Clotilde Coron
email: clotildecoron@gmail.com

The gender

Keywords: gender, job satisfaction, gender-job satisfaction debate, gendered organizations, moderating effects

Extensive research has been conducted on the relationship between gender and job satisfaction. Research conducted in Anglo-Saxon countries has highlighted that women report greater job satisfaction than men despite being in a disadvantaged position at the workplace. However, studies conducted in other countries have indicated opposite results.

One hypothesis put forward in this debate deals with gender differences concerning the antecedents of job satisfaction. This study seeks to explore this hypothesis with the theoretical framework of "gendered organizations", which encourages being attentive toward the interactions between gender and HR practices. Based on GLM models with moderating effects that were used on the French 2017 REPONSE survey, the positive effects of teleworking and performance appraisal on job satisfaction were found to be higher for women than for men, although the effects of part-time work and training were the same for both sexes.

Le débat sur le lien entre genre et satisfaction au travail, à la lumière des « organisations genrées » Résumé : La littérature académique est particulièrement féconde sur les relations entre genre et satisfaction au travail. Des recherches conduites dans des pays anglo-saxons ont montré que les femmes déclarent en moyenne des niveaux de satisfaction au travail plus élevés, alors qu'elles sont généralement désavantagées en matière de conditions de travail par rapport aux hommes. Cependant, d'autres recherches menées dans d'autres pays ont donné des résultats différents. Une hypothèse mise en avant dans ce débat porte sur d'éventuelles différences genrées concernant les antécédents de la satisfaction au travail. Cette recherche vise à explorer cette hypothèse en lien avec le courant théorique des « organisations genrées », qui incite à prêter attention aux interactions entre genre et pratiques de GRH. Elle se fonde pour ce faire sur des modèles de régression linéaire multiple avec des effets de modération, estimés sur les données de l'enquête REPONSE 2017 de la DARES. Elle montre que les effets positifs du télétravail et des dispositifs formels d'évaluation de performance sur la satisfaction au travail sont plus élevés pour les femmes que pour les hommes, alors que les effets du temps partiel et de la formation sont les mêmes pour femmes et hommes.

Mots-clés : genre, satisfaction au travail, débat sur les liens entre genre et satisfaction au travail, organisations genrées, effets de modération

Introduction

The rapid and significant increase in women's participation in the labour market has led to the development of numerous fields of research that deal with gender and the labour market.

In particular, extensive research has been done on the possible differences between women and men's relationship to work.

Job satisfaction is a key element in employees' relationships with work [START_REF] Garner | Les effets du sentiment d'efficacité personnelle sur la relation entre l'équilibre travail-famille et la satisfaction au travail[END_REF][START_REF] Flanchec | Favoriser la satisfaction au travail : Les apports de l'enquête REPONSE 2011[END_REF]. It influences their performance, their commitment, and their intent to stay in a company [START_REF] Brunetto | Emotional intelligence, job satisfaction, well-being and engagement : Explaining organisational commitment and turnover intentions in policing[END_REF][START_REF] Flickinger | The mediating role of leader-member exchange : A study of job satisfaction and turnover intentions in temporary work[END_REF], among other things. A considerable amount of research on this topic seeks to identify the determinants of job satisfaction, which include: managerial support [START_REF] Sawang | Moderation or Mediation? An Examination of the Role Perceived Managerial Support has on Job satisfaction and Psychological Strain[END_REF], values and culture [START_REF] Huang | Social expectations, gender and job satisfaction : Front-line employees in China's retail sector[END_REF], work-family conflict [START_REF] Garner | Les effets du sentiment d'efficacité personnelle sur la relation entre l'équilibre travail-famille et la satisfaction au travail[END_REF], and working conditions [START_REF] Pujol-Cols | Satisfacción laboral : Una revisión de la literatura acerca de sus principales determinantes[END_REF]. With regard to individual determinants, several elements have already been highlighted, such as education [START_REF] Bender | Job Satisfaction of the Highly Educated : The Role of Gender, Academic Tenure, and Earnings[END_REF][START_REF] Clark | Job satisfaction and gender : Why are women so happy at work?[END_REF], level of responsibility [START_REF] Smith | Gender, Pay and Work Satisfaction at a UK University[END_REF], age [START_REF] Clark | Is job satisfaction U-shaped in age[END_REF], and sex 1 [START_REF] Clark | Job satisfaction and gender : Why are women so happy at work?[END_REF][START_REF] Hodson | Gender Differences in Job Satisfaction[END_REF][START_REF] Huang | Social expectations, gender and job satisfaction : Front-line employees in China's retail sector[END_REF]. [START_REF] Hodson | Gender Differences in Job Satisfaction[END_REF] seminal article highlighted the so-called "gender-job satisfaction paradox" [START_REF] Perugini | Gender inequality and the gender-job satisfaction paradox in Europe[END_REF] or the "paradox of the contented female worker" [START_REF] Valet | Social Structure and the Paradox of the Contented Female Worker : How Occupational Gender Segregation Biases Justice Perceptions of Wages[END_REF], i.e. the fact that, despite facing more precarious employment conditions than men [START_REF] Ficapal-Cusí | Gender inequalities in job quality during the recession[END_REF], women report a 1 Throughout the article, we use the word "sex" to refer to the factual, statistical variable, and the word "gender" to refer to gender-related social phenomena. higher level of job satisfaction than men. [START_REF] Clark | Job satisfaction and gender : Why are women so happy at work?[END_REF] put forward a hypothesis to explain the so-called "gender-job satisfaction paradox" based on the fact that women have lower job expectations than men, which could result in higher levels of satisfaction among women than men. However, this assumption has been questioned in the literature [START_REF] Grönlund | The gender-job satisfaction paradox and the dual-earner society : Are women (still) making work-family trade-offs?[END_REF].

Generally, the literature on job satisfaction and gender explores two types of antecedents: demographic antecedents (e.g., age) and situational antecedents associated with an employee's work situation (e.g., type of contract) [START_REF] Pujol-Cols | Satisfacción laboral : Una revisión de la literatura acerca de sus principales determinantes[END_REF]. On the other hand, the theoretical framework of gendered organizations [START_REF] Acker | Hierarchies, Jobs, Bodies : A Theory of Gendered Organizations[END_REF] suggests that organizations are gendered, i.e., they are designed by and for men. Therefore, when studying phenomena related to work and individual relationship to work, one must also look at the organizational level [START_REF] Payne | Manufacturing Masculinity : Exploring Gender and Workplace Surveillance[END_REF], which goes beyond an employee's work situation and includes HRM (Human resource management) practices. Some HRM practices are more women-friendly and then contribute more to un-gender organizations than others [START_REF] Mastracci | Gendered Organizations : How Human Resource Management Practices Produce and Reproduce Administrative Man[END_REF] This study tries to elucidate the relationship between gender and job satisfaction. It focuses on the HR determinants of job satisfaction as well as the possible differences in these determinants based on sex. It aims to answer this research question: Do HR policies which seem to be more women-friendly contribute more to women's job satisfaction? By addressing this question, this study provides a deeper insight into the three following aspects. First, it extends the literature on gender and job satisfaction and contributes to shed light on the ambiguous links between gender and job satisfaction. Indeed, certain previous studies have identified individual [START_REF] Clark | Is job satisfaction U-shaped in age[END_REF][START_REF] Zou | Gender, work orientations and job satisfaction[END_REF], situational, or even national antecedents [START_REF] Huang | Social expectations, gender and job satisfaction : Front-line employees in China's retail sector[END_REF], but only a few have looked into HR practices [START_REF] Brown | Changes in HRM and job satisfaction, 1998-2004 : Evidence from the Workplace Employment Relations Survey[END_REF][START_REF] Kooij | How the impact of HR practices on employee well-being and performance changes with age[END_REF]. Second, it contributes to methodological developments around the "gendered organizations" field by linking it to the issue of job satisfaction, which has not yet been explored in this field. Moreover, the use of a quantitative methodology to understand the influence of HR practices and their relationship with sex helps open up promising research avenues in the field of gendered organizations, which hitherto only inspired mostly qualitative research. Third, this study focuses on the French case, bearing in mind that most research on the gender-job satisfaction paradox has been conducted in Anglo-Saxon countries [START_REF] Huang | Social expectations, gender and job satisfaction : Front-line employees in China's retail sector[END_REF] where the satisfaction differential is very much to the disadvantage of men, which is not true for all countries [START_REF] Eskildsen | Work motivation and job satisfaction in the Nordic countries[END_REF][START_REF] Huang | Social expectations, gender and job satisfaction : Front-line employees in China's retail sector[END_REF][START_REF] Sousa-Poza | Taking Another Look at the Gender/Job-Satisfaction Paradox[END_REF]. Notably, some studies have shown that, contrary to Anglo-Saxon countries, French women report lower job satisfaction than their male counterparts on average [START_REF] Sousa-Poza | Taking Another Look at the Gender/Job-Satisfaction Paradox[END_REF]. This, combined with the low gap between the male and female labour supply in France, makes France an interesting case among European countries [START_REF] Kaiser | Gender-job satisfaction differences across Europe : An indicator for labor market modernization[END_REF].

The study addresses this question through the nationally representative 2017 REPONSE survey and GLM models with moderating effects. The first section examines previous findings and arguments with respect to job satisfaction and gender, which inform this study's hypotheses. The research methods and empirical results are then introduced in the succeeding sections. The final sections provide further discussion and conclusions.

I. Literature review and hypotheses

I.1. Job satisfaction

The concept of job satisfaction holds several definitions in the literature [START_REF] Flanchec | Favoriser la satisfaction au travail : Les apports de l'enquête REPONSE 2011[END_REF]. In a seminal article, [START_REF] Locke | What is Job Satisfaction?[END_REF] defines it as "the pleasurable emotional state resulting from the appraisal of one's job as achieving or facilitating the achievement of one's job values" (p. 316). More recently, the literature has specified the definition by associating it with individuals' perception of their jobs compared to their expectations (Drydakis, 2017). This definition thus emphasizes the notion of perception, which was already stressed by [START_REF] Locke | What is Job Satisfaction?[END_REF]. Perception could depend on the different facets of the work occupied [START_REF] Christen | Job Satisfaction, Job Performance, and Effort : A Reexamination Using Agency Theory[END_REF] and on intrinsic or extrinsic sources of satisfaction [START_REF] Rose | Good Deal, Bad Deal? Job Satisfaction in Occupations[END_REF], as well as on personal values [START_REF] Lange | Social capital and job satisfaction : The case of Europe in times of economic crisis[END_REF]. [START_REF] Rose | Good Deal, Bad Deal? Job Satisfaction in Occupations[END_REF] therefore distinguishes between work satisfaction (i.e., intrinsic aspects related to the fact of working) and job satisfaction (i.e., extrinsic aspects such as material, contractual, etc.). Moreover, perception could refer to affective or cognitive elements [START_REF] Pujol-Cols | Satisfacción laboral : Una revisión de la literatura acerca de sus principales determinantes[END_REF] and could depend on individual emotional dispositions.

The literature on the antecedents of job satisfaction primarily corresponds to the following three approaches2 : the demographic approach wherein the demographic characteristics of an individual are considered as determinants of job satisfaction, the situational approach, which looks at the work characteristics, and the organizational approach, which considers managerial and HR practices implemented by the organization [START_REF] Pujol-Cols | Satisfacción laboral : Una revisión de la literatura acerca de sus principales determinantes[END_REF].

Accordingly, the demographic approach shows the influence of sex [START_REF] Clark | Job satisfaction and gender : Why are women so happy at work?[END_REF], age [START_REF] Clark | Is job satisfaction U-shaped in age[END_REF][START_REF] Eskildsen | Work motivation and job satisfaction in the Nordic countries[END_REF], or education [START_REF] Bender | Job Satisfaction of the Highly Educated : The Role of Gender, Academic Tenure, and Earnings[END_REF] on job satisfaction; the situational approach highlights the influence of part-time [START_REF] Fenton-O'creevy | Moderators of Differences In Job Satisfaction Between Full-Time and Part-Time Female Employees : A Research Note[END_REF] or temporary work [START_REF] Busk | Do Changes in Regulation Affect Temporary Agency Workers[END_REF]; and the organizational approach indicates the effects of determinants such as managerial relationships [START_REF] Flickinger | The mediating role of leader-member exchange : A study of job satisfaction and turnover intentions in temporary work[END_REF], coordination relationships [START_REF] Gittell | Impact of relational coordination on job satisfaction and quality outcomes : A study of nursing homes[END_REF], autonomy [START_REF] Wheatley | Autonomy in Paid Work and Employee Subjective Well-Being[END_REF], or HR practices [START_REF] Brown | Changes in HRM and job satisfaction, 1998-2004 : Evidence from the Workplace Employment Relations Survey[END_REF][START_REF] Kampkötter | Performance appraisals and job satisfaction[END_REF]. Some research combines the demographic approach with the situational or organizational approach by looking at the interaction between individual characteristics (sex, in particular) and work-related characteristics (e.g., part-time work, or work-life balance) [START_REF] Fenton-O'creevy | Moderators of Differences In Job Satisfaction Between Full-Time and Part-Time Female Employees : A Research Note[END_REF][START_REF] Grönlund | The gender-job satisfaction paradox and the dual-earner society : Are women (still) making work-family trade-offs?[END_REF][START_REF] Zou | Gender, work orientations and job satisfaction[END_REF].

I.2. The gender-job satisfaction debate

Sex is a demographic antecedent of job satisfaction. Hodson's seminal article (1989) pointed out that, paradoxically, women report higher average levels of satisfaction than men, despite generally facing materially less advantageous work situations [START_REF] Ficapal-Cusí | Gender inequalities in job quality during the recession[END_REF]. In particular, women could face precariousness [START_REF] Young | Gender Differences in Precarious Work Settings[END_REF], involuntary part-time work [START_REF] Gottfried | Japan : The Reproductive Bargain and the Making of Precarious[END_REF], glass ceiling [START_REF] Coron | Quels effets des mesures d'égalité professionnelle, en fonction de leur difficulté d'appropriation ? Une étude de cas[END_REF][START_REF] Ng | The glass ceiling in context : The influence of CEO gender, recruitment practices and firm internationalisation on the representation of women in management: The glass ceiling in context[END_REF], and lower wages [START_REF] Acker | Doing Comparable Worth : Gender, Class, and Pay Equity[END_REF][START_REF] Bergmann | Variations of the same? A sectoral analysis of the gender pay gap in Germany and Austria[END_REF][START_REF] Stojmenovska | Management gender composition and the gender pay gap : Evidence from British panel data[END_REF] in their workplaces. [START_REF] Clark | Job satisfaction and gender : Why are women so happy at work?[END_REF] main hypothesis asserts that this "gender-job satisfaction paradox" could be explained by the fact that women have lower job expectations partly due to their lower work centrality [START_REF] Sharabi | The meaning of work dimensions according to organizational status : Does gender matter?[END_REF].

This assumption has since been partly questioned by studies that have shown that the "gender-job satisfaction paradox" cannot be attributed to the lower work centrality of women and their eventual work-family trade-offs [START_REF] Grönlund | The gender-job satisfaction paradox and the dual-earner society : Are women (still) making work-family trade-offs?[END_REF]. Studies conducted in non-Anglo-Saxon countries have shown that this so-called "gender-job satisfaction paradox" is not the same in every country [START_REF] Huang | Social expectations, gender and job satisfaction : Front-line employees in China's retail sector[END_REF][START_REF] Lange | Communist Legacies, Gender and the Impact on Job Satisfaction in Central and Eastern Europe[END_REF][START_REF] Sousa-Poza | Taking Another Look at the Gender/Job-Satisfaction Paradox[END_REF]. For example, in Nordic countries, there was no significant difference found between men and women with respect to job satisfaction [START_REF] Eskildsen | Work motivation and job satisfaction in the Nordic countries[END_REF]. A study conducted in various countries showed that the sex differences of job satisfaction vary across the countries, with a "positive" gender gap (male reporting higher job satisfaction) in Spain, for example, and a "negative" gender gap (female reporting higher job satisfaction) in Great Britain and in the United States [START_REF] Sousa-Poza | Taking Another Look at the Gender/Job-Satisfaction Paradox[END_REF]. Other research has pointed out that women and men may have different expectations [START_REF] Hulin | Les attentes différenciées des talents selon le sexe : Une approche par la justice procédurale et la justice distributive[END_REF]. Besides, the gendered segregation of the labour market constrains the possibilities of comparison with male counterparts, which explains why women are satisfied by their wages even if they are aware that they earn less than men [START_REF] Valet | Social Structure and the Paradox of the Contented Female Worker : How Occupational Gender Segregation Biases Justice Perceptions of Wages[END_REF].

I.3. Gendered organizations and gender-focused HR policies

Certain studies on job satisfaction have also focused on the effect of HR or managerial practices, such as performance appraisal [START_REF] Kampkötter | Performance appraisals and job satisfaction[END_REF], development practices [START_REF] Kooij | How the impact of HR practices on employee well-being and performance changes with age[END_REF], or formal HR practices [START_REF] Brown | Changes in HRM and job satisfaction, 1998-2004 : Evidence from the Workplace Employment Relations Survey[END_REF], on job satisfaction. The gendered organizations framework theorized by [START_REF] Acker | Hierarchies, Jobs, Bodies : A Theory of Gendered Organizations[END_REF][START_REF] Acker | Inequality Regimes : Gender, Class, and Race in Organizations[END_REF] claims that organizations are gendered [START_REF] Metcalfe | A feminist poststructuralist analysis of HRD : Why bodies, power and reflexivity matter[END_REF], designed by men and for men, and could therefore indirectly disadvantage women. Among other things, HR practices defined by organizations are inherently gendered, often to the detriment of women [START_REF] Dickens | What HRM means for gender equality[END_REF][START_REF] Mastracci | Gendered Organizations : How Human Resource Management Practices Produce and Reproduce Administrative Man[END_REF], disadvantage women [START_REF] Bobbitt-Zeher | Gender Discrimination at Work : Connecting Gender Stereotypes, Institutional Policies, and Gender Composition of Workplace[END_REF][START_REF] Correll | Constraints into Preferences : Gender, Status, and Emerging Career Aspirations[END_REF][START_REF] Gorman | Gender Stereotypes, Same-Gender Preferences, and Organizational Variation in the Hiring of Women : Evidence from Law Firms[END_REF][START_REF] Ugarte | Gender pay equity : Exploring the impact of formal, consistent and transparent human resource management practices and information[END_REF], and ultimately perpetuate the gender hierarchies within these organizations [START_REF] Mastracci | Gendered Organizations : How Human Resource Management Practices Produce and Reproduce Administrative Man[END_REF]. Therefore, gender-focused HR policies must be implemented to address this issue [START_REF] Ali | Retaining a diverse workforce : The impact of gender-focused human resource management[END_REF][START_REF] Van Der Lippe | Organizational Work-Life Policies and the Gender Wage Gap in European Workplaces[END_REF] and help create women-friendly workplaces. This requires to take into account the somewhat specific women's needs.

One of the main dimensions of gendered organizations is that most of the organizations reward presenteeism [START_REF] Mastracci | Gendered Organizations : How Human Resource Management Practices Produce and Reproduce Administrative Man[END_REF], and value the ideal of a "disembodied worker who exists only for the work" (Acker, 1990, p. 149). This tends to disadvantage women who are more affected by domestic constraints [START_REF] Fang | The Effects of Work-Life Benefits on Employment outcomes in Canada : A Multi[END_REF][START_REF] Mastracci | Gendered Organizations : How Human Resource Management Practices Produce and Reproduce Administrative Man[END_REF][START_REF] Sheridan | Chronic Presenteeism : The Multiple Dimensions to Men's Absence from Part-Time Work[END_REF]. Several studies point out that women place more importance on work-family balance than men [START_REF] Huang | Social expectations, gender and job satisfaction : Front-line employees in China's retail sector[END_REF]. Therefore, part-time work could be a positive determinant of job satisfaction among women, as it allows for more work-life balance [START_REF] Bender | Job satisfaction and gender segregation[END_REF][START_REF] Van Der Lippe | Organizational Work-Life Policies and the Gender Wage Gap in European Workplaces[END_REF]. On the contrary, part-time work, which remains very rare among male [START_REF] Sheridan | Chronic Presenteeism : The Multiple Dimensions to Men's Absence from Part-Time Work[END_REF], does not contribute to male job satisfaction (Fenton-O'Creevy, 1995).

H1. Part-time work increases job satisfaction for women, but has no significant effect on job satisfaction for men.

In the same vein, [START_REF] Van Der Lippe | Organizational Work-Life Policies and the Gender Wage Gap in European Workplaces[END_REF] show that flexibility policies such as teleworking are one of the keys to ensure gender equality. Flexibility policies are notably found to decrease work-family conflict for women [START_REF] Wheatley | Autonomy in Paid Work and Employee Subjective Well-Being[END_REF]. Research then highlights the importance women attach to flexible solutions [START_REF] Bender | Job satisfaction and gender segregation[END_REF][START_REF] Chung | Women's employment patterns after childbirth and the perceived access to and use of flexitime and teleworking[END_REF][START_REF] Grönlund | The gender-job satisfaction paradox and the dual-earner society : Are women (still) making work-family trade-offs?[END_REF][START_REF] Huang | Social expectations, gender and job satisfaction : Front-line employees in China's retail sector[END_REF] such as teleworking.

H2. Teleworking increases job satisfaction for women, but has no significant effect on job satisfaction for men.

The theory of gendered organizations also highlights the weight of the implicit and the need to adopt more standardized procedures that increase transparency [START_REF] Mastracci | Gendered Organizations : How Human Resource Management Practices Produce and Reproduce Administrative Man[END_REF], even though Acker's work recalls that standardized procedures can also incorporate gender bias [START_REF] Acker | Inequality Regimes : Gender, Class, and Race in Organizations[END_REF]. For example, a formal appraisal can reduce the weight of the implicit judgements, knowing that implicit can leave room for gender discrimination [START_REF] Baron | In the Company of Women : Gender Inequality and the Logic of Bureaucracy in Start-Up Firms[END_REF][START_REF] Mastracci | Gendered Organizations : How Human Resource Management Practices Produce and Reproduce Administrative Man[END_REF]. Besides, previous research shows that women tend to attach more importance to procedures than men [START_REF] Jepsen | Female Perceptions of Organizational Justice[END_REF]. Among standardized HR practices, individual performance appraisals have been shown to increase job satisfaction [START_REF] Kooij | How the impact of HR practices on employee well-being and performance changes with age[END_REF]. It can therefore be assumed that having formal performance appraisals increases women's satisfaction more than men's.

H3. Formal individual performance appraisals increase both female and male employees'

job satisfaction, but it increases female job satisfaction more than male job satisfaction. [START_REF] Kooij | How the impact of HR practices on employee well-being and performance changes with age[END_REF] also mention development HR practices and, in particular, training, as determinants of job satisfaction. Yet, another dimension of the gendered organizations is that informal networks, mostly male networks, play an important role in the organizations [START_REF] Mastracci | Gendered Organizations : How Human Resource Management Practices Produce and Reproduce Administrative Man[END_REF]. The implicit organizational functioning tends to deprive women from networks, which are important for career progression [START_REF] Benschop | The Micro-politics of Gendering in Networking[END_REF][START_REF] Kalaitzi | Women leadership barriers in healthcare, academia and business. Equality, Diversity and Inclusion[END_REF]. Hence, although training is positively associated with job satisfaction for both women and men [START_REF] Huang | Social expectations, gender and job satisfaction : Front-line employees in China's retail sector[END_REF], it can be assumed that its effect is greater for women than for men, because training could enable women to meet people outside their team, reduce their social isolation [START_REF] Ibarra | Homophily and Differential Returns : Sex Differences in Network Structure and Access in an Advertising Firm[END_REF][START_REF] Kalev | Best Practices or Best Guesses? Assessing the Efficacy of Corporate Affirmative Action and Diversity Policies[END_REF], and ultimately help them build professional networks.

H4. Training increases both female and male employees' job satisfaction, but it increases

female job satisfaction more than male job satisfaction.

II. Methods

II.1. Sample and data

The data used in this study were obtained from the French REPONSE Survey conducted by the French Ministry of Labour in 2017. This survey corresponds to a nationally representative survey of French workplaces with 10 or more employees and was inspired by the British Survey Workplace Employment Relations Survey (WERS) [START_REF] Bryson | Perceptions of non-pecuniary job quality using linked employer-employee data[END_REF]. It is possible to extrapolate the results obtained in this study by using employee weights as the sample is a stratified random sample with weights.

The survey covers a wide range of topics. At an employee level, there are questions about the individuals, their work, certain managerial practices, their feelings about their work, and their feelings about the unions.

The entire sample consisted of 28,724 employees. After deleting incomplete responses for the main variables of interest, a sample of 26,465 respondents (11,538 females, 14,927 males) was obtained.

II.2. Measures

In this study, the dependent variable (job satisfaction) is based on six questions that are similar to the ones mentioned by [START_REF] Laroche | Union membership and job satisfaction : Initial evidence from French linked employer-employee data[END_REF]. The first one is: "When you think about your work in general, are you…" and the responses are rated using a four-point scale ranging from "1=strongly satisfied" to "4=strongly dissatisfied." The other questions are based on the same scale: "And more particularly, are you satisfied with: Your working hours / Your working conditions / Your wages / Your opportunities for training / Your workplace atmosphere." Responses for each item were rated on a four-point scale ranging from "1=strongly satisfied" to "4=strongly dissatisfied." The order of responses was reversed ("1=strongly dissatisfied" to "4=strongly satisfied") in order to make the results more easily readable. The arithmetic mean of the 6 questions was then computed, which provided an indicator of job satisfaction. The resulting alpha coefficient is 0.80, which is higher than the suggested reliability level of 0.70. Table 1 presents the descriptive statistics as well as correlation matrix of the variables. This indicator combines various indicators suggested by previous research. For example, [START_REF] Clark | Job satisfaction and gender : Why are women so happy at work?[END_REF] used an indicator that groups together an overall satisfaction measurement, followed by measurements on more specific dimensions such as working hours, pay, and atmosphere. Similar to this study, [START_REF] Jones | Training, Job Satisfaction, and Workplace Performance in Britain : Evidence from WERS 2004[END_REF] and [START_REF] Huang | Social expectations, gender and job satisfaction : Front-line employees in China's retail sector[END_REF] The study utilised various types of explanatory variables, which correspond to each aforementioned hypothesis: the fact to work part-time, the possibility of teleworking, having had a personal evaluation interview with a supervisor in the last 3 years, and having had professional training in the last 3 years. All variables were dichotomous ("Yes" or "No").

Concerning the control variables, this study utilised both demographic and situational variables. The literature on educational attainment led to contradictory results at times, particularly because education affects different dimensions of job satisfaction [START_REF] Ganzach | Intelligence, Education, and Facets of Job Satisfaction[END_REF]. Satisfaction linked to job content tends to increase with educational attainment [START_REF] Tlaiss | Predicting women's job satisfaction with personal demographics : Evidence from a Middle Eastern country[END_REF]. However, the level of pay satisfaction tends to decrease with educational attainment [START_REF] Bender | Job Satisfaction of the Highly Educated : The Role of Gender, Academic Tenure, and Earnings[END_REF] and the likelihood of feeling overqualified for a job, which tends to increase with educational attainment, negatively affects job satisfaction [START_REF] Alfes | Reducing perceptions of overqualification and its impact on job satisfaction : The dual roles of interpersonal relationships at work[END_REF]. Overall, educational effects are frequently found to be negative [START_REF] Neil | Gender as a Moderator of Job Satisfaction : A Multivariate Assessment[END_REF][START_REF] Perugini | Gender inequality and the gender-job satisfaction paradox in Europe[END_REF]. In this study, educational attainment was divided into seven levels in ascending order, which correspond to the French educational system: "No educational qualifications" / "Brevet" / "CAP-BEP" / "Bac/high school diploma" / "Bac+2" / "Bac+3 or 4 (undergraduate)" / ">Bac+4 (graduate)."

The literature has also examined the effect of age and job tenure on job satisfaction.

Several studies have confirmed the existence of a U-shaped curve wherein job satisfaction decreases with age and then increases again [START_REF] Clark | Is job satisfaction U-shaped in age[END_REF][START_REF] Eskildsen | Work motivation and job satisfaction in the Nordic countries[END_REF]. In this study, in line with this U-shaped effect, age was categorized into three groups [START_REF] Clark | Is job satisfaction U-shaped in age[END_REF][START_REF] Moullet | Le sentiment d'insécurité de l'emploi en France : Entre déterminants individuels et pratiques managériales[END_REF] : "16-29 years" / "30-49 years" / "More than 49 years", as well as workplace tenure: "Less than 5 years" / "5-10 years" / "More than 10 years."

Promotion opportunities are important predictors of job satisfaction [START_REF] Top | Examining transformational leadership, job satisfaction, organizational commitment and organizational trust in Turkish hospitals : Public servants versus private sector employees[END_REF]. This study utilised the variable "having been promoted in the last 3 years" ("Yes" or "No").

Previous studies have shown that temporary work leads to a reduction in job satisfaction [START_REF] Busk | Do Changes in Regulation Affect Temporary Agency Workers[END_REF][START_REF] Hünefeld | Job satisfaction and mental health of temporary agency workers in Europe : A systematic review and research agenda[END_REF]. In this study, the type of contract variable was divided into two categories (i.e., "permanent contract" and "temporary contract").

Occupational category and function are also usually used as control variables in previous research [START_REF] Valet | Social Structure and the Paradox of the Contented Female Worker : How Occupational Gender Segregation Biases Justice Perceptions of Wages[END_REF][START_REF] Wheatley | Autonomy in Paid Work and Employee Subjective Well-Being[END_REF] In this study, occupation was divided into the six following categories: "specialized worker/skilled worker" / "employee" / "technician" / "engineer and manager" / "other." Function corresponds to the five following categories:

"production/maintenance" / "accounting & finance/R&D" / "other."

The full list of variables is presented in Table 2, together with some descriptive statistics. Table 2 shows that women are more often than men in part-time work and report more often that they have had a performance appraisal in the last 3 years. However, they report less that they can telework and that they have had a professional training in the last 3 years.

II.3. Methods

Four linear regression models were estimated with job satisfaction as the dependent variable. The first model (Model 1) includes sex, education, age, type of contract, part-time work, teleworking, performance appraisal, training, and promotion, as well as the control variables (i.e., workplace tenure, occupational category, and function). The second model (Model 2) includes all the exogenous variables and adds interaction effects with sex. Hence, the following moderators were included: sex x part-time work, sex x teleworking, sex x performance appraisal, and sex x training. Indeed, interaction effects with sex enable the examination of the relationships between job satisfaction, sex, and HR practices. As all of these variables are categorical, significant interaction effects were visualized through plots that show the group means and the corresponding 95% confidence intervals of job satisfaction for each joint level of the regressors (Figure 1). Two additional models were estimated in order to gain a deeper understanding of these relationships, one exclusively for the female population (Model 3) and one for the male population (Model 4). This follows Wheatley's (2017) research design. SAS software was used for all analyses.

III. Main results

Table 3 presents the average satisfaction for women and men depending on the different facets of job satisfaction and indicates whether there are significant differences in job satisfaction between men and women (ANOVA tests). This table indicates that women report a lower average job satisfaction than men for every facet of job satisfaction except for working hours (women are more satisfied than men) and training (no significant difference between women and men). Overall, the job satisfaction computed as the arithmetic mean of the six other facets is higher on average for men than for women.

Table 4 shows the average job satisfaction for the men and women separately and for the sample as a whole, according to different characteristics, and indicates whether the differences in job satisfaction according to each modality of the categorical variable are significant for each sample (i.e., whole sample, female sample, male sample). The difference in job satisfaction according to working time is only significant for men: part-time male workers reported higher job satisfaction. This could be explained by the fact that involuntary part-time work is more common among women than men and is associated with precarious employment [START_REF] Young | Gender Differences in Precarious Work Settings[END_REF]. Therefore, the female part-time workers may include both women who are satisfied because they deliberately chose to work part-time for a better work-life balance and women who are dissatisfied because they would prefer working full-time. Although the data used in this study does not allow us to differentiate between voluntary and involuntary part-time work, controlling for job characteristics would help clarify this point. The three other HRM practices identified in the hypotheses (teleworking, performance appraisal, training) are associated with higher job satisfaction for both men and women.

The level of job satisfaction increases with education for both women and men. This could be attributed to the fact that higher levels of education are linked to better working situations.

However, research has shown that expectations also increase with education [START_REF] Perugini | Gender inequality and the gender-job satisfaction paradox in Europe[END_REF]. Hence, this descriptive result should be examined further through a regression analysis to control for the work situation. The relationship between age and job satisfaction follows a U-shaped curve (i.e., job satisfaction decreases with age and then increases again) for the sample as a whole and for men, but not for women. Promotion increases the level of job satisfaction, as in previous research [START_REF] Top | Examining transformational leadership, job satisfaction, organizational commitment and organizational trust in Turkish hospitals : Public servants versus private sector employees[END_REF], knowing that women are less promoted than men (Table 2). The results for the type of contract contradict previous research [START_REF] Hünefeld | Job satisfaction and mental health of temporary agency workers in Europe : A systematic review and research agenda[END_REF] with temporary workers reporting a higher average level of job satisfaction.

Those descriptive statistics partly explain why women are less satisfied by men: notably, they telework less and they are less trained, whereas telework and training are associated with higher levels of job satisfaction. However, they have more performance appraisals, which contribute to job satisfaction. Table 5 reports the results of the models. Model 1 was applied to the whole sample and did not include moderators. In this model as in Model 2 (with moderators), women report lower job satisfaction than men.

Part-time work is associated with higher levels of job satisfaction for women as for men (Models 3 and 4). This shows that when controlling for job characteristics, women derive the same satisfaction from part-time work as men. This is confirmed by the insignificant interaction effect between sex and part-time work. Therefore, Hypothesis H1 is only partially supported because part-time work increases job satisfaction for men too.

Teleworking is associated with higher job satisfaction for women (Model 3), but not for men (Model 4). Therefore, Hypothesis H2 is supported.

Formal individual performance appraisals increase job satisfaction for both women (Model 3) and men (Model 4). The interaction effect sex × performance appraisal is significant. A closer look at this moderator (Figure 1) indicates that the positive effect of individual performance appraisals is higher for women than for men, therefore supporting Hypothesis H3.

Training is associated with higher job satisfaction for women (Model 3) and for men (Model 4). Hypothesis H4 is only partially supported, as there is no significant difference between women and men (the moderator sex x training is not significant). Concerning the control variables, in all four models, people without educational qualifications report higher job satisfaction. This result, combined with the descriptive statistics, which indicated that the average job satisfaction increases with the educational level, supports the idea that people with educational attainment have better working situations and therefore have greater average job satisfaction. However, they also have higher expectations and consequently lower average job satisfaction when controlling for the job characteristics. This is true for both men and women. In all four models, people aged 50 and over report the highest job satisfaction among all age groups. Promotion increases job satisfaction for both women and men. In all four models, having a temporary job increases job satisfaction. Some of these results are rather surprising as they contradict previous research and are discussed below.

IV. Discussion

This study deals with the relationship between sex, job satisfaction, and HR practices. It attempts to shed some light on the gender-job satisfaction debate. While some previous studies have indicated that women report a higher level of job satisfaction than men [START_REF] Clark | Job satisfaction and gender : Why are women so happy at work?[END_REF][START_REF] Hodson | Gender Differences in Job Satisfaction[END_REF][START_REF] Zou | Gender, work orientations and job satisfaction[END_REF], others have challenged this result, claiming that the relationship between sex and job satisfaction depends on the country [START_REF] Eskildsen | Work motivation and job satisfaction in the Nordic countries[END_REF][START_REF] Huang | Social expectations, gender and job satisfaction : Front-line employees in China's retail sector[END_REF][START_REF] Sousa-Poza | Taking Another Look at the Gender/Job-Satisfaction Paradox[END_REF]. Using a French nationally representative dataset, the results of this study indicate that French women report lower job satisfaction than men.

In line with the theoretical framework of gendered organizations, the following variables related to HR practices were introduced: part-time, teleworking, performance appraisal, training, and promotion. In an attempt to gain deeper insight into gender-job satisfaction relationships, interaction effects were employed and the models were estimated separately for women and men.

Part-time work increases job satisfaction for both men and women, which contradicts previous research that found no effect of part-time work on men's job satisfaction [START_REF] Booth | Job Satisfaction and Family Happiness : The Part-Time Work Puzzle[END_REF][START_REF] Fenton-O'creevy | Moderators of Differences In Job Satisfaction Between Full-Time and Part-Time Female Employees : A Research Note[END_REF]. This could be explained by the fact that the data in the study are very recent (2017) and are specific to France. Indeed, it has been shown that the youngest generations are more in search of work-life balance [START_REF] Pedulla | Can We Finish the Revolution? Gender, Work-Family Ideals, and Institutional Constraint[END_REF].

Moreover, only a few French men work part-time (5.14 % in our data) and the majority of them are voluntary part-time employees (e.g., because they have another professional activity or follow a training course) [START_REF] Pak | Le temps partiel en 2011[END_REF], which could explain why they are more satisfied.

Teleworking is associated with a higher job satisfaction for women, but not for men. This could be explained by the fact that teleworking offers flexibility in terms of working hours without sacrificing salary, which could be appealing to people in charge of domestic tasks who do not want to give up their careers or salaries [START_REF] Chung | Women's employment patterns after childbirth and the perceived access to and use of flexitime and teleworking[END_REF]. This is in line with previous research which shows that flexibility policies help reduce gender inequalities [START_REF] Van Der Lippe | Organizational Work-Life Policies and the Gender Wage Gap in European Workplaces[END_REF].

Having an individual performance appraisal increases both female and male employees' job satisfaction. The size of the positive effect of individual performance appraisals is higher for women than for men. This supports the idea that women benefit more from formal performance appraisals because they can reduce the weight of the implicit [START_REF] Mastracci | Gendered Organizations : How Human Resource Management Practices Produce and Reproduce Administrative Man[END_REF][START_REF] Ugarte | Gender pay equity : Exploring the impact of formal, consistent and transparent human resource management practices and information[END_REF] and because women tend to attach more importance to procedures than men [START_REF] Jepsen | Female Perceptions of Organizational Justice[END_REF].

Training increases job satisfaction for both women and men [START_REF] Kampkötter | Performance appraisals and job satisfaction[END_REF][START_REF] Kooij | How the impact of HR practices on employee well-being and performance changes with age[END_REF][START_REF] Top | Examining transformational leadership, job satisfaction, organizational commitment and organizational trust in Turkish hospitals : Public servants versus private sector employees[END_REF]. It has the same effect for women as men. Again, consistent with the most recent research in non-Anglo-Saxon countries [START_REF] Huang | Social expectations, gender and job satisfaction : Front-line employees in China's retail sector[END_REF], this result updates the literature on the determinants of job satisfaction for women and men as well as on gender and work orientation. Indeed, it shows that similar to men, working women derive satisfaction from their professional development, which contradicts older studies on the subject [START_REF] Clark | Job satisfaction and gender : Why are women so happy at work?[END_REF][START_REF] Hakim | Grateful slaves and self-made women : Fact and fantasy in women's work orientations[END_REF][START_REF] Zou | Gender, work orientations and job satisfaction[END_REF], but is in line with the most recent studies that indicate that women no longer want to make work-family tradeoffs [START_REF] Grönlund | The gender-job satisfaction paradox and the dual-earner society : Are women (still) making work-family trade-offs?[END_REF][START_REF] Huang | Social expectations, gender and job satisfaction : Front-line employees in China's retail sector[END_REF], 2015).

Surprisingly, for the whole sample, having a temporary contract is associated with higher job satisfaction, which contradicts previous research which finds a lower level of job satisfaction among temporary workers [START_REF] Busk | Do Changes in Regulation Affect Temporary Agency Workers[END_REF], or no significant difference between temporary and permanent workers [START_REF] De Witte | Objective' vs `Subjective' Job Insecurity : Consequences of Temporary Work for Job Satisfaction and Organizational Commitment in Four European Countries[END_REF]. This paradox could be explained by the fact that, in France, workers with fixed-term contracts are entitled to a specific financial compensation guaranteed by law, which increases their salary. Another explanation can be found in the heterogeneity of the temporary workers group, between executives who have opted for flexibility and underqualified people, but also between fixedterm contract and temporary agency workers. Indeed, it has been shown that contractors have a higher level of job satisfaction than agency workers [START_REF] Wilkin | I can't get no job satisfaction : Meta-analysis comparing permanent and contingent workers[END_REF].

The results of this study offer three main areas of discussion with previous research. First, the relationship between sex and job satisfaction depends on the country. Contrary to Anglo-Saxon countries [START_REF] Zou | Gender, work orientations and job satisfaction[END_REF], but similar to other countries such as China [START_REF] Huang | Social expectations, gender and job satisfaction : Front-line employees in China's retail sector[END_REF], women in France report lower job satisfaction than men. This cannot be entirely attributed to the fact that they face more precarious working conditions, as women with parttime jobs and temporary contracts report higher job satisfaction. However, this could be due to the fact that they have less interesting jobs, with less autonomy, and lower salary. Indeed, the findings show that the differential of satisfaction between men and women is the most important for satisfaction in terms of pay (Table 3).

Second, this study confirms the strong impact of HR practices on job satisfaction [START_REF] Kooij | How the impact of HR practices on employee well-being and performance changes with age[END_REF] and that certain practices (e.g., teleworking, formal performance appraisals) have a greater effect on women than on men. This could be explained through the theoretical framework of gendered organizations, which assumes that organizations are implicitly designed by men and for men. Therefore, some HR practices that reduce this implicit (e.g., formal performance appraisals in this study) benefit women more than men. Other practices that offer more flexibility (e.g., teleworking in this study) benefit women more than men. However, some other HR practices, as part-time work and training, do not have different effects for women and men. The difference between part-time work and teleworking is interesting. Indeed, both are included in so-called flexibility policies [START_REF] Van Der Lippe | Organizational Work-Life Policies and the Gender Wage Gap in European Workplaces[END_REF], but this study shows that actually they have different effects, as teleworking does not have effect of male satisfaction. Teleworking may benefit women more because it offers the flexibility they need without being associated to a wage loss. This suggests that the theories claiming that work orientation between women and men is profoundly different [START_REF] Hakim | Grateful slaves and self-made women : Fact and fantasy in women's work orientations[END_REF][START_REF] Hakim | Women, careers, and work-life preferences[END_REF]) should be updated. In 2017, French working women want to succeed too, and therefore value more flexible working arrangements (teleworking), which allow for the reconciliation of work and family life without sacrificing either of them [START_REF] Grönlund | The gender-job satisfaction paradox and the dual-earner society : Are women (still) making work-family trade-offs?[END_REF]. This assumption is also supported by the most recent studies carried out in other countries [START_REF] Chung | Women's employment patterns after childbirth and the perceived access to and use of flexitime and teleworking[END_REF].

Third, the descriptive statistics (Table 3) indicate that the differential of satisfaction differs across the dimensions of job satisfaction: it is more important for pay, but less important for working conditions, training, and ambiance. This indicates that, contrary to previous research on the topic conducted in Anglo-Saxon countries [START_REF] Davison | The Paradox of the Contented Female Worker : Why Are Women Satisfied with Lower Pay?[END_REF], French women are aware that they earn less than men [START_REF] Valet | Social Structure and the Paradox of the Contented Female Worker : How Occupational Gender Segregation Biases Justice Perceptions of Wages[END_REF], and this is detrimental to their overall job satisfaction.

Conclusion and implications

Using a nationally representative French survey, this study assesses the extent to which the determinants of job satisfaction vary according to sex. First, the findings indicate that in France, there is no such thing as the paradox of the contented female employee: women report lower levels of job satisfaction, even after controlling for individual characteristics. Among the HR practices, the study shows that teleworking and performance appraisal have more positive effects for women than for men, while part-time work and training have the same effect for women and men.

The findings of the study have theoretical implications as they enable a discussion of [START_REF] Acker | Inequality Regimes : Gender, Class, and Race in Organizations[END_REF] theoretical framework of gendered organizations, which assumes that traditional HR practices are gendered [START_REF] Metcalfe | A feminist poststructuralist analysis of HRD : Why bodies, power and reflexivity matter[END_REF] and may indirectly disadvantage women compared to men [START_REF] Mastracci | Gendered Organizations : How Human Resource Management Practices Produce and Reproduce Administrative Man[END_REF]. Indeed, the results suggest that among HR practices, teleworking and formal performance appraisal benefit women more than men.

Therefore, it can be assumed that these HR practices help reduce gender inequality and undo the gender hierarchies within organizations. The result concerning teleworking is not surprising [START_REF] Chung | Women's employment patterns after childbirth and the perceived access to and use of flexitime and teleworking[END_REF][START_REF] Van Der Lippe | Organizational Work-Life Policies and the Gender Wage Gap in European Workplaces[END_REF]. Previous research shows that formal performance appraisal could introduce transparency and formalized bureaucratic rules that can mitigate bias, but also that performance evaluation could disadvantage women when work qualities that are often associated with male workers are valued [START_REF] Mastracci | Gendered Organizations : How Human Resource Management Practices Produce and Reproduce Administrative Man[END_REF][START_REF] Ugarte | Gender pay equity : Exploring the impact of formal, consistent and transparent human resource management practices and information[END_REF]. The study's findings suggest that the transparency effect is more important than the latter one, as in some previous research [START_REF] Baron | In the Company of Women : Gender Inequality and the Logic of Bureaucracy in Start-Up Firms[END_REF]. The result concerning part-time work indicates that this "flexibility policy" does not particularly benefit women.

Managerially, this implies that teleworking could enhance gender equality and increase women's job satisfaction. Indeed, it allows women to keep working without losing pay (as part-time work implies). Previous studies have already proven that family-friendly policies could help women feel better within organizations [START_REF] Huang | Social expectations, gender and job satisfaction : Front-line employees in China's retail sector[END_REF] and could contribute to the reduction of gender inequalities [START_REF] Van Der Lippe | Organizational Work-Life Policies and the Gender Wage Gap in European Workplaces[END_REF]. The study's results, backed by other recent studies [START_REF] Chung | Women's employment patterns after childbirth and the perceived access to and use of flexitime and teleworking[END_REF], identifies teleworking as a specific family-friendly policy that could most likely help women deal with work-family conflict. Second, having formal performance appraisals also appears to be an effective means of reducing gender inequality within organizations, as they benefit women more than men.

Again, this helps determine the formal policies that could most likely reduce the weight of the implicit within organizations, which are often detrimental to women.

The limitations of the study include the fact that it is based on cross-sectional data; therefore, causation cannot be definitively established. In addition, job satisfaction is certainly influenced by unobservable data such as personality traits or content of the work in itself, which the REPONSE data set does not cover. Another limitation is that the questionnaire does not contain any information about race or ethnicity (due to the French law which prohibits the collection of data on race or ethnicity). Another limitation is related to the impossibility to differentiate between voluntary and involuntary part-time work in the data, even if controlling for the other job characteristics is a first step toward this distinction, as involuntary part-time work is more present in some sectors and occupations. Finally, the data used for the study do not include individual wages, whereas it can be one of the determinants of job satisfaction.

The results call for more extensive research on the gender-job satisfaction debate in non-Anglo-Saxon countries. Further research is needed in order to identify the determinants of job satisfaction for women and men, as well as to understand why the effects of some determinants vary according to sex. The results also suggest that the relationship between sex and job satisfaction will change over time, notably with the current pandemic situation which has made teleworking widespread. This calls for longitudinal studies.

  Significance levels: *=0.1; **=0.01; ***=0.001

Figure 1 .

 1 Figure 1. Sex x Performance appraisal

Table 1 .

 1 used an indicator that includes other dimensions such as training opportunities. Descriptive statistics and correlation matrix

		Mean	SD	1	2	3	4	5	6	7
	1. Overall	2.88	0.68	1
	satisfaction
	2. Working hours	3.05	0.76	0.36*** 1
	3. Conditions	2.83	0.76	0.61*** 0.42*** 1
	4. Pay	2.36	0.81	0.44*** 0.27*** 0.44*** 1
	5. Training	2.60	0.86	0.42*** 0.24*** 0.43*** 0.37*** 1
	6. Ambiance	2.84	0.84	0.52*** 0.26*** 0.53*** 0.29*** 0.38*** 1
	7. Arithmetic mean	2.76	0.55	0.78*** 0.59*** 0.80*** 0.67*** 0.69*** 0.71*** 1
	(=Job satisfaction)
	Significance levels: *=0.05; **=0.01; ***=0.001

Table 2 .

 2 Main variables and descriptive statistics of the REPONSE 2017 sample

		Whole sample	Female	Male
	Number of observations	26,465	11,538	14,927
	HRM practices
	Part-time work
	No	86.00	73.64	94.86
	Yes	14.00	26.36	5.14
	Teleworking
	No	90.37	91.58	89.50
	Yes	9.63	8.42	10.50
	Performance appraisal
	No	21.05	19.67	22.04
	Yes	78.95	80.33	77.96
	Training
	No	53.16	56.25	50.95
	Yes	46.84	43.75	49.05
	Control variables
	Education
	No ed. qualification	7.81	6.02	9.08
	Brevet	5.58	6.08	5.23
	CAP-BEP	23.34	18.28	26.96
	Bac (High school)	19.24	21.02	17.97
	Bac+2	17.31	18.59	16.40
	Bac+3 or 4 (undergrad.)	11.72	15.41	9.08
	>Bac+4 (graduate)	14.99	14.60	15.27
	Age
	16-29	15.75	16.64	15.10
	30-49	57.35	57.08	57.54
	50+	26.90	26.28	27.35
	Workplace tenure
	4-	20.82	22.19	19.84
	5-10	28.11	28.94	27.52
	11+	51.07	48.87	52.64
	Promotion
	No	71.64	74.65	69.49
	Yes	28.36	25.35	30.51
	Type of contract
	Permanent	94.29	93.67	94.74
	Temporary	5.71	6.33	5.26
	Occupational category
	Specialized worker	13.13	8.69	16.27
	Skilled worker	15.04	6.16	21.30
	Employee	19.47	34.97	8.53
	Technician	17.76	15.70	19.22
	Engineer/Manager	23.79	19.62	26.73
	Other	10.81	14.85	7.95
	Function
	Production	27.80	14.61	37.08
	Maintenance	9.42	1.60	14.92
	Accounting/Finance	8.61	13.60	5.10
	R&D	8.18	5.69	9.93
	Other	45.99	64.50	32.96

Table 3 .

 3 Average job satisfaction by gender

		Whole sample	Female	Male
	Job satisfaction***	2.76	2.74	2.77
	Overall satisfaction***	2.88	2.85	2.91
	Working hours*	3.05	3.06	3.04
	Working conditions*	2.83	2.81	2.83
	Pay***	2.36	2.29	2.38
	Training	2.60	2.59	2.58
	Ambiance**	2.84	2.84	2.87
	Significance levels: *=0.1; **=0.01; ***=0.001

Table 4 .

 4 Average job satisfaction by gender and main characteristics

		Whole sample	Female	Male
	HRM practices
	Part-time work			*
	No	2.76	2.74	2.77
	Yes	2.75	2.74	2.81
	Teleworking	***	***	***
	No	2.75	2.73	2.76
	Yes	2.86	2.85	2.86
	Performance appraisal	***	***	***
	No	2.62	2.60	2.63
	Yes	2.79	2.77	2.81
	Training	***	***	***
	No	2.65	2.64	2.65
	Yes	2.88	2.87	2.89
	Control variables
	Education	***	***	***
	No ed. qualification	2.70	2.69	2.70
	Brevet	2.69	2.65	2.72
	CAP-BEP	2.67	2.68	2.68
	Bac (High school)	2.71	2.70	2.72
	Bac+2	2.78	2.76	2.80
	Bac+3 or 4 (undergrad.)	2.82	2.80	2.85
	>Bac+4 (graduate)	2.92	2.87	2.96
	Age	***		***
	16-29	2.79	2.73	2.83
	30-49	2.75	2.75	2.75
	50+	2.76	2.74	2.78
	Workplace tenure (years)	***		***
	4-	2.79	2.76	2.83
	5-10	2.74	2.74	2.75
	11+	2.75	2.74	2.76
	Promotion	***	***	***
	No	2.67	2.66	2.67
	Yes	2.98	2.96	2.98
	Type of contract	***	***	**
	Permanent	2.75	2.73	2.76
	Temporary	2.83	2.84	2.83
	Occupational category	***	***	***
	Specialized worker	2.60	2.57	2.62
	Skilled worker	2.67	2.62	2.68
	Employee	2.69	2.69	2.67
	Technician	2.79	2.81	2.77
	Engineer/Manager	2.94	2.90	2.96
	Other	2.74	2.72	2.76
	Function	***	***	***
	Production	2.69	2.62	2.70
	Maintenance	2.76	2.76	2.76
	Accounting/Finance	2.87	2.84	2.91
	R&D	2.92	2.90	2.93
	Other	2.75	2.73	2.77
	Significance levels: *=0.1; **=0.01; ***=0.001

Table 5 .

 5 Models

		Model 1	Model 2	Model 3	Model 4
		(Whole sample)	(Whole sample)	(Female sample)	(Male sample)
	Intercept	2.61***	2.61***	2.56***	2.62***
	Sex
	Female	-0.03***	-0.04**
	HR practices
	Part-time (ref. No)
	Yes	0.07***	0.09***	0.06***	0.10***
	Teleworking (ref. No)
	Yes	0.02*	0.02	0.04*	0.01
	Performance appraisal (ref. No)
	Yes	0.08***	0.07***	0.10***	0.06***
	Training (ref. No)
	Yes	0.17***	0.17***	0.16***	0.17***
	Interaction effects
	Sex x Part-Time
	Sex x Teleworking
	Sex x Performance appraisal		*
	Sex x Training
	Control variables
	Education (ref. CAP-BEP)
	No ed. qualification	0.07***	0.07***	0.06*	0.08***
	Brevet	0.04	0.04**	0.01	0.06**
	Bac (High school)	-0.00	-0.00	-0.00	-0.01
	Bac+2	0.00	0.00	-0.02	0.01
	Bac+3 or 4 (undergrad.)	0.01	0.01	0.00	0.02
	>Bac+4 (graduate)	0.01	0.01	-0.01	0.03
	Age (ref. 30-49)
	16-29
	50+

Another approach, that is not presented here, deals with the determinants related to individual personality traits[START_REF] Brunetto | Emotional intelligence, job satisfaction, well-being and engagement : Explaining organisational commitment and turnover intentions in policing[END_REF][START_REF] Kampkötter | Performance appraisals and job satisfaction[END_REF].


Thibaud Lasguignes
email: thibaud.lasguignes@laas.fr

Guillaume Gobin

Olivier Stasse
email: olivier.stasse@laas.fr

LiDAR-based localization system for kidnapped robots

Keywords: LiDAR, place recognition, kidnapped robot, humanoid robot, perception

Place recognition is the ability to recognize previously seen places in the world. When the environment is known, the robot may localise itself when it starts and whenever it needs to verify where it is. We propose a solution to implement place recognition capability using a geometric representation of the environment build with a LiDAR. Nowadays, large Field Of View LiDARs allows to get a dense and precise representation of the environment. Assuming that a 3D map of the environment is available, we propose to build a compressed codebook based on FPFH descriptors. The codebook is then used to find the robot localization with one LiDAR image. The system has been tested on real and simulated measurements and shows promising results. The pose estimation can be thoroughly enhanced with point cloud registration methods.

I. INTRODUCTION

The context of this work is the capability for a robot to localize itself in a large industrial environment such as an aeronautic factory. In this context, few textures are present and many unusual large objects are present in the environment. Still it is possible to apply a LiDAR-based localization system [START_REF] Lasguignes | Icp localization and walking experiments on a talos humanoid robot[END_REF], implemented on a Talos robot [START_REF] Stasse | TALOS: A new humanoid research platform targeted for industrial applications[END_REF], for allowing a precise estimation of the robot localization in a known environment. A limitation of this system is the need for an estimate of the robot initial pose. When the visual-inertial odometry or the base estimator is started, each makes an initial assumption about their world origin.

Thus, the pose M p 0 of the robot in the environment when the localization system is started needs to be estimated in order to initialize the SLAM system by providing the estimation in the known world. In the experiment presented in [START_REF] Lasguignes | Icp localization and walking experiments on a talos humanoid robot[END_REF], an approximation of the Mocap estimate, that was used as ground truth, was used as the initial pose.

This problem of knowing the initial pose of the robot in the environment is called the kidnapped robot problem. This problem is equivalent to the place recognition problem that has attracted interest in the last years. The place recognition tries to recognize a known part of the environment to help the initialization of the system or correct the drift that can be present in state estimation and odometry mechanisms, performing loop closure.

A. TALOS and its sensors

TALOS is a humanoid robot of 1.75m weighting 100kg with 32 degrees of freedom. It has been designed to perform complex locomotion and bi-handed manipulation involving high payload.

Initially, it was equipped with a single RGB-D camera on the head. To enhance its sensing capabilities, the head was replaced to integrate new sensors. Fig 1 shows the new head installed with a RGB-D camera Intel ® RealSense TM D435i [START_REF] Intel | Intel ® realsense ™ depth camera d435i[END_REF] on the bottom, a tracking camera Intel ® RealSense TM T265 [START_REF]Intel ® realsense ™ tracking camera t265[END_REF] in the middle and an Ouster OS1-64 [START_REF] Ouster | High-resolution os1 lidar sensor: robotics, trucking, mapping[END_REF] LiDAR on top.

In this work, only the LiDAR on the top of the head is used. This LiDAR has an horizontal field of view of 360 • with a vertical one of 33.2 • sampled by a total of 64 vertical beams. It can produce up to 1 310 720 points per second, with an accuracy of 3cm up to 60m and 10cm up to 120m.

B. Contributions

The contribution of this work are:

• Propose a solution the the place recognition problem using FPFH descriptors and VLAD encoding, with a RANSAC and ICP refinement

• Evaluate the system on simulated and real measurement using a LiDAR with a horizontal Field of View of 360 • II. RELATED WORK As place recognition is an important problem it is widely studied topic. Its formulation dependent on the environment scale, the used sensors, the application, etc.

There are two common choices of visual sensors: camera and LiDAR. Each sensor has its pros and cons as summarized in [START_REF] Barros | Place recognition survey: An update on deep learning approaches[END_REF]. For example, cameras have a limited Field of View (FoV) whereas nowadays LiDAR can have a 360 • FoV on one axis. However, in terms of cost and energy consumption, cameras are often cheaper and less energy-consuming than LiDAR. The target environment needs to be taken into account as cameras are dependent of textures whereas LiDAR mostly relies on reflective materials. Other sensors overcome the dependance to textures of monocular cameras by being able to produce depth information, either with stereo-vision or infrared projector and cameras. However, these depth information are less precise than LiDAR's. With the evolution of technology and particularly MicroElectroMechanical Systems (MEMS), cameras integrate LiDAR systems such as the Intel-RealSense L515 LiDAR Camera [START_REF] Intel | Intel ® realsense ™ lidar camera l515[END_REF], enhancing the range and precision of the depth information.

Depending on the sensors used, different features are used. In case of a camera, the system may be using SIFT [START_REF] Lowe | Object recognition from local scale-invariant features[END_REF] or ORB [START_REF] Rublee | Orb: An efficient alternative to sift or surf[END_REF] whereas Scan Context [START_REF] Kim | Scan context: Egocentric spatial descriptor for place recognition within 3d point cloud map[END_REF] or FPFH [START_REF] Rusu | Fast point feature histograms (fpfh) for 3d registration[END_REF] and others 3D descriptors may be used in case of using a LiDAR.

Other method such as in [START_REF] Komorowski | Minkloc++: Lidar and monocular image fusion for place recognition[END_REF] try to combine both worlds instead of using only one of these visual sensors. In this work, features are extracted from the LiDAR using MinkLoc3D [START_REF] Komorowski | Minkloc3d: Point cloud based large-scale place recognition[END_REF], presented on Section II-B, and from the monocular with a part of ResNet18 [START_REF] He | Deep residual learning for image recognition[END_REF]. These two features are lately aggregated in a single one which is matched to a database.

The LiDAR-based methods may differ in the type of information processed.

A. Segment-based methods [START_REF] Douillard | Scan segments matching for pairwise 3d alignment[END_REF] presented the concept of segments or how to use the segmentation of a point cloud to reduce its computational cost.

This concept is used by [START_REF] Dubé | Segmatch: Segment based loop-closure for 3d point clouds[END_REF] and [START_REF] Dubé | Segmap: 3d segment mapping using data-driven descriptors[END_REF] to perform place recognition and SLAM. In both works, the point cloud is segmented and features are extracted for each segment. Then, using these features, the segments are matched to known ones from a map in a learning approach. These matches are then given to a geometric verification system based on RANSAC to evaluate the consistency of each match.

On this same principle, [START_REF] Tinchev | Learning to see the wood for the trees: Deep laser localization in urban and natural environments on a cpu[END_REF] applies a similar method but the feature is learnt and the final pose is estimated with PRObabilistic SAmple Consensus (PROSAC) [START_REF] Chum | Matching with prosac -progressive sample consensus[END_REF] instead of the usual RANSAC method. The main advantage of their method is the design of the network that is able to run on a single CPU whereas numerous network-based method needs a GPU to be time-efficient. [START_REF] Ramezani | Online lidarslam for legged robots with robust registration and deep-learned loop closure[END_REF] presented an online LiDARbased SLAM system combining the Autotuned-ICP (AICP) [START_REF] Nobili | Overlap-based icp tuning for robust localization of a humanoid robot[END_REF] for point cloud matching, and the Efficient Segment Matching (ESM) [START_REF] Tinchev | Learning to see the wood for the trees: Deep laser localization in urban and natural environments on a cpu[END_REF] to detect loop-closure.

B. Geometry-based methods

The main characteristic of LiDAR is the ability to provide a measure of the environment as a 3D point cloud, giving strong geometric information. Whereas methods divide the point cloud into segments, others take the complete point cloud and use its geometric information to compute local and global features.

[10] presented a new descriptor called Scan Context, a 2D-shaped descriptor used to describe 3D LiDAR scans. This descriptor divide the space into azimuthal and radial bins, similarly to [START_REF] Belongie | Shape matching and object recognition using shape contexts[END_REF], with each bin being represented in the descriptor by the maximum height of the points in the space division. A way to compute the similarity between the descriptors in order to be robust to the sensor's orientation is also presented in the paper. This descriptor is then used to detect loop-closure.

[23] presented an algorithm for the registration between a local point cloud and a large-scale point cloud. The system is based on the selection of local subsets, called super-points, which are described with unsupervised auto-encoders. The super-points from the local measure are matched to the ones of the large-scale point cloud acting as base. These matches are then used to make a coarse registration, later refined by an Iterative Closest Point (ICP) method. [START_REF] Qi | Pointnet: Deep learning on point sets for 3d classification and segmentation[END_REF] proposed PointNet, a deep neural network taking raw 3D point clouds and learning local features. The initial work focus on classification and segmentation tasks but it has opened the door of deep neural network to point cloud based systems.

[25] presented a place recognition solution based on PointNet and NetVLAD [START_REF] Arandjelovic | Netvlad: Cnn architecture for weakly supervised place recognition[END_REF]. The first one is used to extract local descriptors, shortened of its maxpool aggregation layer used for its original purpose. NetVLAD is then fed with these descriptors in order to extract a global descriptor.

[13] presented an alternative approach called MinkLoc3D. This approach uses a convolutional neural network to compute local descriptors. A generalized-mean (GeM) pooling is then used to produce global descriptors.

The global descriptors obtained are used in a base-query manner. The measurement, called query, is described and compared to the descriptors available in a database.

C. Intensity-based methods

The geometry-based method may lack the appearance information available in camera-based systems. Most LiDAR provides, in addition to geometric information, intensity information that depends mostly on the texture and material of the object. Fig. 2 shows an intensity image that can be acquired with the Ouster OS1-64 set at 1024 samples per turn. Thus, works were proposed combining this intensity information with the geometric one. [START_REF] Guo | Local descriptor for robust place recognition using lidar intensity[END_REF] proposed a new descriptor, called ISHOT, combining the geometric information, represented by a SHOT descriptor [START_REF] Tombari | Unique signatures of histograms for local surface description[END_REF], [START_REF] Tombari | A combined texture-shape descriptor for enhanced 3d feature matching[END_REF], to the intensity. This descriptor is then used in a place recognition algorithm for local descriptor evaluation and mapping. Fig. 2: Intensity image reconstructed, the data is from an experiment of [START_REF] Lasguignes | Icp localization and walking experiments on a talos humanoid robot[END_REF], it has been divided in two parts for visibility purposes.

[30] proposed to use the vision-based ORB descriptor of [START_REF] Rublee | Orb: An efficient alternative to sift or surf[END_REF] applied to the LiDAR intensity. The ORB features are then converted into a bag-of-words vector using DBoW [START_REF] Galvez-López | Bags of binary words for fast place recognition in image sequences[END_REF] and compared to a database.

D. Attention-based methods

Point Contextual Attention Network (PCAN) [START_REF] Zhang | Pcan: 3d attention map learning using contextual information for point cloud based retrieval[END_REF] is a neural network adding an attention map in the process. The system extract local features using PointNet. Then these features are fed to PCAN that output a per-point attention map, used to tune NetVLAD which is used to aggregate the local features into a global descriptor.

[33] proposed a self-attention and orientation encoding network (SOE-NET). They integrate an orientation-encoding process into PointNet to extract local features. A self-attention unit influencing the aggregation performed by NetVLAD is applied on the set of features to extract a global descriptor of the input point cloud.

III. VLAD-BASED SOLUTION TO THE KIDNAPPED ROBOT

PROBLEM

In this section, we discuss the solution proposed. We also discuss the results obtained and some observations made during this work. More details on what is presented can be found in [START_REF] Gobin | Localisation d'un robot humanoïde TALOS par information géométrique et visuelle combinée à l'apprentissage[END_REF].

A. Pipeline

The proposed solution is based on the pipeline of Point-NetVLAD [START_REF] Uy | Pointnetvlad: Deep point cloud based retrieval for large-scale place recognition[END_REF]. During a first step, it creates a local descriptor and during a second step it creates a global signature. In our case, it was decided to use the FPFH at a point p as the local signature L (p). Two signatures were tested for the global signature G (C s ) of a cloud C s . One based on the computation of a normalised sum of the local descriptors, the second one using the Vector of Locally Aggregated Descriptors (VLAD) encoding over the FPFH.

B. Local Descriptor: the Fast Point Feature Histogram

Fast Point Feature Histograms (FPFH) [START_REF] Rusu | Fast point feature histograms (fpfh) for 3d registration[END_REF] are features proposed as an improvement of the Point Feature Histogram (PFH) [START_REF] Rusu | Aligning point cloud views using persistent feature histograms[END_REF], [START_REF] Rusu | Learning informative point classes for the acquisition of object model maps[END_REF] which reduces the computational complexity.

PFH has a theoretical computational complexity for a given point cloud with n points of O(n • k 2 ) [START_REF] Rusu | Fast point feature histograms (fpfh) for 3d registration[END_REF], with k the number of neighbors for each point p in the point cloud. FPFH reduces this computational complexity to O(n • k) by reducing the pairs computed.

Taking each pair (p i , p j ) of the query point and a point in the neighborhood (p i being the point in the pair with the shortest angle between its normal and the vector linking the points), a Darboux u × v × n frame is defined as:

u = n i , v = (p j -p i ) × u, w = u × v (1)
Then, three features are computed with:

f 1 = v • n j f 2 = (u • (p j -p i ))/ p j -p i f 3 = arctan(w • n j , u • n j ) (2)
Each pair considered is then stored in an histogram, with the bin index defined as:

idx = 4 ∑ i=1 f i • d f i max -f i min • d i-1 (3)
with []-operator being the integer part operation, d the number of subdivision of the feature's maximum theoretical value range ( f i maxf i min ). After being increased by 1, each bin's value is normalised with the total number of point pairs

(k • (k + 1)/2).
The histogram of these features are computed only on pairs composed of a given point p and its direct neighbors. This simplified histogram is called the Simplified Point Feature Histogram (SPFH).

To compute the final Fast Point Feature Histogram, the SPFH of a seek point is weighted by its neighboring SPFH values:

FPFH(p) = SPFH(p) + 1 k k ∑ i=1 1 ω i • SPFH(p i ) (4)
where ω i represents the distance between p and p i in a given metric space.

Then the final histogram is normalized for each features for comparison purposes. In our work, the FPFH is computed with 33 bins, 11 per feature, using the implementation available in Open3D [START_REF] Zhou | Open3D: A modern library for 3D data processing[END_REF].

C. Global Descriptor 1) FPFH average signature: The first method defined was to group the FPFH computed on each points of the scene in a global one. We propose to define the signature in a bi-channel way composed of:

1) the normalised sum of the descriptors 2) the standard deviation of this normalised sum Given C s a point cloud and a normalisation function Normalize(), the formulations of the normalised sum and its standard deviation are respectively presented in Eq. 5 and Eq. 6.

S (C

s ) = Normalize ∑ p∈C s L (p) (5)
σ S (C s ) = Normalize ∑ p∈C s L (p) 2 (6)
The global signature is then:

G (C s ) = S (C s ) σ S (C s ) (7)
2) VLAD encoded signature: The VLAD encoding is based on a dictionary of words. To obtain this dictionary, it has been decided to use a k-means algorithm.

Given k centroids, the k-means algorithm is performed over the sets of local descriptors of the different views from the data-base used to build the codebook. Once the dictionary obtained, a view is classified by assigning each local descriptor d to a word c i in our codebook using a Nearest Neighbor search. Then, for each word of the dictionary, the distance to its affiliated descriptors in the view is aggregated over each dimension of the local descriptor. The distances for each word are concatenated and used as the VLAD descriptor. This complete encoding allows to reduce a point cloud of n points, with n × 3 informations, to a descriptor of size k × D, with D the dimension of the local descriptor and k the number of words in the dictionnary.

The word association is performed thanks to a Nearest Neighbor algorithm applied on the codebook with the distance defined as an Euclidean distance of FPFH.

The final complete pipeline is presented in Fig. 3. The circled part correspond to the process of building the memory of the system that can be made offline. The bottom part of the figure correspond to the process made online for each new request.

3) Defining the codebook: As stated in the previous section, the VLAD mechanism needs a codebook. This codebook, obtained with the k-means algorithm, presents a main parameter: the number of "words".

This number of words can be either arbitrarily defined or optimised. We tested the two possibilities, with a first codebook defined with 33 words after having tested various values of codebook. A second evaluation was performed with a codebook optimised with the "Elbow Method" [START_REF] Tibshirani | Estimating the number of clusters in a data set via the gap statistic[END_REF]. This method allows to define the optimal number of words to represent a set.

For a set of data D to be clustered with k clusters and K k (D i ) the function that provides the corresponding cluster of the i-th data, the method computes the "Within-Cluster Sum of Squared errors" (WCSS) defined in eq. 8, often called inertia of the k-means fitting.

E (D, k) = ∑ i ∥D i -K k (D i )∥ 2 (8)
Repeating this computation for multiple values of k, we obtain a convexe function of the error. Indeed, the closest the number of words is to the number of data in the set, the smallest the error is. The optimal number of words k opt to represent the set is then defined as the inflection point of this function E (D, k).

The main drawback of such a method is the computation time. To obtain the optimal number of words, the computation needs to be performed over an interval [1; k max ] with a high enough number k max to find the inflection point. To reduce this computation time, the process is performed iteratively. First the inflection point is roughly estimated by computing the WCSS at regular values over the interval [1; k max ]. Then this computation is refined by computing WCSS for more precise values around the previous estimate. This method allows to avoid computing each value in the interval while still keeping a global view of the shape of E (D, k).

As an example, the first evaluation will be made on an interval of [1; 501] with values stepped by 25 to obtain the first estimate k rough . Then the same data is completed with WCSS computed around k rough stepped by 1 to refine the estimation of k opt .

Fig. 4 shows the Elbow method computed for the "Real" dataset. Firstly, E (D, k) is computed with k ∈ [1 : 25 : 501] and the method estimate the inflection point at k opt,1 = 26. Secondly, the computation is refined by computing the WCSS around k opt,1 with k ∈ [1 : 25 : 101]. In the second step, the inflection point is evaluated at k opt,2 = 16. Lastly, the step is repeated with k ∈ [1 : 1 : 31] and the method estimate the final inflection point at k opt,3 = 31.

D. Refining the pose estimation

The process presented above provide the estimation of the pose of the query cloud in the environment as one of the poses of the dataset. However, as the dataset is sampled over the environment, the nearest pose can be spaced from the real pose of the robot. Moreover, as neither the FPFH nor the VLAD are influenced by the rotation of the point cloud and because the LiDAR has a 360 • of horizontal field-of-view, the orientation is not accurate. Therefore, we refined the pose estimated by registering the point clouds from the query and the dataset candidates.

This registration is performed with two steps: a coarse estimation using RANdom SAmple Consensus [START_REF] Fischler | Random sample consensus: a paradigm for model fitting with applications to image analysis and automated cartography[END_REF] and a refinement using a Point-to-Plane ICP [START_REF] Chen | Object modelling by registration of multiple range images[END_REF] method. The RANSAC method is applied using the FPFH computed for the VLAD encoding to estimate correspondences. Then the coarse estimation is used to initiate the locally convergent ICP.

This registration is successively performed on the n top candidates from the VLAD-encoding recognition, n being defined arbitrarily for the tests. Later, the finer alignment, using the alignment scores defined in the original work for each method, is used to give the estimated pose.

E. Datasets

There are 2 datasets that were produced. The first one was produced using a simulated version of the Bauzil Room. A second dataset has been built in a real setup. Fig. 5 shows the real Bauzil Room in 2021 and a simulated version viewed from opposed points of view. 1) Simulated sets: For the simulated experiments, the middle platforms with the stairs were removed from the reality and the simulation. The simulation uses a modeled LiDAR on the architecture and noise-model of the Ouster OS1-64. The database has been generated with the robot placed along a (x, y) grid. The query-base has been built with the robot randomly placed in the room, covering the same (x, y) space as the database. Both bases are generated with the sensor at a constant height of 1.65m, the approximate heigh of the sensor on the robot when in its half-sitting pose. Fig. 6 shows examples of the distribution of the poses from the simulated dataset. In the figure, the bases sizes have been reduced for visualization purposes. Each smaller axis represent a pose present in the database. The data-base shown is generated over a 8 × 11m grid graduated every meter. The query-base is generated with 50 random poses from the same 8 × 11m space.

In the generation of the simulated data-bases and querybases, the orientation is left aside. Indeed, the LiDAR has a 360 • horizontal field of view. Moreover, when we start the robot, it is assumed that the LiDAR (x, y) plane is parallel to the world's (x, y) plane.

In the case of a noiseless sensor, the data is really smooth and the FPFH descriptors are highly discriminating as shown in Fig. 7 by the clustering of the FPFH in 4 groups. In this example, the FPFH were computed with a 50cm radius and a limit of 4000 used neighbors.

2) Reality sets: The robot has been put in different places of the Bauzil room with its poses estimated using the available Motion Capture system. Thus, the zone measured has been limited by the zone covered with the Mocap cameras. Again, the measures for the data-base were taken with an approximate 1m grid on (x, y) axes. Whereas the query-base is taken with random (x, y) positions. Moreover, the clouds were captured on positions where the robot was standing still for 10s to avoid noise from the robots movements.

IV. EXPERIMENTAL RESULTS

This solution has been evaluated on three VLAD codebook created using the proposed method. Two were build using the real and the simulated datasets, and are respectively called "Real" and "Simulated". The third one was created from merging the real and simulated dataset and is called "Combined". Each dataset consists of a data-base and a querybase. The experiments are summarized in Table I. TABLE I: Data-base and Query-base for the tests performed, with their respective number of clusters in the codebook of the data-base and queries in the query-base.

Both pose estimations steps are evaluated: the VLADencoding recognition, the RANSAC coarse registration and the ICP refinement.

A. VLAD-encoding registration

To define the results, it is proposed to compare 3 positions, visible in Fig. 8: The Ground Truth (GT) position of the robot, the Nearest position existing in the data-base, considered as the must give from the system, and the Recognized position given by the system. A test is then considered as correct if the system has given the Nearest position as the Recognized one.

Table II summarize the percentage of correct matches in the top candidates, according to the previous statement.

We can observe that the system succeed poorly on the top candidate for the "Real" but the good recognition stays mainly (FPFH radius: 0.5 meter, FPFH maximum neighbors: 4000) in the 5 top candidates. For the "Simulated" and "Combined" tests, we can observe that in 3 tests out of 4, the nearest pose in the data-base is given as the top 1 candidate. Going down to the 5-th candidate rise significantly the percentage of success.

The results for both cases are promising for the efficiency of the RANSAC and ICP refinement as there are high probability to register two close data.

B. RANSAC coarse estimation

For the RANSAC and ICP estimations, the error evaluated is the final translation error and the rotation error, as a global rotation and as Roll-Pitch-Yaw errors. A case is considered successful if the error in translation is below 10cm and the error in rotation is below 5 • . These thresholds have been fixed relatively to the problematic: initializing the localization system presented in [START_REF] Lasguignes | Icp localization and walking experiments on a talos humanoid robot[END_REF]. We experimentaly determined that the localization mechanism needs an initialization with 50cm of translation tolerance and 30 • of rotation in the ⃗ z-axis.

Table III present the percentage of queries for which the system respects either one of our criteria or both, using only the RANSAC refinement. The results shows that RANSAC has a high level of success for the orientation estimation. However, the translation criteria is respected in less than half the cases.

Table IV shows statistics of the translation error for each cases. It is observable that for both tests, the mean translation error is not far from the criteria. Table V presents the statistics of the rotation error. We can see that the mean error is of 2

C. ICP refinement

Table VI present the percentage of queries for which the system respects either one of our criteria or both, using and ICP refinement over a RANSAC coarse estimation. The results show an improvement over the RANSAC algorithm. Whereas the rotation criteria is less respected, the percentage of success on the translation criteria is higher. Tables IV and V summarize respectively the translation and rotation statistics on the RANSAC and ICP refinement. These results shows that while the percentage of success is higher, the failure errors are also higher, with a maximal translation error at least multiplied by 6. The FPFH computation and VLAD encoding took a mean time of 10s with 95% of the time allocated to the FPFH computation.

The coarse estimation using the RANSAC algorithm took a mean time of 40s, using the FPFH descriptors previously computed. However, depending of the randomisation, the range of time consummed in the RANSAC estimation goes from 20s to 90s.

Lastly, the ICP refinment, took a mean time of 10s taking as initialisation the RANSAC estimation.

Thus, a complete query took a mean time of 1min10s with longer computations rising up to 2min for a single query. This time consumption is high but acceptable in the case of a single computation when the robot is started or of sparse computation over the time to relocalise the robot in long runs.

V. CONCLUSION

We presented a pipeline to recognize the place from where a LiDAR measurement is taken in a known environment. It is supposed that a quantity of data from the environment taken with the sensor is available to create a database to refer to. The system uses the FPFH descriptor to describe locally the data and a VLAD-encoding to describe the complete measurement. This FPFH+VLAD-encoding is used to compare a new query to the known database, allowing to propose candidates from the database that are close to the request. These candidates are then used to perform a point cloud registration using a Point-to-Plane ICP initialized by a RANSAC estimation.

The systems has been tests with simulated data and measurements taken with a LiDAR in the real environment. The VLAD-encoding recognition shows a percentage of success close to 90% in the 5 best candidates. Using these candidates, the RANSAC and ICP refinement allows to localize the measurement with a mean error of less than 15cm in translation and less than 2 • in rotation.

The results shown are of the order of magnitude of those obtained with deep neural network-based methods such as PointNETVLAD [START_REF] Uy | Pointnetvlad: Deep point cloud based retrieval for large-scale place recognition[END_REF] with 80% of success. However, deep networks are runned on GPU with really fast estimations, in range of 5 -10ms, whereas our solution has only been tested on CPU with a slower computation time. In future works, this system will be deployed on the robot and verified on new environments and databases from the state of the art such as [START_REF] Maddern | 1 Year, 1000km: The Oxford RobotCar Dataset[END_REF] or [START_REF] Liu | A large-scale dataset for indoor visual localization with high-precision ground truth[END_REF] to be compared to other solutions.

Fig. 1 :

 1 Fig. 1: New experimental head of the TALOS robot, with the D435i on the bottom, the T265i in the middle and the OS1-64 LiDAR on the top.

Fig. 3 :

 3 Fig. 3: Architecture of the VLAD-encoding recognition system.

Fig. 4 :

 4 Fig. 4: Computation of the Elbow Method for the "Real" dataset.

Fig. 5 :

 5 Fig. 5: The Bauzil room and its simulated version in Gazebo.

Fig. 6 :

 6 Fig. 6: Visualization of the poses generated distribution. The number of poses is reduced for visualization purposes.

Fig. 7 :

 7 Fig. 7: Visualization of a simulated cloud clustered in 4 groups.

Fig. 8 :

 8 Fig. 8: Visualization of the 3 proposed positions: the Ground Truth in red, the Nearest in orange and a potential Recognized one in blue, other positions in the data-base in black.

TABLE II :

 II Percentage of correct recognitions with the VLAD-encoding depending on the number of top candidates.

  • , below the threshold defined.

	Test	"Simulated"	"Real"	"Combined"
	Success on translation error	36.20%	36.36%	41.94%
	Success on rotation error	99.00%	96.10%	98.61%
	Global success	36.20%	36.36%	41.94%

TABLE III :

 III Percentage of successful estimations with the RANSAC refinement only. (FPFH radius: 0.5 meter, FPFH maximum neighbors: 4000)

	Test	Mean Median	Min	Max	RMS	STD
	"Simulated"	12.69	11.37	1.53	58.69	14.44	6.89
	"Real"	14.45	12.28	2.14	43.44	17.00	8.95
	"Combined"	12.49	10.88	0.88 133.55	15.11	8.49

TABLE IV

 IV

		: Translation error of the pose estimation using
			RANSAC, in cm.
	(FPFH radius: 0.5 meter, FPFH maximum neighbors: 4000)
	Test	Mean	Median	Min	Max	RMS	STD
	"Simulated"	0.0214	0.0170	0.0005	0.2715	0.0295	0.0203
	"Real"	0.0348	0.0306	0.0053	0.0843	0.0401	0.0199
	"Combined"	0.0211	0.0154	0.0001	0.2720	0.0304	0.0219

TABLE V :

 V Rotation error of the pose estimation using RANSAC, in rad. (FPFH radius: 0.5 meter, FPFH maximum neighbors: 4000)

TABLE VI

 VI

	: Percentage of successful estimations with the
	RANSAC+ICP refinement.
	(FPFH radius: 0.5 meter, FPFH maximum neighbors: 4000)

TABLE VII :

 VII Translation error of the pose estimation using RANSAC and ICP, in cm. (FPFH radius: 0.5 meter, FPFH maximum neighbors: 4000) 1) Time consumption: The time consumption of the system has been observed. The computation have been performed on

	Test	Mean	Median	Min	Max	RMS	STD
	"Simulated"	0.0219	0.0006	0.0000 4.3512 0.2758 0.2750
	"Real"	0.0233	0.0186	0.0030 0.2891 0.0422 0.0352
	"Combined"	0.0214	0.0006	0.0000 4.3721 0.2575 0.2566

TABLE VIII :

 VIII Rotation error of the pose estimation using RANSAC and ICP, in rad. (FPFH radius: 0.5 meter, FPFH maximum neighbors: 4000) a computer, using an Intel ® Core TM i5-8400H CPU at 2.50GHz with 32GB of RAM.

ACKNOWLEDGEMENTS

This work was supported by the cooperation agreement ROB4FAM. The use of the experimental platform TALOS was supported by ROBOTEX 2.0 (Grants ROBOTEX ANR-10-EQPX-44-01 and TIRREX-ANR-21-ESRE-0015).