by the monarch's age. Monarchy affects the impact of the leader's age on the conflict likelihood exactly as democracy does, but for completely different reasons: Whereas democracy affects this relationship by shortening time horizons, monarchy does by lengthening them to infinity. H4: In monarchies, the age of the leader does not impact the risk of civil war.

Finally, the remaining autocracies, which are not based on either a single party or the military or an aristocratic class, do not clearly provide any institutional procedure in terms of access to and succession in power. Although these regimes are heterogeneous, their most important common feature is the fact that leaders are not backed up by a preexisting organization on which they can rely and to which they can delegate some of the decision-making power to stabilize their rule. In this regard, this category of regimes resembles that of "civilian autocracies" from the classification provided by [START_REF] Cheibub | Democracy and Dictatorship Revisited[END_REF]. However, to avoid conceptual confusion and since Cheibub et al. include party regimes in the category of civilian autocracies while we treat them separately, we prefer to refer to those regimes as "weakly institutionalized autocracies". In those regimes, we should expect a negative relationship between the leader's age and the risk of civil war.

H5: In weakly institutionalized autocracies, the age of the leader decreases the risk of civil war

To sum up, elections are not the only way to get rid of unwanted leaders. Both military dictatorships and single-party regimes provide institutional procedures to change or control the leader, in case of political crisis. By providing such procedures, these regimes allow people to hope for a non violent alternation before the death of the leader. Monarchies are different because they provide a hereditary succession so the monarch's death cannot be considered as meaningful alternation. Finally, only weakly institutionalized autocracies display the conditions which link leaders' age and civil war. Governments change only with the death of the leader3 , and this change can be regarded as an alternation. In other words, in those regimes, the expected benefits from civil wars are higher, except when the leader is old.

The data

Dependent variable

Our dataset covers 149 countries for the period from 1946 to 2001. Our dependent variable is a dummy that takes on the value of 1 in years in which an internal conflict breaks out or if there have been at least two years since the last observation of the conflict. Since we only focus on conflict onset, subsequent conflict years are coded 0. To measure civil war, we use the UCDP / PRIO Armed Conflict Dataset [START_REF] Gleditsch | Armed conflict 1946-2001: A new dataset[END_REF][START_REF] Harbom | Armed conflict, 1946-2009[END_REF], that defines armed conflict as a "contested incompatibility that concerns government or territory or both, where the use of armed force between two parties results in at least 25 battle-related deaths" and in which one of the two parties is the government of a state (Gleditsch et al. 2002, 618-619). We include conflicts over government and conflicts over both government and territory; however, we exclude separatist conflicts, since they do not concern the central government and hence are not necessarily related to alternation in power.

Overall, in the period considered, 171 civil conflicts broke out, being 2.5% of the sample.

Regimes

According to our hypothesis, the impact of leaders' age should vary with political regimes. To identify relevant regimes, we use a dataset of political regimes by [START_REF] Alvarez | Classifying political regimes[END_REF], recently updated by [START_REF] Cheibub | Democracy and Dictatorship Revisited[END_REF]. The reasons for this choice are twofold. First, it is the only dataset which provides both a clear operational definition of democracy (which is consistent with the authors' coding rules) and a distinction of several autocratic subtypes4 . Second, their classification relies upon Przeworski's argument about democracies being "regimes in which parties lose elections" and explicitly refers to the pacifying effect of alternation (elections being, in their framework, the democratic counterpart of the leader's aging). This makes their approach on political regimes especially relevant to our argument, since their definition of democracy explicitly relies upon alternation through contested elections, and we expect age to be a substitute for elections when voting is not enough to get rid of the leader. More specifically, in their classification, a regime must meet four requirements to be classified as a democracy: The chief executive must be directly or indirectly chosen by popular election; the legislature must be popularly elected; there must be at least two parties competing in elections; and, in the cases where the three first rules apply, an alternation in power must have taken place under the same electoral rules as the ones that brought the chief executive to power (Cheibub et al. 2010, 69). In other words, all elective regimes in which the incumbent always wins are automatically classified as non-democracies, even though they display seemingly democratic institutions. Thus, the residual category of dictatorships includes all regimes in which alternation in power either occurs through other mechanisms than elections or does not occur at all.

As previously stated, one of the main advantages of the regime classification by [START_REF] Cheibub | Democracy and Dictatorship Revisited[END_REF] is that it combines a theoretically grounded empirical distinction between democracies and dictatorships and a differentiation between autocratic subtypes5 . With regard to the latter, they distinguish between civilian autocracies, monarchies, and military dictatorships. Monarchies rely on family and kin networks, and military dictatorships on the armed forces and juntas. The residual category of civilian dictatorship encompasses all regimes in which the leader is neither monarchic nor military (Cheibub et al. 2010, 89). The authors regard the latter category as a highly heterogeneous set of regimes. Even if this definition fits our definition of the poorly institutionalized autocracy, it still includes single-party regimes, which we expect to behave differently from the typical civilian dictatorship. Fortunately, disaggregated data are available: We use the variable "de facto" that measures the existence of at least one legal opposition party, to distinguish single-party regimes from other civilian autocracies6 .

Descriptive statistics on the distribution of political regimes and on the frequency of intrastate conflict are shown in Table 1. Note that monarchies are rare in our sample, and that only six intrastate conflicts out of 171 broke out in monarchies. Data are abundant for democracies, military regimes and weakly institutionalized autocracies.

TABLE 1 ABOUT HERE

Age of leaders and leader duration

The leaders' age is the main explanatory variable. Data are provided by the Archigos database [START_REF] Heinz | Introducing Archigos: A Dataset of Political Leaders[END_REF], which captures the age of the person that exercises power de facto in each country. In years where two (or more) leaders were reported, we select only the age of the leader in office on January First. This allows us to avoid reverse causation issues: the leaders' age is measured prior to the conflict. However, we also add a dummy that indicates the years in which a change of leadership occurred.

Figure 1 displays the distribution of the leader's age by regime type.

FIGURE 1 ABOUT HERE

The main problem with the leader's age is that it is correlated to the number of years the leader has been in office. Thus, the leader's age effect on civil war could be due to the negative correlation between the leader's spell in office and the probability of a conflict outbreak: We could reasonably expect that the longer leaders stay in office, the lower the risk of civil conflict onset, either because they have had time to reinforce their control on the country or because their long tenure precisely indicates they have been popular enough to avoid being violently overthrown. In order to distinguish both effects, we also use a variable called leader duration which measures the number of years the leader has been in office.

Age and leader duration are obviously correlated, but their Spearman's rho is relatively low (0.3).

Descriptive data are displayed in Table 2.

TABLE 2 ABOUT HERE

Descriptive data reveal that weakly institutionalized autocracies are the most gerontocratic, slightly more than democracies. However, they are not those in which the average leader's spell in office is the highest. Monarchs and party leaders govern roughly ten years on average, while dictators in weakly institutionalized autocracies stay in office roughly six years on average. This difference can be partly explained by the fact that monarchs tend to access office earlier, and that the average regime duration is relatively low for weakly institutionalized autocracies: They display the shortest timespan of all the regimes.

Control variables

In addition to the dependent and independent variables, we use a number of control variables that have been found to be associated with civil war, and whose omission might bias our results. We first control for the level of economic development, measured as gross domestic product (GDP) per capita [START_REF] Bolt | The First Update of the Maddison Project: Re-Estimating Growth Before 1820[END_REF]: Previous studies have identified poverty as one of the most robust predictors of civil war, either because it lowers the opportunity costs of enlisting as a rebel [START_REF] Collier | Greed and grievance in civil war[END_REF] or because it affects state capabilities and counter-insurgency capacities [START_REF] Fearon | Ethnicity, insurgency, and civil war[END_REF]. We also add a measure of ethno-linguistic fractionalization (ELF), based on data from [START_REF] Cederman | Why do ethnic groups rebel? New data and analysis[END_REF]. Country size [START_REF] Buhaug | Relative capability and rebel objective in civil war[END_REF] and population [START_REF] Fearon | Ethnicity, insurgency, and civil war[END_REF] have also been found to increase the risk of civil war: We thus include the natural log of country size, drawn from the World Bank data, and of population, based on data from [START_REF] Ross | Oil and Gas Data[END_REF] 7 .

We also include a dummy variable which takes on the value of 1 in years a change of leadership occurs, and a Cold War dummy. Since regime change can induce conflicts [START_REF] Regan | Changing lanes or stuck in the middle: Why are anocracies more prone to civil war?[END_REF], we control 7 Following previous studies on civil war, we use the natural log of GDP per capita (see [START_REF] Collier | Greed and grievance in civil war[END_REF], population (see [START_REF] Collier | Greed and grievance in civil war[END_REF][START_REF] Fearon | Ethnicity, insurgency, and civil war[END_REF] and country size (see [START_REF] Buhaug | Relative capability and rebel objective in civil war[END_REF]. GDP and population are lagged one year to avoid potential reverse causation issues.

for regime duration, based on Cheibub et al.'s (2010) data. Table 3 displays the basic descriptive statistics.

TABLE 3 ABOUT HERE

Empirical analysis

We estimate the probability of civil conflict onset through a logit regression. To address potential timedependence problems, we add a variable measuring the time in years since the most recent occurrence of civil conflict [START_REF] Collier | Greed and grievance in civil war[END_REF], based on the UCDP / PRIO's measure of civil war.

We use two different strategies. First, we distinguish five subsamples, namely democracy, military dictatorship, single-party regime, monarchy, and weakly institutionalized autocracies. Second, we conduct analyses based on interaction terms: over the whole sample, we estimate the impact of each political regime interacted with the leader's age. This allows us to better assess the conditional impact of age. Each of the models reports the odds ratios of the independent variables. Finally, we use robust standard errors clustered by leader.

Subsamples

We first run our model for each regime type. Table 4 displays the results.

TABLE 4 ABOUT HERE

Results indicate that age has a negative and significant impact on the dependent variable in the case of weakly institutionalized autocracies (Model 5): In those regimes, the risk of civil war decreases by 5% as the age of the leader increases by one year. Furthermore, consistently with our expectations, the impact of age is almost inexistent in the cases of democracies, party regimes and military dictatorships. This lends preliminary support for Hypotheses 1, 2, 3, and 5. We also perform three robustness checks to control the sensitivity of our results. First, we run the two latter models with country and year fixed effects. The structure of our data makes the use of fixed effects models somewhat tricky, because all countries and years in which the dependent variable does not vary -i.e., countries experiencing only peace or years in which no conflict was reported -are left out of the model. Although the fixed effects are too conservative and many observations are lost in the regression, the impact of age in weakly institutionalized autocracies holds in all estimates. Second, we try to correct for the problems of the high proportion of zeroes in our dependent variable: According to [START_REF] King | Explaining rare events in international relations[END_REF], logistic regressions tend to produce biased coefficients and probabilities estimates in rare-events data. We thus use their correction procedure and rerun our models using rare-events logit. Again, neither the coefficients nor the significance of our variables of interest vary substantially. Finally, we also test the linearity of the age coefficient in weakly institutionalized autocracies. We find that the effect is monotonic, but not necessarily linear, since the model using the square of age performs as well as that displayed in table 4, and we cannot distinguish between them 8 . Contrary to our theoretical expectations, age of the monarchs does impact the likelihood of civil conflict, and the effect is positive (Model 4). Thus, Hypothesis 4 is rejected. These results, however, have to be interpreted cautiously: The number of observations has dropped to 302, which limits the validity of the inference, and two control variables (Cold War and leader change) are omitted from the estimation due to perfect prediction of the 0 outcome 9 . However, one possible explanation for this unexpected finding could be that some monarchies are vulnerable to succession conflicts. According to 8 We do not reproduce those results in the paper for space reasons. All these estimations are available upon request from the authors. 9 A closer look on the data reveals that only six conflict outbreaks are reported in monarchies (which is mainly due to the relatively small number of monarchies in the sample). None of those occurred after the end of the Cold War, and five out of six occurred in a period of leadership change (which lends some support to the succession crises interpretation). Cheibub et al.'s (2010, 85) definition, if hereditary succession is the constitutive feature of monarchies, primogeniture is not: This means that, in some cases, there is no designated successor. Although the successor still has to be chosen within the ruling family, and the decision is the prerogative of a small council of family leaders, this leaves some room for negotiation and for potential conflict. If succession conflicts occur, they are more likely to break out at the end of the monarch's time in power (that is, as his death approaches). Hence, if a relationship between the leader's age and the risk of conflict exists, the correlation should be positive rather than negative.

Overall, the control variables display the expected signs, but they fail to attain statistical significance in most models. Cold war has no discernible impact on the dependent variable. Country size is significant only in monarchies. Population has a positive impact in each model, but is only significant in democracies and monarchies. The effect of ELF is positive and significant in democracies and military regimes. GDP affects the risk of conflict in military dictatorships and in weakly institutionalized autocracies, whereas regime duration is only significant in the case of monarchies. Surprisingly, the duration of peace positively affects the risk of conflict in monarchies; but, again, results for monarchies have to be interpreted carefully. Perhaps the most interesting finding is that change of leadership has a positive and strongly significant impact on the risk of civil war in military dictatorships, one-party regimes and weakly institutionalized autocracies, but not in democracies. This lends support to the idea that, although the degree of concentration of power varies across authoritarian regime types, democracy is the only regime in which change of leadership does not destabilize the whole regime.

Estimates with interaction terms

Table 5 displays coefficients for age, regimes and the interaction of both. In the first estimate, military regimes are the reference and the impact of other regimes is compared to them. In the second estimate, the impact of the leader's age in weakly institutionalized autocracies, which are our most relevant regime, is compared with its impact in the other regimes taken as a whole.

TABLE 5 ABOUT HERE

In both models, we find that weakly institutionalized autocracies are more likely to experience civil conflicts than the other regimes, but this risk significantly decreases as the dictator gets older. With regard to the magnitude, the odds ratios show that the risk of civil wars is roughly seven times higher in weakly institutionalized autocracies than in other regimes. However, for each year added to the leader's age, there is a drop of roughly 3% in the odds of civil war. This means that an 80 year old leader is about four times less likely to experience a civil war than a 30 year old leader. This does not compensate for the impact of the regime, but considerably decreases the risk of civil war for old leaders. Note that the results hold even though we control for how long the leader spends in office.

These results, taken together, are consistent with [START_REF] Przeworski | Minimalist conception of democracy: A defense[END_REF] thesis: in regimes in which there is no procedure to choose (and change) the leader, the risks of civil war are higher. For this reason, intrastate armed conflicts are expected to be more common in weakly institutionalized autocracies.

However, other factors can also explain this result, in particular the fact that it is easier to overthrow a regime which is not based on a solid institutional setup [START_REF] Acemoglu | Persistence of civil wars[END_REF]. Although this last factor is probably relevant, the specific impact of leader's age in those regimes argues in favor of Przeworski's mechanism. In those regimes, an old leader is regarded as a proxy for a future alternation in power, and this decreases the risk of civil war.

Note also that in the other regimes (including monarchy), the leader's age does not affect the risk of civil war. Thus, there is some support for Hypothesis 4; Hypotheses 1, 2, 3, and 5 are strongly supported.

With regard to the other variables, the classic variables such as GDP per capita, ELF and the population size have the expected coefficient and are significant at least the 10% level. Leader change also increases the risk of civil war.

The same abovementioned robustness checks are performed. Findings hold when standard errors are clustered by countries or by year; they hold under country and year fixed effects; and they are confirmed using rare-events logit. The dummy for weakly institutionalized autocracies remains positive and significant, while the interaction term with the leader's age remains significant and negative 10 .

Conclusion

This article argues in favor of [START_REF] Przeworski | Minimalist conception of democracy: A defense[END_REF] argument according to which the expected time of reign of a leader impacts the risk of civil war: When submitted to an unwanted ruler, people have the choice to revolt or to wait until the next change of leadership. If no alternation in power can be expected in the near future, rebellion then becomes the preferred option. Peaceful alternation can occur either through institutionalized mechanisms (like elections) or through the leader's death: This is why, in regimes that lack such institutionalized alternation mechanisms, the leader's aging reduces the probability of a rebellion.

We find here that in democracies, the age of the leader does not impact the risk of civil conflict, while in those regimes we called weakly institutionalized autocracies, the leader's age correlates negatively with the outbreak of civil war. This finding contributes to understanding why primitive and agrarian societies were typically ruled by old men, while this is much less the case of contemporary regimes. However, we also show that simply contrasting democracies -that display regular mechanisms to get rid of the leader -with autocracies -that lack such mechanisms -may be an oversimplification. After taking into account the institutional diversity of contemporary authoritarian regimes, we show that the impact of the leader's age on civil conflict is dependent on the institutional context: In military dictatorships, party regimes, and monarchies, the age of the leader does not have any discernible effect on civil wars, while it is highly relevant to explain the occurrence of civil conflict in weakly institutionalized autocracies. Two conclusions can be drawn from these findings: First, some autocratic regimes also display alternation mechanisms that have partially similar effects to those provided by democracies. Second, strong institutions that are clearly conceived to control the leader reduce the impact of his personal characteristics on the behavior of citizens.

Figure

  Figure 1: Distribution of leaders' age per regime type

Table 1 : Distribution of political regimes and intrastate conflict outbreaks

 1

		N	Conflict outbreaks	Conflict outbreaks (%
			(frequency)	years)
	Military	1534	62	4.04
	Monarchy	587	6	1.03
	Weakly inst. autocracy	1468	46	3.13
	Single-party	802	18	2.24
	Democracy	2585	39	1.51

Table 2 : Regime duration, leader's age and leader's spell in office by regime type (1946-2001)

 2

	N		Average	Average	Average
			regime	leader's age	leader's spell in
			duration		office
	Democracy	2585	31.0	58.8	3.0
	Military dictatorship	1534	12.5	53.3	7.6
	Single-party regime	802	12.9	57.7	9.7
	Monarchy	587	32.5	51.6	10.4
	Weakly institutionalized autocracy	1468	12.4	59.1	6.4
	TOTAL	6976	22.2	56.9	6.1

Table 3 : Descriptive statistics by regime

 3

		Democracy Military Monarchy Party	WI autocracy Sample
	Cold War (N. obs.)	1641	1232	467	725	1005	5114
	Post Cold War (N. obs.)	944	302	120	77	463	1906
	ELF: Mean (Std. dev.)	0.304	0.412	0.533	0.500	0.485 (0.319) 0.404
		(0.266)	(0.306)	(0.335)	(0.319)		(0.309)
	(ln) GDP / capita: Mean	8.567	7.364	8.103	7.269	7.534 (0.824) 7.895
	(Std. dev.)	(0.949)	(0.730)	(1.128)	(0.790)		(1.039)
	(ln) Country size: Mean	12.208	12.604	11.797	12.625	12.316	12.328
	(Std. dev.)	(1.847)	(1.516)	(2.063)	(1.688)	(1.873)	(1.797)
	(ln) Population: Mean (Std.	16.174	15.947	14.753	15.686	15.915	15.907
	dev.)	(1.484)	(1.319)	(1.569)	(1.413)	(1.652)	(1.530)
	Peace duration: Mean (Std.	18.827	13.099	14.929	14.249	11.195	15.058
	dev.)	(17.175)	(11.827)	(12.567)	(11.830)	(12.233)	(14.476)
	Leader duration: Mean (Std.	3.013	7.555	10.407	9.668	6.420 (6.703) 6.108
	dev.)	(3.986)	(8.250)	(9.529)	(8.383)		(7.267)
	Leader change (% of obs.) 24.14	14.28	6.30	6.11	11.31	15.68
	Regime duration: Mean	31.003	12.486	32.596	17.372	15.406	22.216
	(Std. dev.)	(31.852)	(10.076)	(28.061)	(13.773)	(13.017)	(24.346)

Table 5 : Determinants of civil conflict (odds ratios)

 5

		Ref.: military dictatorship	Ref.: all institutionalized regimes
	Age	1.010	1.000
	WI autocracy	8.115**	7.067**
	WI autocracy * age	0.959**	0.970**
	Monarchy	0.587
	Monarchy * age	0.992
	One party	1.423
	One party * age	0.987
	Democracy	0.439
	Democracy * age	0.996
	Leader duration	0.978	0.994
	Regime duration	0.997	0.993
	Leader change	3.233***	3.064***
	Peace duration	0.998	0.998
	GDP / capita	0.779*	0.701***
	Country size	0.956	1.005
	Population	1.196**	1.147*
	ELF	2.898***	2.742***
	Cold War	0.776	0.848
	Constant
	N	6443	6443
	Pseudo R2	0.08***	0.07***

*** p < 0.01, ** p < 0.05, * p < 0.1

This does not mean that dictators are necessarily older than elected officials: Since the typical dictator does not rule by consent, there are few ways of preventing a young dictator from seizing power.

Strictly speaking, another peaceful way is voluntary retirement. But this is very rare[START_REF] Heinz | Introducing Archigos: A Dataset of Political Leaders[END_REF]).

While numerous classifications of political regimes are now available, most of them are not appropriate for our argument. For example, the recent dataset from[START_REF] Boix | A complete dataset of political regimes, 1800-2007[END_REF] also provides a transparent coding of regimes based on a minimal, binary definition of democracy, but no distinction between autocratic subtypes.[START_REF] Hadenius | Pathways from authoritarianism[END_REF] use the mean of each country's Freedom House and Polity scores and a somewhat arbitrary cutoff to distinguish authoritarian regimes from democracies. The datasets byGeddes (1999) and[START_REF] Geddes | Authoritarian regimes: A new dataset[END_REF] exclusively code autocratic regimes and provide no operational definition of democracy at all.

Note that, while the coding procedure for democracies and dictatorships is identical in both versions of the dataset, the classification of authoritarian subtypes has changed. We use the autocratic subtypes identified by[START_REF] Cheibub | Democracy and Dictatorship Revisited[END_REF].

The variable "de facto" takes the value of 0 when there is no party, 1 when only one party exists, and 2 when there are two parties or more. Thus, we code dictatorships as single-party regimes when "de facto" equals 1, and as civilian otherwise. Note that the variable "de jure" also measures party systems. Yet, "de jure" refers to the legal existence of parties (i.e., if parties are constitutionally allowed) and does not measure whether opposition parties actually exist.

All these estimations are available upon request from the authors.


Edmund Ronald

Marc Schoenauer

Genetic Lander: An Experiment in Accurate Neuro-Genetic Control

The control problem of soft-landing a toy lunar module simulation is investigated in the context of neural nets. While traditional supervised back-propagation training is inappropriate for lack of training exemplars, genetic algorithms allow a controller to be evolved without di culty: Evolution is a form of unsupervised learning. A novelty introduced in this paper is the presentation of additional renormalized inputs to the net; experiments indicate that the presence of such inputs allows precision of control to be attained faster, when learning time is measured by the number of generations for which the GA must run to attain a certain mean performance.

1

Introduction to Neuro-Genetic Control The research presented in this document is part of an ongoing investigation concerning heuristic methods of trajectory planning and control. The underlying methodology is to control a dynamical system by means of a neural net. As training exemplars are not available, classical backpropagation PDP] cannot be employed to train the net; our solution is to view the matrix of weights as a vector of real numbers, and to optimise controller performance by means of a genetic algorithm. The reader will nd an overview of evolutionary methods in neural-net training in Yao 93].

For our purposes, the basic feasibility of neuro-genetic trajectory planning was established in Schoenauer & Ronald 94], a study of genetic net training applied to the truck backer-upper benchmark problem ( Nguyen & Widrow 90]). Our experimentation with the truck problem indicated that achieving the convergence of the GA to nd a controller net requires modest amounts of computer time,but the GA does not adequtely ne-tune the net for precision control.

Figure 1. shows a typical experiment with our truck-backer upper simulation. It can be seen that the truck makes a very good start at docking, from many starting positions, but is unable to follow up its good start with a precise end-manoeuvre. This problem with local ne tuning in neural net training by GA has been mentioned by Hiroaki Kitano Kitano 90] who contemplating the biological implications of this inadequacy believes that "A need for a supplementary scheme for ne-tuning is clear...a cascaded scheme of natural selection, adaptation and learning is a necessary consequence for survival". The methodology we developped for controlling the truck is very similar to that employed for the lunar lander, so we shall review this earlier work. We shall then outline our motives for switching to the simpler and better known lunar lander problem, and de ne the objective of the numerical experiments which form the core of this paper.

The truck backer-upper problem is fully speci ed in Nguyen & Widrow 90]. We can give an abridged description by saying that a driver must back up a truck with trailer system, with the aim of positioning the back of the trailer accurately at a loading dock.

To solve this problem by means of neuro-genetic learning, a neural net controller that "drives" the net was evolved by means of a genetic algorithm. This neural net driver takes the position and orientation of the trailer, as well as the truck/trailer angle as its 4 inputs. The truck is assumed to move backwards by small uniform steps, and so the only output computed by the neural net is the angle of the steering wheels. A population of such "neural drivers" is evolved by means of a GA with the tness function some combination of docking accuracy and trajectory length.

In the truck study we investigated two possible approaches to neuro-genetic control: On-line learning, and o -line learning.

It can be seen that o -line learning is extremely time-consuming, as a representative subset of the input space must be trained for. In the case of the truck, on the y training took a few minutes on a workstation rated at 100 SpecFp 92, while training times exploded to several hours for a driver able to start from 15 predetermined starting positions. Bear in mind that as the dimensionality of the space of staring con gurations increases, the cardinality of test ensembles spanning that space increases exponentially. Thus o -line training may lose its appeal due to combinatorial explosion.

As can be seen in Figure 1, the convoluted trajectories of the truck backerupper do not encourage intuitive interpretation of the control strategies adopted by the nets we evolve. In particular, a human operator will nd the truck rather hard to dock by hand, and it thus becomes di cult to judge, other than by the numbers, whether a net has a "better" strategy than another net.

For the above reasons, the choice of a simpler problem was deemed preferable, to allow us to investigate ways in which accurate solutions could be syntehsized on the y in a small number of generations. Ideally, such a speed-up of the learning process would demonstrate the feasibility of using a GA for real-time control.

In the hope of increasing control precision, and perhaps even of gaining a speedup su cient to demonstrate the feasibility of real-time neuro-genetic control, we decided to tackle a simpler problem than the truck, to wit the lunar lander, which has also been studied in Suddarth 88]. In our study of lunar lander we introduced a modi cation in the neural domain of the neuro-genetic method, namely larger nets with input data renormalisation.

Data renormalisation is the the main novelty studied in detail in this paper. This simply entails supplying the controller with redundant, rescaled, copies of its inputs. Although trivial to implement, this technique allowed us to achieve good accuracy with short learning times, for both the truck backer-upper and the lunar lander problems. The experiments reported below show a strong speedup of convergence, yielding much improved results: Convergence to accurate control occurs in fewer generations, mis-convergence occurs more rarely, and the mean accuracy of control improves dramatically.

Lunar Lander Dynamics

This paper deals with training a neural net to land a simulated rocket-driven lunar-lander module, under a gravity of 1.5 m=s 2 . This simulation has given rise to numerous computer games since the advent of interactive computing, and will be familiar to most readers.

The lunar module is dropped with no initial velocity from a height of 1000 meters. The fuel tank is assumed to contain 100 units of fuel. Burning one unit of fuel yields one unit of thrust. Maximum thrust is limited to 10 units and the variation of the mass of the lunar module due to fuel consumption is not taken into account. The simulation time-slice was arbitrarily xed at 0.5 seconds.

The input parameters relayed to the neural net once every time-step are the speed, and the altitude. The net then computes the desired fraction of maximal thrust, on a scale from 0 to 1, which is then linearly rescaled between 0 and 10 units. control action in study.

Best

A very nice lunar landing e ected in this study is shown in Figure 2. This achieved a landing speed of 7 10 ?7 m=s, ie. 0:7mm=s, hardly enough to mark the lunar surface! Such excellence would hardly be necessary in practice. This result was obtained by straightforward application of neuro-genetic control, with no data renormalization.

It was attained at the price of a long run, namely almost 2000 generations. The control action is also exemplary in the economy of fuel in the deceleration phase: For the main deceleration burst, thrust is pulsed in what amounts to almost a square wave to its maximal permissible value. The remarkable landing softness is attained by means of a long -and very smooth-hover phase which begins immediately after deceleration.

The best landing we achieved in this study is shown in Figure 3. The landing speed of 7 10 ?9 m=s, ie. 0:002mm=s is a 2 orders of magnitude improvement over the previous result, and was attained in half as many (1035) generations. This is an achievement of data renormalisation: The net was presented with the two previously cited state inputs, namely speed and altitude, and another pair consisting of the same variables pre-multiplied by a factor of 10. The interesting features of the best "Armstrong", as displayed in Figure 3, are its surprising precision, and the fact that this precision is attained either in spite of, or more probably, because of the displayed sawtooth shape and roughness of the thrust control. Of course, control by rocket to t a speed tolerance of 20 Angstroms/s seems rather implausible in reality.

A classical 3-layered net architecture was employed, with complete interconnection between layers 1 and 2, and 2 and 3. The neural transfer function (non-linear squashing) was chosen to be the usual logistic function F, a sigmoid de ned by F(x) =1 1+e ? x

In our work the parameter was xed, = 3:0. 1 Each individual neuron j computes the traditional PDP] squashed sum-of-inputs o j = F( P i w j i x i ) Regarding the sizing of the middle layer, we chose to apply the Kolmogorov model Hecht-Nieslen 90] which for a net with n inputs and 1 output requires at least 2n+1 intermediate neurons.

Only two net architectures occur in this paper. Both types have only one output (controlling the lunar module's thrust). The canonical method for solving the control problem entails 2 inputs, namely speed and altitude, appropriately normalised between 0 and 1. However, the optimisation by input renormalisation which forms the core of this paper entails adding two inputs to the above cited net, therefore employing 4-input nets. As in both cases we have adhered to the Kolmogorov paradigm, we are studying 2-5-1 and 4-9-1 nets, which respectively have 21 and 55 weights/biases. With the topology xed, training these nets for a given purpose is a search in a space of dimension 21 or 55. In the neuro-genetic approach, this search is e ected by a genetic algorithm.

The Genetic Model

The experiments reported in this paper were done with a homebrew generalpurpose genetic algorithm package embodying the principles described both in Holland 75], and Goldberg 89]. Our genetic algorithm software subjects a small population of nets to crude parody of natural evolution. This arti cial evolutionary process aims to achieve nets which display a large tness. The tness is a positive real value which denotes how well a net does at its assigned task of landing the lunar module. Thus our tness will be greater for slower landing speeds. The details of the calculation of the tness are found below.

For the purpose of applying the genetic algorithm, a net is canonically represented by its weights, i.e. as a vector of real numbers. During the course of this work, two distinct homebrew GA software packages were employed. One package followed the rst methods presented by John Holland in that it uses bit-strings to encode oating-point numbers. The second software package, described below, was a hybridized GA which directly exploits the native oating-point representation of the worktations which it was run on. The hybridization towards real numbers is described in Radcli e 91] and Michalewicz 92] log / log scales.

In our opinion, two facets of learning, as evidenced by these graphs, are of interest: Long-term learning, ie. asymptotic behaviour (best observed on the lin / log plot) and on the other hand fast learning ie. in few generations as best observed in the log / log plot.

{ The asymptotic behaviour of the mean landing speeds demonstrates the superiority of the renormalised over the non-renormalized nets by the fact that the 4 presented curves are layered, in the order un-normalised / 1 / 100 / 10. In fact, in ultimate mean precision attained over 2000 generations the 10-normalised net wins by half an order of magnitude. { The close-up, immediate behaviour of the GA demonstrates that this gain carries over to the fast-learning region. A new graph, in which we assess the ratio of the number of generations (normalised/ un-normalised) to reach some speed between 0.1 and 1.0 m/s. Figure 6 shows the speed-up to be truly useful, with computation proceeding faster by a factor of 25 at the speed of 0.1 m/s (4 inches/s).

Discussion

The above comparison of computational costs employs the number of generations as a metric. However, in fact the normed nets are larger, (55 vs. 21 weights), and thus slow down the programs by a measured factor of about 2. This is more than o set by the gains in learning performance.

A rather surprising feature can be discerned in the log / log graph: at generation 1, the average best performance per run is already well under 10 m/s for the 1-normalised net. This led us to investtigate more closely the properties of pure random search.

The results are displayed in Figure 7. The "Generations" referred to in the legend correpond to packets of individuals of the same size as the population in the GA. Pure random search in the space of nets consistently outperforms genetic search for very fast learning, when very approximate precision of control is sufcient. This seemingly counter-intuitive result seems to indicate that random search may supply a basis for real-time control.

In conclusion, we believe that the ne-tuning problem cited by Kitano 90] can be overcome in control applications by optimising the net architecture specifically for genetic learning. This optimisation can be aided by employing the GA itself to tune the normalisation coe cients Schoenauer & Ronald 94]. In biological terms, this means we supply supplementary neural pre-adapted for optimal sensitivity at di erent levels of sensory stimulation.

However, speed remains an issue and as regards real-time control, cascaded random search may yet have its revenge over the sophisticated methods of evolutionary computation.

Figure 1 :

 1 Figure 1: 8 random starting points for truck and ensuing docking tra c.

Figure 2 :

 2 Figure 2: Best non-normalised Figure 3: Best overall control action in study.control action in study.

  Figure 4: Mean performance, Figure 5: Mean Performance, lin / log scales.log / log scales.

Figure 6 :

 6 Figure 6: Computational speedup achieved through normalisation.

Figure 7 :

 7 Figure 7: Random search outperforms genetic learning for rst "generations".

{ In on-line learning, neural net "drivers" are generated on the y; they only solve the control problem for one starting con guration. { In o -line learning one attempts to train a driver who is able to reach the goal from any starting con guration.

An experiment in searching for appropriate values of is reported inSchoenauer & Ronald 94]

This article was processed using the L a T E X macro package with LLNCS style

with both programs were consistent, and only the experiments with the oating point package are detailed in this document.

The genetic algorithm progresses in discrete time steps called generations. At every generation the tness values of all the nets in the population are computed. Then a new population is derived from the old by applying the stochastic selection, crossover and mutation operators to the members of the old population.

{ Selection is an operator that discards the least t members of the population, and allows tter ones to reproduce. We use the roulette wheel selection procedure as described in Goldberg 89], with tness scaling and elitism, carrying the best individual over from one generation to the next. { Crossover mixes the traits of two parents into two o spring. In our case, random choice is made between two crossover operators: Exchange of the weights beteween parents, at random positions. Or assigning to some of the weights of each o spring a random barycentric combination of its parents' weights. { Mutation randomly changes some weights by adding some gaussian noise.

The experiments described in the next section used the following parameters in the GA: The net connection weights forming the object of the search were con ned to the interval ?10; +10] thereby avoiding over ow conditions in the computation of the exponential. Population size was held to 50 over the whole length of each run, tness scaling was set to a constant selecetive pressure of 2.0, crossover rate was 0.6, mutation rate 0.2, the gaussian noise had its standard deviation set to half the weight space diameter, ie. 10.0, decreasing geometrically in time by a factor 0.999 at each generation.

Results

A spectrum of experiments was carried out with the bit-string and real-number GA's, to determine the e ect of various parameter changes on the control accuracy and speed of convergence of the on-line neuro-genetic control method. A single starting point (speed=0m/s, altitude=1000m) was employed across the board.

For all tests, 2 state variables were taken as basis for the inputs to be presented to the net: NormSpeed = Speed=100; NormAltitude = Altitude=1000 the tness of a controller was computed to be fitness = 1 (0:1 + Speed crash 2 ) Thus the tness for a net is some number between 0.0 and 10.0

The following controller architectures were investigated: The 1-renormalized net gets precisely the same inputs as the 2-input net, only of course, it gets them twice.

In the diagram below the two net architectures are diagrammed. We have denoted by r i the renormalisation coe cients; the experiments consist of setting r 3 and r 4 to 1, 10, or 100, with r 1 and r 2 set to 1.

A total of 60 GA runs was made for each of these architectures, with the population size set to 50 individuals. For each run, at each generation, the best individual's performance was saved to disk. At the end of each batch of 60 runs, the mean at each number of generations of each architecture's best individuals' performance was computed. The corresponding graph is plotted in Figs 4 and 5, in linear and logarithmic scales:


Dhiraj Kumar

come

Numerical modeling and simulation of polymerization reactions in coiled flow inverters