Susanne Fürniss

Innovation crushing cultural memory: harps in South Cameroon

Introduction

Musical instruments are particular carriers of cultural knowledge and history. Their variability over time may be a testimony to the individual or collective creativity which is inherent in a living tradition. Instruments may also be indicators of social, cultural and religious change. The objective of this essay is to illustrate this phenomenon through the study of the eight-stringed ngueme harp among the Fang Ntumu in South Cameroon. 1 On one hand, historical sources -recordings, photos and descriptions -going back to the German colonization at the beginning of the 19 th century show some harps with a sculpture representing a man. On the other hand, the current practice of a harp with a polychrome female sculpture in the context of the syncretic Bwiti cult (see below, p. 2-3). The difference between these instruments -all of them named ngomo or ngueme according to dialectraises the question of how such a change could have occurred 2 . What are the aesthetic or symbolic implications of the transformation of this instrument?

This article illustrates and deepens an observation made in 1985 by Pierre Sallée in his doctoral thesis on the harp in Gabon. 3 This French researcher, who passed away too soon, had noted that, although the Fang no longer remember it, a harp of slightly different morphology had existed in their culture long before the reintroduction of this instrument through the borrowing of the Bwiti cult in which the harp is currently practised among the Fang. I corroborate this finding with material evidence from South Cameroon. 4 [p. 260] Harps in Cameroon, Gabon, and Equatorial Guinea Harps are to be found in Cameroon in the North among Tchadic populations 5 and in the South among the Ntumu (a subgroup of the Fang people), a majority of whom live in Gabon and in Equatorial Guinea (figure 1). In Gabon, the harp is played by several ethnic groups among which the Fang subgroups Ntumu and Mveng or Mvaï in the North and Meke in the Center are the most relevant for the present study.

[p. 261]

The harp among the Fang and related people The Fang play the harp as part of the Bwiti cult. This cult has been taken over from the Tsogho who are supposed to be at the origin of this syncretic Fang ritual. There is a very rich literature concerning this ritual in Gabon (see below, p. 15). The musical and organological aspects have been particularly worked on by Pierre Sallée7 for the whole of Gabon; by Sylvie Le Bomin8 and Émeline Lechaux9 for the Bwete of the Tsogho; and by Marie-France

Mifune 10 for the Bwiti of the Fang, which interests us here. In Cameroon, the cult is named Buti in the Ntumu dialect. Its harp has been described by Hervé Rivière. 11 The harp has a parallelepiped body with a flat base so that the instrument can stand vertically without support. The body is extended upwards by a sculpted summit. Regardless of the ethnic group concerned, this summit shows a more or less stylised female sculpture. According to Sallée,12 this characteristic trait is one of the relevant morphological features to identify the 'Gabonese instrument' -and by extension that of South Cameroon -among the other harps of Africa. More recent field research by Sylvie Le Bomin throughout Gabon, by Marie-France Mifune among the Fang in northern Gabon and by this author in southern Cameroon corroborate this characteristic (figure 2). The Fang instrument is particularly coloured which, according to Marie-France Mifune, 13 is clearly a specific characteristic that distinguishes it from other Bwiti harps at the present time. This is in line with the observation made by Jacques Binet 14 for all the sculptures relating to the Fang Bwiti. The Bwiti harp represents, for the Fang, the first sacrificed initiate, Nyingone Mebeghe, the female ancestor of the Fang cosmogony assimilated in this syncretistic context also to the Virgin Mary. 15 As a result, the different morphological elements allude to the female body.

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Fieldwork in Cameroon 2018-2019

Ntumu harps in Cameroon today

Fieldwork among the Ntumu in 2018 and 2019 led me to three Buti-temples in the town of Ambam, one of which, named Miwaliatsengue, is the original temple in the region. The founder of this temple, Yebe Abesolo Julien, handed over his knowledge to his son Obam Yebe Joseph (figure 10) who was the temple master until his death in 2019. He trained many others in harp-making (figure 3). His son Meli Obam Yebe Anicet (figure 2b) is a gifted craftsman and has guaranteed the safeguarding of knowledge and practice until now. Besides already being a ritual master, he is a harp maker with an extraordinary creativity and sense for diversity and variation. The instruments in the other two temples, Miwaliatsengue 2 and Kokonangondo, were mostly made by disciples of Obam Yebe Joseph. Some of these harps are called 'training' harps which do not feature in the Buti ceremonies, while others are their main support. 16 The sculptures represent a woman with white skin and European features (figure 4). If the hair is visible, it is smooth -often with a parting -and the head is covered with a veil. This veil may be part of the sculpture itself or it may be a piece of cloth placed on the head of the figure who -in a ritual situation -is also dressed in a cape. Sometimes hands are carved, joined in prayer, and allusions to the Christian cross are seen.

[p. 263]

All have a sound board with three sound holes: two small ones -called 'eyes' or 'breasts', a large one called 'mouth' or 'vagina' depending on the symbolic level -and a symmetrical vertical axis, often alternating red and white colours which take up a symbolism that is omnipresent in the cult. While a discussion of the symbolism of shapes and colours of the Buti harps is beyond the scope of this essay, there are several key texts dedicated to this cult. 17

A Ntumu harp: 1990s Cameroon

An inventory of the musical instruments of the Fang Ntumu, published in 1999 by the late French ethnomusicologist Hervé Rivière, shows -besides a Bwiti harp corresponding to the observed characteristics -a different type of sculpture representing a male.18 Rivière gives little contextual information: 'It is played both as a solo and as a vocal accompaniment, as in the fifties in Gabon' 19,20 Therefore, in 2018 I also went to the villages near the small town of Ma'an in which he had conducted his fieldwork between 1995 and 1997, in order to understand the meaning of this very different instrument.

I had the opportunity to meet the maker of this harp, Chamberlain from Nkong Meyos, and to discuss with him the differences between the two types of instruments. The instrument he built for Hervé Rivière is called Akamənam 'defend the village' or Bəwu 'the deceased' [p. 264] corresponding to the eponymous invoking ritual. The male-shaped sculpture is supposed to represent a village chief who has taken good care of his clan. It is used to sing invocations, to ask for the protection of ancestors or to inform the village of a danger. In relation to the name Akamənam 'defend the village', several persons told me independently of each other that, at the beginning of the twentieth century, the harp with a male sculpture had been played by elders in the meeting-place in the middle of the village. During the time of colonisation, harp-playing prevented many men and women from being caught by the German colonial administration. When the Germans came to a village during daytime, they mostly only found the elders while the other adults were in the fields behind the houses. As the Germans loved to listen to music and did not understand Fang language, the elders played the harp in order to warn the other villagers and to tell them to stay away as long as the colonisers were around.

But my interlocutors insisted that the main addressees of harp playing were the ancestors which refers to the second name of this instrument, Bəwu 'the deceased'. The ancestors were called upon during the ceremony Bəwu for help in difficult moments both for the community and individuals. The harp was mobilised when there were problems in the village, particularly in relation to women's fertility problems and land sharing. Traditional wrestling ceremonies Məsing were organised in the latter case and the harp was played the day before the fighting to invoke the support of the ancestors.

Pierre Sallée and René Bureau22 have documented the ancient funerary function of the Fang harp in Gabon: 'The new Fang generations know that such an instrument once existed; they name it ngoma along and specify that its function was funerary; its music accompanied the last sighs of a dying man'. 23 My colleagues Sylvie Le Bomin and Jean-Emile Mbot confirm this aspect 24 with a precision that explicitly mentions the ancestors: if an old and very weak person on the verge of death was late in dying, the harp would have been played to make it easier for them to pass into the other life. It is as if the playing of the harp attracted the ancestors to come and take one of their own.

From a morphological point of view, the harp collected in the 1990s has only six strings made of twisted skin strips. Although the maker of the recent harp gave no information about the number six as such, he underlined that the even number of strings results from the fact that the instrument would have been revealed by the ancestors. The material of the strings, which differs from the nylon used for the current Buti harps, 25 is another indication of the [p. 265] instrument's link with the ancestors. Indeed, according to the people of Ma'an, all instruments played for the ancestors must imperatively be made entirely of natural materials. 26

Museum Artefacts and Written Sources of the early Fang harp

A diversion through the museum collections will be useful to better understand the problem and to get an idea of the older harps, Fang in general and Ntumu in particular. Male-shaped harps can be found in different museums. I have identified twenty-eight Fang harps in museum collections in Europe and Cameroon. 27 Compared to the relative homogeneity of the Bwiti harp, these instruments show a great variety of sculptures, body bases and soundboard mountings, but all of them have eight strings. Whereas eight of them have sculptures of females, seven harps show male figures (figure 6). For many of them, the hair is carved with more prominence than the instrument of Chamberlain 28 like, for example, the instrument housed at the Ethnographic Museum of the 25 The difference in materials for the strings has already been noted by Sallée (1985, p. 55), but without any explanation as to its symbolism. 26 In the particular context of invocation of ancestors, the harp has nowadays been replaced by a large lamellophone, Tam-tam, which is easier and quicker to make than the harp. It has nine lamellas, the odd number signifying its inferiority to the harp. As for the materials of the lamellas, the instrument played outside a ritual context has iron lamellas which will be removed and replaced for the invocation by bamboo lamellas.

27 See the list of inventoried Fang harps in the appendix. The harps have been described and photographed as part of the KUNDI programme by several people: Géraldine Robillard, Noé Coussot, Marie-France Mifune, and Susanne Fürniss.

28 Studies have to be still done however in order to distinguish clearly the representations of African men of merit from European orientated sculptures which might already belong to what nowadays is called 'airport art', i.e. artefacts that have been produced for Western travelers and that allude to Western images.

Forest People in Yaoundé (figure 6a) which represents a typically male hairstyle named àsík in Ewondo language.29 [p. 266] Fifteen other museum instruments represent either a geometrical form, a head of an animal or a sculpture similar to those of the Fang statuary relating to the Byeri cult for the ancestors. 30 These instruments entered the collections between 1935 and 1997 and some of them date back to the end of the 19th century,31 a period prior to the Bwiti cult in Fang culture. They are [p. 267] a bridge to the written sources from the early 20th century that describe observations of precolonial Fang culture and corroborate this special original link to the ancestors that is still in memory nowadays in a small part of the Fang Ntumu country. The same variety is also documented by the Swiss missionary Ferdinand Grebert who stayed in Fang country in the centre of Gabon from 1913 to 1931 and made a precious series of drawings of great precision and beauty (figure 7).

Grebert's drawing also shows a bow-lute with a sculpture relating the instrument to the Byeri cult for the ancestors. A statuette of this type was fixed as a 'guardian' on the lid of the bark boxes containing the skulls of the ancestors who were at the centre of this cult. Some rare harps with sculptures of this type are reproduced as photographs in Laburthe-Tolra & Falgayrette 33 and in Sallée. 34 The ancient Ntumu harp The earliest currently known representations of Ntumu harps from South Cameroon are Günter Tessmann's illustrations published in his ethnographic monograph Die Pangwe. 35 They show either a spoon-like sculpture or a representation of an ancestor's guardian (figure 8a). Tessmann was the head of the Lübecker Pangwe Expedition (1907-1909) and stayed mainly in Ntumu area in Equatorial Guinea and Cameroon between. In the section 'Music' of his monograph -which has been written by Erich Moritz von Hornbostel on the basis of Tessmann's field data -we find the following description of this instrument:

Bowharp, ngomo F[ang], ngüe'me Nt[umu] (cf. Figs. 130 and131). The troughshaped body made of the wood of Alchornea caloneura Pax (ndamaba) is covered with a table made of the bark of Ficus vogeliana Miq. (lo, etito), which is pierced by two sound holes. The upper extension of the body, sometimes carved in the form of an animal or human head, has an arched string carrier made of the wood of the Uapaca guineensis Muell. Arg. (asa'm).36 The eight strings run from pegs (of any wood) through the soundboard and are fastened under it by short crossbars of raphiamark (a special one for each string!). The strings are made either from raffia [p. 268] fibres (kanga dzan) or (less well) from the stems of the orchid Myrsacidiuum productum Kranzl. (anzuma, oko ojob), which have been freed from the outermost layer of bark, or (even less well) from oil palm fibres (kangamalen); finally, as a makeshift, e.g. if a string breaks during playing, twisted strips of stems (nden) of Sarcophrynium velutinum are used (and not fresh ones, but old ones with which cassava rolls are wrapped). The strings are plucked with the bare fingers. The harp is used for accompaniment of songs. The bowed harp of the Pangwe is the descendant of the ancient Egyptian instrument that has advanced furthest to the southwest. 37 33 Philippe Laburthe-Tolra & Christiane Falgayrettes (eds), Fang (Paris, 1992). 34 Sallée, 'L'arc et la harpe', pp 56-57. 35 Günter Tessmann, Die Pangwe: völkerkundliche Monographie eines westafrikanischen Negerstammes (Berlin, 1913), pp 329-330. 36 According to POWO (2019) these trees have no common English names: Alchornea caloneura Pax (Euphorbiaceae), synonym of Discoglypremna caloneura (Pax) Prain, is a forest tree, to 90 ft. high or more. Ficus vogeliana (Miq.) Miq. (Moraceae) is a forest tree, 15-60 ft. high. Uapaca guineensis Muell. Arg. (Phyllanthaceae) is a tree to 90 ft. high, with stilt-roots. 37 Hornbostel, 'Musik', p. 328. 8b), about a hundred kilometres from Cameroon and of which Sallée says: 'The document is of primary importance because it was probably the last specimen of this ancient Fang harp'. 41 Identical Equato-Guinean instruments named nguièmé or ngòmá are to be seen in Aranzadi 42 and in Iñigo de Aranzadi's private collection, dated from the 1950s and originating from the actual region of Kie-Ntem that borders Cameroon and Gabon. 43 The number of strings (eight) seems to be constant. 44 An important difference from today's Buti harps of the Ntumu is the number of two often almost rectangular sound-holes, arranged diagonally on the soundboard. According to Tessmann, the soundboard was made of beaten bark, which is the case only for one instrument in Berlin. 45 However, none of the other historical Ntumu instruments have a painted or otherwise decorated box or soundboard, as is the case today. Tessmann's description does not, however, indicate anything about the base of the instrument. Observation of the ancient Ntumu instruments -photos, drawings and objects -reveals that they all have a foot, which is not in principle the case for Gabonese 38 Ibid., p. 330. 39 Archives CNRS-Musée de l'Homme: https://archives.cremcnrs.fr/archives/items/CNRSMH_E_1959_002_004_003_11, accessed on 16 December, 2020. 40 III C 20582. 41 Sallée, 'L'arc et la harpe', p. 60. 42 Isabela de Aranzadi, Instrumentos musicales de las etnias de guinea ecuatorial (Madrid, 2009), p. 183. 43 Personal communication by Isabela de Aranzadi, 26 May 2021. 44 Hornbostel mentions only in a footnote that a photograph of Trilles (1912, p. 86) would show a seven-stringed instrument. While the photograph in question does not make it possible to determine with certainty the number of strings on the instrument that is depicted, Trilles himself writes elsewhere twice that the harp ngomé (Trilles 1910, p. 175) or mvègne (Trilles 1909, p.955) has seven strings. This might be a regional variant, as Trilles has stayed in Central Gabon among another Fang subgroup. 45 III C 20582.

instruments, 'apart from a few exceptions due to the ancient harps of the Fang'. [START_REF] Sallée | L'arc et la harpe[END_REF] Sallée also highlights the parallelepipedal sound box with a rounded back and the slightly curved stringholder. [START_REF] Sallée | L'arc et la harpe[END_REF] He assumes that the harp with these morphological characteristics is a specific feature of the Ntumu, as much as the poetic and musical practice associated with this instrument. 48 [p. 270] The playing context of the ancient Ntumu harp Written sources from the beginning of the 20th century provide little information about the context of playing the harp among the Ntumu, and Fang in general. Trilles provides an impressive body of songs from oral literature, notably tale-songs or songs relating to myth. [START_REF] Trilles | Les Légendes des Bena Kanioka et le folk-lore Bantou[END_REF] He transcribed and translated not only the lyrics but also the sung melody. The scores contain references to formulas played by the harp.

This instrument is specifically mentioned in connection with a 'Song of Teachings' or 'Teaching of the Ancestor', Esangela. 50 However, the content of the songs noted by Trilles does not seem to be related to the above-mentioned function of establishing the link with the ancestors by invoking their assistance. As to Tessmann, he does not provide any clues as to the ethnographic context and/or function of its playing. Although his monograph contains many linguistic transcriptions, the words of these harp songs are not included.

Figure 9: Transcription by Erich Moritz von Hornbostel51 of a harp song recorded by Günter Tessmann (N° 35) between august 1908 and february 1909 in Bebai, Equatorial Guinea, on the border to Cameroon

[p. 271] However, he not only made descriptions and photographs, but also sound recordings on wax cylinders. These recordings, which are held by the Berlin Phonogrammarchive, contain three recordings of songs accompanied by the harp (cylinders 22, 35 and 36). The only indications given by Tessmann directly on the recordings are, for no. 22 'Solo performance on the Negroe-harp' and for nos. 35 and 36 'Harp with choir'. Hornbostel made the musical transcription of cylinder 35 (figure 9) under the title 'Harp-Song with Choir', but the words are not noted as it is the case for some others of his transcriptions. More than 110 years later, Régis Ollomo Ella, professor of linguistics at the Omar Bongo University in Libreville, would transcribe and translate the words of this song. 52 It is the lament of a distraught orphan. He plays the harp alone in the courtyard and mourns his dead mother who is about to be buried at the foot of a Kevazingo tree, Guibourtia tessmannii, a tree considered sacred.

Refrain: Son of my mother, I'm dying. I am distraught. Who will still say sweet words to me? Soloist: I sing on my harp, poor me, for you are now going to rest at the foot of the Kevazingo. Choir: Refrain Soloist: I wander along the courtyard, as we mourn the nephew of the village Mbang. Choir: Refrain Soloist: I sing on my harp, poor me, for we are crying Mama, the one who gave birth to me. Choir: Refrain Soloist: I go, I come, I wander, because we are mourning the nephew of the village Mbang. Choir: Dear brother, I am dying. I am distraught. Who will still say sweet words to me? Soloist: I sing on my harp, poor me. We mourn Andeme Ndong, my mother.

Choir: Refrain

Here we see that the loop is closed. The context that appears through the lyrics of this song shows its proximity to the funerary context still remembered in [p. 272] recent decades: 'Traditionally, the Fang play the harp in the court of the man who is about to die'. 53 All the information relating to the playing context of the ancient Ntumu harp shows that it belongs to a coherent cultural complex which no longer exists as such today. As we can see by comparing the Ntumu harp made in the 1990s with those collected and documented at the beginning of the 20th century, the memory of the morphological aspects has only been maintained in relation to the sculpture representing a male chief who had well taken care of his community. The instrument as such was no longer in use in that time, which confirms the observation made by Pierre Sallée for Northern Gabon in 1985: 'The instrument is not attested in the Woleu-Ntem today'. 54 In order to understand the particular position of 52 Régis Ollomo Ella carried out this transcription and translation as part of our collaboration in the ARCHIFANG project. See Susanne Fürniss & Régis Ollomo Ella, 'Les enregistrements de musique fang par Günter Tessmann', in Susanne Fürniss, Walzenaufnahmen aus Südkamerun/Enregistrements sur cylindre de cire du Sud-Cameroun. 1907-1909, CD, (Berlin 2021), 126-153. 53 Bureau, Bokayé!, p. 88; the metadata of Herbert Pepper's photograph (figure 9) also mention a lament. 54 Sallée, 'L'arc et la harpe ', p. 55. the Ntumu among the other Fang subgroups, it will be necessary to look closely at the history of their movements and the contacts and influences which, during the first half of the 20th century, shaped the harp and its use within the Buti cult in South Cameroon today.

History: Of migrations and borrowings

The first arrival of the harp in South Cameroon

It is clear that there was a harp among the Ntumu before the adoption of the Buti. A study of their settlement in the area they now occupy and of the cultural history of the last century shows that the harp arrived in two waves and from different directions. The Ntumu have not always been in the area they currently occupy between South Cameroon, North Gabon, and Equatorial Guinea. They arrived in this region with the other Fang subgroups during several decades of a migration which began towards the end of the 18th century in the North-East Cameroonian savannah, probably in the Adamaoua. According to Alexandre, 55 the Fang have arrived around 1850 near Oyem in Gabon -which is less than 100 kilometres south of Ambam in Cameroon. The Ntumu remained in their present area while other sub-groups continued their south-westward progression towards central Gabon and the Atlantic coast where the Fang migration ended at the end of the 19th century.

Tessmann is the first to mention the fact that the Ntumu brought a harp with them during their migration. 56 For his part, Swiderski confirms this hypothesis through mythology: 'The myth tells that when the Fang came from [p. 273] Ozambogha, their homeland, the ancestors, their first parents, father Ngoo and mother Ngoo, recommended that they take with them not only their skulls (bieri), but also their sacred musical instruments [including the Ngombi harp]'. 57 But it is Sallée who brings a precision which makes us understand a possible difference between the Ntumu and the other Fang subgroups that might explain the instrumental particularity of the ancient Ntumu harp:

While there is no doubt that the Fang brought a harp in the nineteenth century, this contribution seems to have been made only by the only Western branch of their migration (Ntumu and perhaps Okak). The Eastern migration, that of the "fierce Osyeba" of the Ogowe, who are none other than the Mëkë according to De Brazza does not seem to have known it. 58 It is assumed that playing the harp was abandoned as a result of the social and religious crises caused by colonisation and increasing Christianisation, which condemned the cult of ancestors (see below, p.15-16). 59 As noted above, a copy of the old harp survived near Minvoul in Gabon until the late 1950s and its memory was revived, albeit truncated, at Ma'an in Cameroon in the 1990s. But in both cases, the practice had not been documented for several decades, as the last testimonies have been collected between 1910 and 1930 approximately. It should be remembered that a large part of the Fang people also live in Equatorial Guinea.

As modern state borders do not correspond to cultural boundaries, the innovative Bwiti movement from central Gabon was also introduced into Equatorial Guinea. From there it spread to Cameroon, but with strong links to Northern Gabon. Indeed, Yebe Abesolo Julien sent his sons and family members to Oyem to perfect their spiritual knowledge.

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The Bwiti, the ancestors, and the harp The Buti harp alone represents profound transformations in Fang culture. The latter experienced a major crisis following colonisation, which fought against traditional social authorities. This was coupled with the missionary repression of the traditional Fang cult of the ancestors, the Byeri 69 a 'familiarist religion of allegiance to the protection of the fathers, esa'. 70 The Fang were thus deprived of their modes of ritual expression and their symbolic capital. 71 In response to this degradation, which led to the gradual extinction of the Byeri, the Fang sought a way to adapt or transform their institutions. Balandier places the first negative effects of colonisation to 1918, which corresponds to the time of the spread of Bwiti among the Fang of northern Gabon. 72 While Louis Perrois indicates that this date corresponds to that of the last manifestations of Byeri, 73 Trézenem 74 places the extinction of Byeri in the 1930s.

There must therefore have been a good twenty years of cohabitation of cults, either within the same subgroup or among different ones.

The borrowing of the Bwiti by the Fang gave rise to the creation of a new ritual institution based on a double syncretism which André Mary calls 'internal' and 'exogenous' syncretisms. 75 Fernandez resumes the process:

Bwiti was, from the first, reformative-type cult of nativistic inclinations. It represented in the early years of the century the attempt by a minority of Fang to rework their own ancestral cult, Bieri, by adding elements from the more elaborate rituals and cosmologies of neighbouring Bantu peoples, with whom the Fang had been brought into contact by their conquest of Northern Gabon. [...] The shift towards Christian symbolism occurred much later. For a surprising length of time Bwiti resisted the authority of Christian evangelisation. After World War II, however, an increasing number of Christian elements found their way into most branches of the cult, so that at the present time there is a Christian dimension to most cult symbolism. 76

Among the elements of internal syncretism, the harp plays an important role in the transformed continuity of the cult of the ancestors. Whereas the latter [p. 276] was materialised by the preservation of ancestor skulls in relic boxes -guarded by sculpted 'guardians' to whom the sculptures of some of the harps seen above resemble -the harp becomes the substitute for these boxes. 77 This is the transformation from the 'cult of the bone' to the 'cult of the harp', 78 a fact confirmed to me by a Buti master in Ambam. In this reinterpretation, the harp as seen by the Fang Mveng 'embodies the spirit of an ancestor'. 79 Studies on the Bwiti in Gabon and the myths relating to this field provide further details about the rooting of the Fang harp in the dialogue between living humans and their dead ancestors. Thus, Swiderski reports the following mythological word collected from the Fang of the Estuary region:

The ngombi [harp] -said the ancestors -is the dwelling of the dead. It is this ngombi who will take your words from the earth to bring them to the dwelling of the dead and who will take the words of the dead to bring them to the earth; this ngombi will be the intermediary between the dead and the living so that they may gather in one place. [...] It is a perfect example of the possible exchange between the dead and the living. 80

But as we have seen above, today's harps represent two sanctified women, the first sacrificed initiate, Nyingone Mebeghe, and the Virgin Mary. Swiderski assumes that the myth of Nyingone Mebeghe would be specific to the Fang since it would be unknown to the holders of the initial Bwiti cult. Playing the harp is seen as a source of strength and blessing that transforms the player's words into sacred words. 81 Thus, the harp is a person, it is initiated, clothed, bathed, it has a proper name and must be treated with the utmost respect. 82 This means that it is not exposed to everybody's eyes. In my attempt to make an inventory of the harps in the three temples of Ambam, I was not able to photograph or see all the sacred harps.

Similarly, for those shown to me, the handling of this sacred body that the harp represents was strictly reserved for community members. The harps are always placed on a mat or a tablecloth. Some, higher in the hierarchy of harps, are placed on a tiger-cat skin, a symbol of royalty and sacredness which isolates the harps from the profane ground.83 [p. 277]

Conclusion

Let us return to my initial questions about the link between the ancient Ntumu instruments documented by Tessmann in 1908-09, the one made in Ma'an in 1995-97 as a reactivation of the memory of the old instrument, and the Buti harps in 2018 with their magnificent creative diversity. Our journey through time, places, written sources, photographs and drawings, objects and recordings helps us to understand the mechanism of cultural transformation that first led to the abandonment of the practice of the ancient harp. Arriving with the Fang during their migration from the North, this eight-string harp has a sculpture at the top of the body representing various beings -animals, ancestors, men -or geometric forms. It has a foot and a laced soundboard. It symbolises a close link with the community of ancestors that humans join when they die. Our journey then showed how another harp arrived from the South by way of the Bwiti cult. It has the same number of strings, a sculpture in the same place, but depicts a Western-type female figure. Moreover, it has a flat base and a nailed polychrome soundboard. The Fang then transposed the initial symbolism to this new harp, while adding others, either from the Fang cosmogony or from Christianity, both of which provide elements of this new religious practice. The importance of this kind of research lies in the fact that in this region, where oral tradition is still predominant as far as cultural practices are concerned, there is hardly any collective memory of the ancient practices of the harp. Also, colonial and post-colonial sources concerning South Cameroon -like museum collections, sound archives and writings gathered in libraries -are scattered over several European countries. The harps in the museums of Yaoundé are very rare exceptions. These sources are not available on a local level, nor on a national or regional one. The access is even more difficult for sources in German language, as the ancient German protectorate Kamerun is now francophone (Cameroon and Gabon) or hispanophone (Equatorial Guinea). Thus, it is important that a study of this singular instrument, the harp, brings together these dispersed data and makes it possible to understand the link between current musical and religious practices and the historical testimonies of precolonial religion, craftsmanship and music.

It must be said that the material transformations and symbolic transfers that the harp has gone through are no longer known to everyone. I met Buti-practicers in Ambam and the most competent bearers of the tradition near the Equatoguinean border, in the villages where Tessmann had stayed in 1908-1909. In this area where the Buti cult is well established, the historical recordings and Tessmann's and Rivière's drawings and photos have not met with a significant response. Fifty years ago, the cultural innovation of the Buti [p. 278] cult has occupied a place that had already been empty for several decades. As the Buti harp has absorbed the symbolic elements of the older instrument, the memory of the older instrument has faded and was replaced by the new one. In a region with less Buti activity, however, the memory has been able to be maintained and transmitted for a longer time. Thus, a century after the last first-hand testimonies of the old harp, we have been able to reconstruct a coherent link between the old and the current harps and corroborate the place of each of them in the cultural history of the Ntumu of South Cameroon.

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Figure 1 :

 1 Figure 1: Map of South Cameroon, Equatorial Guinea, and Gabon6; underlined: Fang subgroups; arrow: area of the author's fieldwork.

Figure 2 :

 2 Figure 2: Bwiti/Buti harps in Gabon and Cameroon: a) Thierry N'No, Fang-Mveng, Gabon, Minvoul; b) Meli Obam Yebe Anicet, Fang-Ntumu, Cameroon, Ambam.

Figure 3 :

 3 Figure 3: Genealogy of harp makers in Ambam, Cameroon.

Figure 4 :

 4 Figure 4: Two Buti-harps in Ambam, Cameroon.

Figure 5 :

 5 Figure 5: A male-shaped harp made in 1995-7 for Hervé Rivière21

Figure 6 :

 6 Figure 6: Male-shaped harps in museum collections: a) Yaoundé, Musée ethnographique des peuples de la forêt; b) Berlin, Ethnologisches Museum: III C 36845.

Figure 7 :

 7 Figure 7: Grebert's drawing of Fang chordophones: A) harp-zithers mver; B) harps engomi; C) and D)bow-lutes akarankam 32 .

Figure 8 :

 8 Figure 8: Ancient Ntumu harps: a) Drawing by Günter Tessmann;38 b) Photo by Herbert Pepper.39

Figure 10 :

 10 Figure 10: Obam Yebe Joseph (1953-2019) at the tomb of his father Yebe Abesolo Julien who introduced the Buti-cult in South Cameroon in the 1970s.

The reader will find in this article several endogenous names for the harp, as well as for the cult in which it is practiced today. The Ntumu of Southern Cameroon are a sub-group of the Fang, of which other sub-groups live mainly in Gabon and Equatorial Guinea. There are several dialects according to which the harp is called ngomo

Régis Ollomo Ella, 'Onyùmə ńyùmà, le règne olfactif chez les Fang-Ntumu du Gabon', Revue d'ethnoécologie, 18 (2020), 2.

Sallée, 'L'arc et la harpe'.

Sylvie Le Bomin, Dossier de presse des nuits de Bwiti, culte des ancêtres des Tsogho du Gabon(Montpellier, 2002); Sylvie Le Bomin et al., 'Ce que "faire ensemble" peut vouloir dire en musique', Cahiers d'ethnomusicologie, 21 (2008), 175-204.

Émeline Lechaux, 'Tisser le fil de la mémoire: contribution à l'histoire des répertoires musicaux des cérémonies de bwétè chez les Mitsogo du Gabon' (PhD, EHESS, Paris & UOB Libreville, 2015).

The harps for training are made without a specific ritual protocol (Mifune, Personal communication, 4 January 2021).

Hervé Rivière, 'L'instrumentarium musical des Ntumu', p. 128.

All translations from non-English speaking sources are by the author.

Rivière, 'L'instrumentarium musical des Ntumu', p. 126.

Ibid., p. 128.

Bureau, Bokayé!

Sallée, 'L'arc et la harpe', p. 60.

Personal communication, November 2019.

Information from Thérèse Fouda, Director of the MEPF. Ewondo is a Bantu-language from the same group as Ntumu: A70.

Louis Perrois, La statuaire fang: Gabon(Paris, 1972).

The harp from Berlin (IIIC36845, Figure6b) was collected in 1895, but only given to the Museum in 1949.

Ferdinand Grebert, Monographie ethnographique des tribus Fang du Gabon. Unpublished manuscript (Geneva, 1940: Société des Missions évangéliques de Paris), pp. 24-25.

Swiderski, Ibid.,

4 This research has been conducted in the framework of two projects conducted at the Musée de l'Homme in Paris by my colleague Sylvie Le Bomin and myself. The data for this article have been collected thanks to the financial support of several institutions: field work in Cameroon (2018 and 2019) by the Muséum National d'Histoire naturelle (ATM NGI project) and the Alliance Sorbonne Universities directly (KUNDI project) or via the Institut for Heritage OPUS (ARCHIFANG project) ; documentary research in the collections and the Phonogramm Archive of the Ethnology Museum in Berlin via the Collegium musicae

Diffusion of the Bwiti cult and the second arrival of the harp in South Cameroon

As the contemporary harp is closely linked to the religion of the Bwiti, it is necessary to retrace the progression of this cultural practice from its origins in the South of Gabon to the Ntumu, first in Gabon and then in southern Cameroon. While the first Ntumu harp arrived in southern Cameroon with the Fang migration from the North, the 'modern' harp arrived from the South. 60 Indeed, the Bwiti has its origin mainly among the Tsogho and Apinji of southern Gabon. [START_REF] Trézenem | Notes ethnographiques sur les tribus Fan du Moyen Ogooué (Gabon)[END_REF] Today it is practised by many ethnic groups of this country, among whom 'the Fang were the last population to have borrowed it '. 62 As is also the case for the Bwiti of the Tsogho, the Fang have different branches of the cult, which diversifies practices and [p. 274] sometimes makes comparison difficult. 63 In his comparative work on Bwiti music among the Fang in the north and in the centre of Gabon, Sallée shows that there are consistent differences. 64 The encounter of the Fang with this cult took place far from the lands of the Ntumu, in the logging camps of the provinces of Moyen-Ogoué and the Estuary (figure 1), a point of convergence of logging workers coming from several regions of Gabon. 65 It was through this labour migration that the Bwiti cult was first brought into this region by Tsogho and Apinjipeople at the end of the twentieth century. It was then adopted there by other logging workers from different origins. As Marie-France Mifune points out, written sources do not mention the presence of the Bwiti among the Fang before the First World War. 66 Her field research in a Bwiti-community from the branch disumba mongo na bata north of Minvoul, a few kilometres from the Cameroonian border, has made it possible to clarify the time and circumstances of the transmission of this cult to the Fang: according to the original myth collected from the disumba mongo na bata community, the first Fang initiated to the Bwiti would have arrived in the Estuary around 1850 in Pierre Savorgnan de Brazza's boat. He would have been initiated into the disumba branch around 1890. 67 The cult then spread northwards and reached the border of Cameroon, according to Balandier,68 in the period between 1920 and 1925.

In South Cameroon, however, the Ntumu had not yet adopted the Bwiti at that time. In fact, among the three temples of the town of Ambam is the one founded by Yebe Abesolo Julien from which the Buti spread in the region. Yebe Abesolo Julien had been initiated to the branch diboki in Equatorial Guinea in the 1950s. About twenty years later, that is, several decades after it had been attested in the north of Gabon, he introduced this branch of the Buti in Southern Cameroon. The harp, as a key element of this cult, was therefore reimported to South Cameroon in the 1970s only.


Anas Laaraibi
email: rahmane-anas.laaraibi@ens-rennes.fr

Corentin Depontailler
email: corentin.depontailler@ens-rennes.fr

Gurvan Jodin
email: gurvan.jodin@ens-rennes.fr

Damien Hoareau
email: damien.hoareau@ens-rennes.fr

Nicolas Bideau
email: nicolas.bideau@univ-rennes2.fr

Florence Razan
email: florence.razan@ens-rennes.fr

An innovative wearable sensing system based on flexible piezoresistive sensors to estimate upper body joint angle using a Nonlinear AutoRegressive eXogenous Neural Model

Keywords: Wearable sensors, low-energy flexible sensors, smart garment, piezoresistive polymer, upper body movements, body joint angle, BLE, mechanical bending, IoT, NARX. I

The widespread adoption of instrumented textiles has made a significant impact in various domains, encompassing health monitoring, rehabilitation, biomechanics, and sports. This study specifically focuses on the development and evaluation of a smart garment that employs lowenergy flexible sensors embedded within the fabric to effectively monitor upper body movements. These sensors utilize a piezoresistive polymer integrated into the garment and establish a connection with an electronic board for data acquisition. Wireless data transmission is achieved through the utilization of Bluetooth Low Energy (BLE) technology, with the garment showcasing an impressive average power consumption of approximately 10 𝜇W. To ensure the sensor's performance and reliability, a comprehensive characterization process is meticulously conducted utilizing a dedicated test bench. Furthermore, this study conducts a comparative analysis between two distinct estimators utilized for determining the flexion/extension angles of the upper body joint. The first estimator leverages a Nonlinear AutoRegressive eXogenous (NARX) neural network model, while the second estimator employs a viscoelastic model. Through extensive evaluation, it becomes evident that the NARX neural network model outperforms the viscoelastic model, showcasing superior accuracy with a root-mean-square error of 4.85°. Consequently, the NARX neural network model emerges as the preferred option for accurately estimating the flexion/extension angles of the upper body joint.

devices provide continuous monitoring of physical activities, health parameters and lifestyle, thanks to sensors to measure physiological parameters like heart rate, body temperature, and movements. However, the design and optimization of these systems present technical challenges that require innovative solutions and interdisciplinary collaboration.

Several alternatives to wearable technology for monitoring movements are available. These alternatives include video cameras, such as Kinect cameras [START_REF] Kim | Ergonomic postural assessment using a new open-source human pose estimation technology (openpose)[END_REF], GPS and LPS technology like Catapult [START_REF] Catapult | d.). about us[END_REF], optoelectronics systems like Vicon [START_REF] Vicon | Vicon motion systems ltd[END_REF] and Qualisys [START_REF] Qualisys | d.). about us[END_REF], and motion sensors such as IMU sensors [START_REF] Hoareau | Evaluation of in-cloth versus on-skin sensors for measuring trunk and upper arm postures and movements[END_REF] and force/pressure sensors. Each alternative has its own advantages and limitations: video cameras (real-time, limited precision/range), GPS/LPS (accurate position, imprecise tracking), optoelectronics (high accuracy, complex setup), motion sensors (common, design challenges).

In addition to wearable technology, the integration of flexible sensors into garments for monitoring human motion offers significant advantages. Various types of flexible sensors, including capacitive sensors [START_REF] Zhang | Highly sensitive capacitive pressure sensor based on a micropyramid array for health and motion monitoring[END_REF], fiber optic polymers [START_REF] Yue | Flexible wearable optical sensor based on optical microfiber bragg grating[END_REF], piezoelectric sensors [START_REF] Guan | Hierarchically architected polydopamine modified batio3@p(vdf-trfe) nanocomposite fiber mats for flexible piezoelectric nanogenerators and self-powered sensors[END_REF], and piezoresistive polymers [START_REF] Jeong | Finger-gesture recognition glove using velostat[END_REF], have undergone extensive research and have been proven effective in accurately sensing pressure or strain to monitor movement.

Yu et al. [START_REF] Yu | Human motion state recognition based on flexible, wearable capacitive pressure sensors[END_REF] discussed the development of a novel type of flexible, wearable capacitive pressure sensor aimed at recognizing human motion states. The article recognizes that the effectiveness of flexible sensors in recognition has been limited by factors such as sensor sensitivity and stability. Accurately discerning changes in capacitance values of the sensor has also been a challenging task due to noise interference. Wang et al. [START_REF] Wang | Flexible and optical fiber sensors composited by graphene and pdms for motion detection[END_REF] presented the development of a stretchable optical fiber sensor made with graphene and PDMS. The sensor is capable of detecting human movement and has potential applications in health monitoring systems. However, the article mentions that the sensor's sensitivity may be affected by temperature changes, and its performance may degrade over time due to environmental factors. Mokhtari et al. [START_REF] Mokhtari | Wearable electronic textiles from nanostructured piezoelectric fibers[END_REF] discussed the potential of nanostructured piezoelectric fibers in smart garments, focusing on applications such as energy harvesting and force measurement. The article acknowledges the challenges associated with widespread adoption and emphasizes the need to enhance durability, washability, and comfort for long-term viability. Zhang et al. [START_REF] Zhang | Static and dynamic human arm/hand gesture capturing and recognition via multiinformation fusion of flexible strain sensors[END_REF] proposed a method for capturing and recognizing human arm/hand gestures using flexible strain sensors. However, the study acknowledges several challenges in the field, including the need to address inconsistencies in capturing dynamic behaviors and the lack of accurate gesture recognition techniques. Abro et al. [START_REF] Abro | A novel flex sensor-based flexible smart garment for monitoring body postures[END_REF] conducted a study on a flexible smart garment integrating flex sensors to monitor body postures. The study emphasizes the benefits of flex sensors but also reveals important limitations in the smart garment context. Notably, flex sensors cannot withstand washing, have a restricted range of motion, and are unidirectional. Furthermore, their fragility poses an additional drawback.

Recent research has demonstrated exceptional detection performance; however, the seamless integration of the technology has not yet been fully optimized, and certain commercial solutions have been constrained by price or performance limitations. Notwithstanding these constraints, piezoresistive sensors have garnered significant popularity in various scientific advancements due to their cost-effectiveness and flexibility. Consequently, they are well-suited to fulfill the current requirements for human motion detection.

Our manuscript focuses on the development of a low-cost and portable sensing system utilizing flexible piezoresistive sensors to estimate the angle of the upper body joint. Our approach entails comparing different models to comprehensively analyze the data acquired by the sensors, enabling us to deliver precise and reliable angle measurements.

The article begins by introducing a garment incorporating piezoresistive sensors connected to an electronic board, ensuring the system's portability. We demonstrate the garment's capability to detect resistance changes corresponding to alterations in joint angles while simultaneously examining the system's energy consumption. Subsequently, we describe the design and characterization process of the piezoresistive sensors, which comprise a piezoresistive elastomer and a conductive textile. These sensors are integrated into a fabric and sewn using a sewing machine, after which they undergo comprehensive characterization on a dedicated test bench. The resulting solution is not only cost-effective but also reliable, enabling resistance measurements of the sensors during static and dynamic movements. The paper concludes with a comparative analysis of two models: a neural network model and a viscoelastic model. We assess their effectiveness in estimating the bending angle of the upper body based on the measured resistance.

II. SYSTEM DESCRIPTION

A. Description of the piezoresistive effect

The piezoresistive effect is a change in the electrical resistivity of a material when mechanical stress is applied, as illustrated in Fig. 1. In other words, the application of mechanical pressure, tension, or bending decreases the distance between charge particles within the Velostat and increases the number of conductive paths, leading to resistance variations. The designed sensor is based on a single layer of polyolefins carbon black, namely, Velostat (3M Electronics division, Saint Paul, USA) [18]. It is a piezoresistive material made of polymer sheet and having a high resistivity (<500 Ωcm). It can be used in flexible electronics, portable electronics and matrix sensors.

The sensitivity of the Velostat to applied pressure is mainly defined by two physical factors: quantum tunneling and percolation [START_REF] Dzedzickis | Polyethylene-carbon composite (velostat®) based tactile sensor[END_REF].

Quantum tunneling affects the conductivity of a composite material when the distance between the conductive particles inside the polymeric materials varies due to the applied pressure, which deforms the material. Therefore, the particles in the Velostat interact electrically through interparticle tunneling.

The percolation is related to a change in conductivity between the insulating and the conductive state of a material caused by the change of applied pressure.

The system's complete resistance consists of two parts: a) the contact resistance between the electrodes and the piezoresistive polymer, and b) the piezoresistive effect. This results in a significant change in resistance when we manipulate the sensor, providing it with the sensitivity to detect the application of a load (i.e., applied pressure or mechanical deformation).

B. Smart Garment

1) Sensors description: Our proposed smart garment comprises four embedded piezoresistive sensors. Each sensor design adopts a sandwich structure consisting of five layers, as illustrated in Fig. 2. The sensor construction begins with a layer of Velostat positioned at the middle, with two conductive textile tapes placed above and below the Velostat.

The conductive textile material used is obtained from an A4 sheet of silver-plated knitted fabric (STATEX Shieldex® Technik-tex P130 + B [START_REF] Statex-Shieldex-Techniktex | Statex shieldex techniktex p130 + b()[END_REF]). It is composed of 78% Polyamide and 22% Elastomer, serving as electrodes to provide the necessary voltage to the piezoresistive material.

To ensure optimal contact between the electrodes and Velostat, a non-conductive thread has been used to sew the conductive textile onto the piezoresistive material. Furthermore, we have incorporated a layer of polyimide, specifically Kapton®, which serves two crucial purposes:

• Firstly, the inclusion of Kapton minimizes potential interference in voltage changes, ensuring precise and accurate sensor readings. By reducing external disturbances, we can obtain reliable data on the garment's movement detection capabilities; • Secondly, Kapton acts as a protective barrier, effectively isolating the sensors from the external environment. This shielding helps safeguard the sensors from potential damage or contamination, thereby prolonging their lifespan and maintaining their functionality over time.

These sensors demonstrate dynamic resistance changes across a defined mechanical angular range spanning from 5 to 160 degrees. Furthermore, in accordance with prior research [START_REF] Laaraibi | Flexible dynamic pressure sensor for insole based on inverse viscoelastic model[END_REF], it has been established that these sensors also exhibit sensitivity to pressure.

2) Sensors positioning on the garment: Proper placement of the sensors on the garment is crucial for identifying areas where mechanical bending can be applied to the sensors. For this study, we opted to integrate the sensors at the back of the shoulders and on the elbows. Fig. 2 illustrates the sensor locations on the garment.

The dimensions of the sensors have been chosen in relation to the studied zone in order to capture the pressure and the mechanical flexion of the elbows and the shoulders. For this reason, the elbow sensors are 10 cm x 7 cm and the shoulder sensors are 7 cm x 5 cm. The designed piezoresistive sensors are sewn with classic sewing thread on the garment. Moreover, the electrical connection of the sensors with the electronic board is made by winding the conductive wires around the copper areas on both the top and bottom layers.

The smart garment composed of 4 piezoresistive sensors (𝑁 𝑠 = 4) validates the presence of motion by simply detecting changes in resistance. To capture the signals, a customized printed circuit board (PCB) has been developed. It incorporates a voltage divider bridge to convert the resistance variation (output from the piezoresistive sensors) into voltage changes. Additionally, an electronic board, namely the Nano 33 BLE (Arduino, Ivrea, Italy), equipped with an analog-to-digital converter (ADC) and a Bluetooth module is integrated to transmit the converted data to a laptop running a custom algorithm within the MATLAB environment.

3) Dynamic behavior and quantitative results: In the analysis of the garment-based detection system depicted in Fig. 3 Fig. 3 (1) illustrates the observed detection in the right elbow sensor (blue area) during a 135°flexion. Similarly, the red area in Fig. 3 (2) depicts the response of the left elbow sensor to the same flexion. It is important to note that a value of 𝑁 𝑟 less than 1 indicates the detection of a flexion. Fig. 3 (3) illustrates the movement of the left shoulder and a 90°flexion of the left elbow, resulting in a decrease in resistance in both the shoulder and elbow sensors. This change is visually represented by the purple area.

On the other hand, Fig. 3 (4) displays the movement of the right shoulder (yellow area), which differs from that of the left shoulder. In this scenario, the right elbow remains unflexed, maintaining its initial position at 0°. Consequently, the variation in resistance is only detected by the right shoulder sensor.

The normalized resistance evolution from Fig. 3 demonstrates the potential of integrating flexible sensors into clothing to detect movement, specifically changes in angle. The remainder of the article focuses on a methodology to reconstruct the rotational angle from resistance measurements obtained from a single sensor.

4) Resistance measurement technique:

As presented on the electrical diagram on Fig. 4, resistance measurements are made through the General Purpose Input/Output (GPIO) ports using a voltage divider bridge, placing the sensor resistance, 𝑅 𝑖 𝑠𝑒𝑛𝑠𝑜𝑟 , in series with a fixed known reference resistor, 𝑅 𝑟 𝑒 𝑓 . The analog input voltage of the analog to digital converter (𝑉 𝑖 𝑜𝑢𝑡 ) is linked to the resistance by equation [START_REF] Aroganam | Review on wearable technology sensors used in consumer sport applications[END_REF].

Where, 𝑉 𝑖 𝑜𝑢𝑡 the voltage at the sensor, 𝑉 𝑖𝑛 the supply voltage, 𝑅 𝑖 𝑠𝑒𝑛𝑠𝑜𝑟 the i-th sensor resistance and 𝑅 𝑟 𝑒 𝑓 the reference resistor. A 470Ω reference resistor 𝑅 𝑟 𝑒 𝑓 is chosen to maximize the output voltage amplitude across the entire 𝑅 𝑖 𝑠𝑒𝑛𝑠𝑜𝑟 range of 10KΩ to 100Ω.

C. System energy consumption

The analysis of the system's energy consumption involves estimating the average power consumption for each transmitted data frame between the system and the laptop and calculating the operating time. The average power of the system, denoted as 𝑃 𝑎𝑣 , is determined using Equation (2) and is found to be 56 mW.

𝑃 𝑎𝑣 = 1 𝜏 ∫ 𝜏 0 𝑉 𝑠𝑡𝑜𝑟 (𝑡) • 𝐼 𝑠𝑦𝑠𝑡 (𝑡) • d𝑡, (2)
The time interval between 0 and 𝜏 which is used to calculate the average power, corresponds to a whole number of program operation periods once the system reaches a steady state.

As explained in Section II-B.4, the sensors are powered by GPIOs through a bridge divider. The GPIOs alternate driving the voltage dividers to interrogate all the sensors, with an interrogation duration of 𝑡 𝑜𝑛 = 750 𝜇s occurring every 100 ms. To save energy, the GPIOs are not driven most of the time.

The average power consumption of the garment sensors, denoted as 𝑃 𝑎𝑣,𝑔𝑎𝑟 𝑚𝑒𝑛𝑡 , is indeed 10 𝜇W, as given by Equation [START_REF] Iqbal | A review of wearable technology in medicine[END_REF].

𝑃 𝑎𝑣,𝑔𝑎𝑟 𝑚𝑒𝑛𝑡 (𝑡) = 1 𝜏 𝑁 𝑠 ∑ 𝑖=1 𝑉 2 𝑖𝑛 (𝑡) 𝑅 𝑟 𝑒 𝑓 + 𝑅 𝑖 𝑠𝑒𝑛𝑠𝑜𝑟 (𝑡) • 𝑡 𝑜𝑛 𝑁 𝑠 , (3)
In this equation, 𝑁 𝑠 is the total number of sensors, and 𝑅 𝑖 𝑠𝑒𝑛𝑠𝑜𝑟 represents the resistance of the i-th sensor. Furthermore, the developed smart garment is equipped with a rechargeable lithium-ion battery consisting of a single cell with nominal characteristics of 3.7V and 380mAh. With the observed power consumption, the battery can ensure a lifetime of 25 hours, which corresponds to over 3 days of daily use for 8 hours each day.

III. CHARACTERIZATION OF PIEZORESISTIVE SENSORS AND EXPERIMENTAL SETUP

A. Design of piezoresistive sensors

In this section, we provide a comprehensive characterization of a piezoresistive textile sensor, aiming to gain a deeper understanding of the material's behavior and establish a link between the sensor's resistance measurements and the bending angle. The tested sensor design follows a sandwich structure, as depicted in Fig. 5.

B. Experimental setup 1) Electromechanical characterization of conductive textile alone:

Prior to characterizing the realized piezoresistive sensor, we conduct thorough static and dynamic studies on the conductive textile alone. These studies serve as a crucial foundation for understanding the behavior and properties of the conductive textile, which plays an integral role in the sensor. By examining the conductive textile in isolation, we gain valuable insights into its electrical conductivity, mechanical stability, and performance under various conditions. This preliminary analysis ensures a comprehensive understanding of the conductive textile's characteristics, forming a solid basis for subsequent characterization and evaluation of the complete piezoresistive sensor.

The static characterization involves subjecting the conductive textile strip to a tensile test on a specialized test bench, as depicted in Fig. 6. This test allows us to study the behavior of the textile and record its resistance as a function of the length of stretching. To measure the variation in resistance, we utilize the analog output of an Arduino through a voltage divider bridge, as explained in section III-B.2. Simultaneously, the length of stretching is determined using an ultrasonic telemeter, ensuring accurate data collection. In the dynamic study, we sew the conductive textile onto the garment at the elbows, enabling us to capture real-time data. The recorded information is then transmitted wirelessly via Bluetooth Low Energy (BLE), facilitating convenient and seamless communication between the sensor and other devices or applications. This dynamic study provides insights into the behavior of the conductive textile during movement and allows for the evaluation of its performance in practical scenarios.

2) Electromechanical characterization of piezoresistive sensors:

Following the characterization of the conductive textile and gaining an understanding of its behavior, we proceed to characterize the developed piezoresistive sensor in the section III-A on a dedicated test bench. During this characterization, we record both the resistance and bending angle of the sensor using a specially designed plastic instrumented hinge. This hinge is constructed using 3D printed PLA and laser cut acrylic, ensuring its precision and durability.

To measure the bending angle, a potentiometer is securely attached at the center of the joint. Its initial position corresponds to a bending angle of 0°, providing a reference point for further measurements. As the sensor undergoes bending or flexing, the potentiometer captures the changes in the bending angle, allowing us to accurately quantify and record the sensor's response.

The experimental device depicted in Fig. 7 consists of several components that play specific roles in the characterization process. It includes a rotating joint (2) responsible for applying mechanical bending to the tested piezoresistive sensor (1). Additionally, a reference angle sensor in the form of a potentiometer ( 5) is incorporated to measure the angle of rotation, denoted as 𝜃. The acquisition card (3) is utilized to collect and process data from the sensor.

During the process of characterization, the electrical resistance of the piezoresistive sensor is precisely measured utilizing an Arduino board, specifically designated as 𝑅 𝑏𝑒𝑛𝑑𝑖𝑛𝑔 . This measurement procedure offers valuable insights into the sensor's electrical characteristics and its behavior when subjected to mechanical bending. To accurately determine the resistance of the sensor, a voltage divider configuration was employed, as visually depicted in Fig. 8. The corresponding mathematical equation utilized for this determination is represented as Equation 4.

𝑅 𝑏𝑒𝑛𝑑𝑖𝑛𝑔 = 𝑅 𝑟 𝑒 𝑓 • 𝑉 𝑏𝑒𝑛𝑑𝑖𝑛𝑔 𝑉 𝑖𝑛 + 𝑉 𝑏𝑒𝑛𝑑𝑖𝑛𝑔 , (4)

IV. MODELING OF PIEZORESISTIVE SENSORS

This section utilizes two distinct methods to determine the mechanical bending based on the electrical resistance of the sensors. The first approach employs viscoelastic modeling, while the second approach utilizes a neural network model known as Nonlinear AutoRegressive eXogenous (NARX). Both models have been developed utilizing a single dataset containing 6057 samples, all collected at a consistent sampling rate of 10 Hz.

The source code and datasets are available on the following open-source repository: https://gitlab.com/satie. sete/flexangleestimate.

Further comparison between predicted data and measured data for both models has been performed in this paper using the Root Mean Square Error (RMSE) and the normalized error through equations ( 5) and ( 6) respectively.

𝑅𝑀𝑆𝐸 = √ 𝑀𝑆𝐸 = √ 𝜏 1 (𝜃 𝑖 -θ𝑖 ) 2 𝜏
(5)

𝑒𝑟𝑟 (%) = 𝜃 - θ 160 • 100 ( 6
)
Where 𝜃 is the measured reference angle by the test bench, and θ is the angle estimated by both models. The normalization is relative to the maximum observed rotation, i.e., 160°.

The overall view of the modeling of piezoresistive sensors section is represented by the diagram in Fig. 9.

A. Viscoelastic model

Due to the nature of the polymer, which is a viscoelastic material, the resistance of this sensor is a function of the material properties of the polymer composite, the mechanical bending and the strain. The modeling is decomposed twofold, as illustrated in Fig. 10. Linear dynamic viscoelasticity and timeindependent nonlinear piezoresistive relationship are assumed. In our case, a phenomenological approach is used to describe relationship between an imposed bending angle, denoted as θ𝑣𝑖𝑠𝑐𝑜𝑒𝑙𝑎𝑠𝑡𝑖𝑐 , and the corresponding damped response of the resistance as a function of the strain, denoted as 𝜀. As shown in Fig. 11, this relationship is characterized by a nonlinear function proposed in equation [START_REF] Qualisys | d.). about us[END_REF]. Additionally, a set of differential equations, proposed in equations ( 8), [START_REF] Zhang | Highly sensitive capacitive pressure sensor based on a micropyramid array for health and motion monitoring[END_REF], and (10), relate the bending angle to the strain.

𝑅 𝑏𝑒𝑛𝑑𝑖𝑛𝑔 = 𝑅 0 • (1 -𝜀) • 𝑒 -𝛾• 𝜀 , (7)
where, 𝑅 𝑏𝑒𝑛𝑑𝑖𝑛𝑔 denotes the resistance of the sensor, 𝑅 0 the initial resistance, 𝜀 the strain, and 𝛾 the relaxation parameter.

𝜀 = 𝜀 0 + 𝜀 1 , (8) θ𝑣𝑖𝑠𝑐𝑜𝑒𝑙𝑎𝑠𝑡𝑖𝑐
= ( 𝐴 1 • 𝜀 1 ) + (𝐵 1 • 𝜀 1 ), (9)
θ𝑣𝑖𝑠𝑐𝑜𝑒𝑙𝑎𝑠𝑡𝑖𝑐 = 𝐴 0 • 𝜀 0 , (10)
where, θ𝑣𝑖𝑠𝑐𝑜𝑒𝑙𝑎𝑠𝑡𝑖𝑐 the bending angle, 𝐴 0 , 𝐴 1 and 𝐵 1 the internal variables of the viscoelastic model. In this study, we have employed the viscoelastic model described by [START_REF] Laaraibi | Flexible dynamic pressure sensor for insole based on inverse viscoelastic model[END_REF] to estimate the bending angle applied to the sensors.

To estimate the model's bending angle θ𝑣𝑖𝑠𝑐𝑜𝑒𝑙𝑎𝑠𝑡𝑖𝑐 shown in Fig. 10, we require the parameter values 𝐴 0 , 𝐴 1 , 𝐵 1 , and 𝛾 illustrated in Fig. 11. To determine these values, we formulated an optimization problem as presented in Equation 11. To solve this problem, we utilized MathWorks MATLAB with the Genetic Algorithm solver.

The four parameters (𝐴 0 , 𝐴 1 , 𝐵 1 , and 𝛾) were optimized by minimizing the mean square error (MSE) using Equation 11between the measured bending angle 𝜃 on the test bench and the bending angle θ𝑣𝑖𝑠𝑐𝑜𝑒𝑙𝑎𝑠𝑡𝑖𝑐 calculated by our algorithm 1. minimize

𝑥 𝑓 0 (𝑥) = 𝜏 ∑ 𝑖=0 ||𝜃 𝑖 -θ𝑖 𝑣𝑖𝑠𝑐𝑜𝑒𝑙𝑎𝑠𝑡𝑖𝑐 (𝑥)|| 2 (11)
Starting with Algorithm 1, we first determined the strain 𝜀 as a function of 𝑅 𝑏𝑒𝑛𝑑𝑖𝑛𝑔 , 𝑅 0 , and 𝛾 using Equation 7through the trust region dogleg method available in MathWorks MATLAB 2023a software.

Subsequently, we applied the implicit Euler method to solve the standard linear solid model described by Equations 9 and 10 in order to find the bending angle θ𝑣𝑖𝑠𝑐𝑜𝑒𝑙𝑎𝑠𝑡𝑖𝑐 .

B. NARX Model

The NARX (Nonlinear AutoRegressive eXogenous) concept is an extension of the Autoregressive Exogenous (ARX) approach, which is a commonly used technique for identifying linear black box systems. NARX models are a type of recurrent dynamic neural network that are well-suited for modeling a wide range of nonlinear dynamic systems, including time series. This makes NARX models a powerful tool in many different areas, including signal processing, control systems, and more. In particular, they have been used to model and analyze complex systems with nonlinear dynamics, such as financial markets, weather patterns, and biological systems. The flexibility and versatility of NARX models make them a valuable tool for a wide range of applications in science, engineering, and beyond [START_REF] Boussaada | A nonlinear autoregressive exogenous (narx) neural network model for the prediction of the daily direct solar radiation[END_REF].

To improve the performance of the NARX model in nonlinear time series prediction, it is important to take advantage of its memory capacity by incorporating past values of the predicted or true time series. The architecture of the NARX model is depicted in Fig. 12, which employs Tapped-Delay-Lines (TDLs) to create the network's dynamics.

There are two types of NARX neural network architectures, namely :

• Series-parallel architecture (open-loop), given by equation ( 12); • Parallel architecture (close-loop), given by equation [START_REF] Yu | Human motion state recognition based on flexible, wearable capacitive pressure sensors[END_REF]. ŷ(𝑡) = 𝑓 𝑦(𝑡), 𝑦(𝑡 -1), 𝑦(𝑡 -2), . . . , 𝑦(𝑡 -𝑛 𝑦 ),

𝑢(𝑡 + 1), 𝑢(𝑡), 𝑢(𝑡 -1), . . . , 𝑢(𝑡 -𝑛 𝑥 )]

𝑢(𝑡 + 1), 𝑢(𝑡), 𝑢(𝑡 -1), . .

. , 𝑢(𝑡 -𝑛 𝑥 )]

To implement the proposed model, two types of inputs are required: the target output of the neural network denoted 𝜃 and a set of inputs 𝑅 𝑏𝑒𝑛𝑑𝑖𝑛𝑔 that are specific to the system being modeled. The structure of the model, as defined in our study, is illustrated in Fig. 13.

NARX Resistance measurement [Ω] 3D printed joint θ ! NARX [°] Angle measurement θ [°] Time [s]
Fig. 13: Inputs and output for the proposed NARX neural network model, which the bending angle estimated by this model is denoted as θ𝑁 𝐴𝑅𝑋 .

The proposed model is implemented using the MATLAB 2021a software, utilizing a NARX model. The implementation follows Algorithm 2, as outlined below.

The parameters employed in programming this model are outlined in Table I. The necessary data was obtained by conducting measurements on the test bench depicted in Fig. 7. With these settings, the input and target vectors are randomly partitioned into three distinct sets as described below:

Algorithm 2 NARX model

• 70% of the data is allocated for training purposes.

• 15% of the data is reserved for validating the network's generalization and for halting the training process before overfitting.

• The remaining 15% of the data is utilized to independently test the network's generalization ability.

V. RESULTS AND DISCUSSION

A. Experimental results related to textile conductive characterization

Initially, the resistance of the conductive textile alone is determined by assessing its behavior when subjected to stretching along its length using a test bench. This characterization process involves evaluating the conductive textile's resistance in both the weft and warp directions. In Fig. 14, the static characterization results of the conductive textile are presented, where the blue curve depicts a reduction in resistance as the conductive textile is stretched in the weft direction. It is worth noting that the length of stretching is fixed at 10 cm for both the warp and weft directions.

Nevertheless, when the conductive textile is stretched in the warp direction (as shown by the red curve in Fig. 14), it exhibits a parabolic response. This behavior renders the warp direction unsuitable for use as a sensor within the intended range. Consequently, a dynamic characterization is exclusively conducted in the weft direction, which is considered more reliable for the desired purpose.

In the subsequent phase, the conductive textile attached to the elbow is characterized specifically in the weft direction. The objective is to detect movement by monitoring the change in resistance during stretching, as depicted in Fig. 15. This characterization process allows us to establish a relationship between resistance variations and movement, enabling the textile to serve as a reliable sensor. Fig. 15 provides a visualization of the dynamic characterization of a conductive textile. The plot illustrates the weft resistance of the textile (shown by the blue curve) and the corresponding filtered resistance (represented by the red curve).Although the signal remains free from noise, the desired signal exhibits an exceptionally low amplitude, presenting a significant challenge in detection.

During movements, peaks appear before the resistance decreases, making it challenging to identify the specific movement and its progression. The resistances recorded are consistently close to 5 Ω, further complicating the interpretation of performed movements. Additionally, the sensor's behavior remains somewhat unstable, adding to the difficulty in accurately interpreting the detected movements.

However, while textiles alone may not possess sufficient piezoresistive properties to serve as standalone sensors, it has been observed that the resistance of the conductive textile remains relatively stable, typically around 4 Ω. This stability makes it an ideal candidate for use as a flexible and adaptable electrode within a garment-embedded sensor. Further details on this concept will be discussed in the subsequent section of this study.

B. Experimental results related to the piezoresistive sensors

This section provides an overview of the experimental results obtained from the developed piezoresistive sensor, which was described in detail in Section III-A. The performance of the sensor was thoroughly evaluated through comprehensive characterization under both quasi-static and dynamic conditions.

1) Quasi-static characterization: Using the joint test bench shown in Fig. 7, the piezoresistive sensor was characterized to determine its resistance as a function of the bending angle. Quasi-static characterization was performed to avoid any viscoelastic effects, with a 3-minute waiting period between each data point. Consequently, eight different measurement tests were conducted on the studied sensor, and the dispersion and mean values were calculated.

For each data point, eight measurements were realized. From these measurements, the average resistance was calculated, represented by the dashed blue line on the blue graph in Fig. 16. The maximum error bar was calculated by subtracting the maximum measurement from the average, while the minimum error bar was calculated by subtracting the minimum measurement from the average. The results obtained in Fig. 16 illustrate the qualitative behavior of the sensor, which perfectly detect the resistance variations as a function of the angle. Furthermore, we conclude that the repeatability is the main unsolved problem of the Velostat. This is due to the differences observed in the 8 tests.

Subsequently, the sensor underwent continuous cycles of increasing and decreasing angles ranging from 0°to 160°, with a resting period of 3 minutes between each consecutive angle before measuring the resistance. The response of the sensor to increasing (blue curve) and decreasing (red curve) bending angles is illustrated in Fig. 17. As observed in previous characterizations [START_REF] Hopkins | Examination of the performance characteristics of velostat as an in-socket pressure sensor[END_REF], the sensor exhibits hysteresis in both responses, which can be largely attributed to viscoelasticity.

In this context, hysteresis refers to the maximum difference in output observed during the increasing and decreasing phases. To quantify this, the error was calculated as a percentage of the full-scale output using equation 14.

𝐻𝑦𝑠𝑡𝑒𝑟𝑒𝑠𝑖𝑠(%)

= 𝑅 𝑖𝑛𝑐𝑟 𝑒𝑎𝑠𝑖𝑛𝑔 -𝑅 𝑑𝑒𝑐𝑟 𝑒𝑎𝑠𝑖𝑛𝑔 𝑅 𝑚𝑎𝑥 -𝑅 𝑚𝑖𝑛 • 100% (14)
Here, 𝑅 increasing and 𝑅 decreasing represent the responses during ascending and descending bending, respectively, while 𝑅 max and 𝑅 min denote the maximum and minimum values of the sensor responses. The determination of hysteresis followed the same quasi-static characterization process.

2) Dynamic characterization: Fig. 18 depicts the dynamic characterization of the piezoresistive sensor's resistance, along with the corresponding angle 𝜃, as measured on the test bench. The red curve represents the applied rotation angle over time. Initially, the angle is set to zero, followed by progressively increasing dynamic variations. The blue curve illustrates the measured resistance response at the corresponding time instances. Notably, the resistance of the piezoresistive sensor decreases as a result of mechanical bending.

C. Data processing and joint angle estimation

This section presents the results for both viscoelastic and NARX neural network models.

1) Viscoelastic model: The inverse viscoelastic model algorithm, as detailed in Section IV-A, is implemented for analysis. To initiate the parametric optimization process, an initial dataset, as shown in Fig. 19, is utilized. Subsequently, additional datasets will be introduced to evaluate the performance of the model. The viscoelastic model provides a mechanical angle estimate with an RMSE of 12.88°, as demonstrated in Fig. 19. Although this error was calculated using the optimized dataset with a sample size of 6057, only 500 samples are displayed in the Fig.

for brevity.

2) NARX model: The other model that has been implemented is the parallel architecture of the NARX model, as shown in the Fig. 20, with the parameters defined in Table I. Comparing Fig. 19 and Fig. 21, it appears that the NARX model is more accurate for low angles, and has fewer overshoots for high values.

Fig. 22 shows that the majority of the errors are less than 5% for the NARX model, and it clearly indicates that the proposed NARX model is more accurate than the viscoelastic model. The results obtained from the study indicate that the NARX neural network model shows a high degree of accuracy in estimating piezoresistive sensor data, achieving an impressive accuracy of approximately 5°. On the other hand, the viscoelastic model demonstrates an accuracy of nearly 13°. Such levels of accuracy position the proposed wearable garment as a credible alternative in the estimation of elbow and shoulder flexion angles, when compared to other solutions such as the OpenPose system with an RMSE of over 8°for right elbow flexion, or the Kinect system which records an RMSE exceeding 10°for the same task, as reported by [START_REF] Kim | Ergonomic postural assessment using a new open-source human pose estimation technology (openpose)[END_REF].

VI. CONCLUSIONS

In conclusion, this work presents a groundbreaking and cost-effective sensing system that utilizes flexible piezoresistive sensors to accurately estimate the angle of upper body joints. We conducted a comprehensive comparative analysis of two models, a neural network, and a viscoelastic model, to process the sensor data, resulting in precise and reliable angle measurements.

The development of our garment, which incorporates piezoresistive sensors connected to an electronic board, offers a practical and portable solution for detecting resistance changes corresponding to joint movements. Notably, our study highlights the system's low energy consumption, ensuring extended use without frequent recharging.

The meticulous design and characterization of the piezoresistive sensors, utilizing a piezoresistive elastomer and a conductive textile, produced promising results with consistently reliable resistance measurements during both static and dynamic movements. This approach paves the way for numerous applications in healthcare, rehabilitation, and various other fields where accurate joint angle measurement is essential.

Overall, the perspectives for this research are exciting and wide-ranging, with potential applications in various fields. The low power consumption of the proposed system makes it a potential candidate to be power from harvested energy, thus shifting forward the paradigm of wearable sensors towards more integrated and comfortable solutions.

Fig. 1 :

 1 Fig. 1: Velostat diagram with particles inside the material are represented by white circles, (a) normal state; (b) with pressure; and (c) mechanical bending.

Fig. 2 :

 2 Fig. 2: An in-depth look at the smart garment using piezoresistive sensors: (1), (2): Sensors on elbows; (3), (4): Sensors on shoulders; (a): Conductor wires; (b): Electronic board; (c): Battery.

  , changes in normalized resistance values (𝑁 𝑟 ) serve as crucial indicators of movement. The normalized resistance is a criterion defined as follows 𝑁 𝑖 𝑟 = max(𝑅 𝑖 𝑠𝑒𝑛𝑠𝑜𝑟 , 300Ω)/300Ω, with 𝑅 𝑖 𝑠𝑒𝑛𝑠𝑜𝑟 the i-th sensor resistance. These values are reliable indicators used to trigger detection when 𝑁 𝑟 falls below 1, indicating significant motion in the corresponding joint. To ensure the accuracy of the motion data, a sampling frequency of 10 Hz was employed to capture the sensor signals. The dataset used for analysis comprises 700 data samples. However, to maintain space and improve clarity, only 265 representative samples are presented in the Fig.3.

Fig. 3 :

 3 Fig. 3: Motion Detection via Embedded Sensors in Garment: (1) Right Elbow, (2) Left Elbow, (3) Left Shoulder, and (4) Right Shoulder, leveraging changes in normalized resistance values (𝑁 𝑟 ) as indicators of movement; triggering detection when 𝑁 𝑟 is less than 1.

2 Fig. 4 :

 24 Fig. 4: Measuring Resistance with GPIO: Voltage Divider Bridge Method in Action

Fig. 5 :

 5 Fig. 5: Manufacturing of a piezoresistive sensor with electrodes made of conductive textile material: (a) The 5 layers of the sensor, where (1) is the conductive textile tape (0.55 mm), (2) the polyamide elastane fabric, (3) the conductor wire and (4) the piezoresistive layer (0.1 mm thick); (b) The sandwich structure before final closing.

Fig. 6 :

 6 Fig. 6: Test bench made to measure resistance and strain: (1) Conductive textile (10 cm x 5 cm), (2) Sliding guide, (3) Acquisition board, (4) Ultrasonic sensor.

Fig. 7 :

 7 Fig. 7: The joint for the characterization of the piezoresistive sensor as a function of the angle, (1) the piezoresistive sensor, (2) 3D printed hinge, (3) Acquisition board, (4) acrylic, (5) potentiometer.

Fig. 8 :

 8 Fig. 8: Illustration of a Voltage Divider Circuit with a Fixed Reference Resistor (𝑅 𝑟 𝑒 𝑓 = 470Ω) and Sensor Resistance (𝑅 𝑏𝑒𝑛𝑑𝑖𝑛𝑔 ), demonstrating the Supply Voltage (𝑉 𝑖𝑛 ) and Voltage at the Sensor (𝑉 𝑏𝑒𝑛𝑑𝑖𝑛𝑔 ).

Fig. 10 :

 10 Fig. 10: The viscoelastic model of electrical resistance as a function of strain 𝜀 and bending angle θ𝑣𝑖𝑠𝑐𝑜𝑒𝑙𝑎𝑠𝑡𝑖𝑐 .

Fig. 11 :

 11 Fig. 11: Standard Linear Solid (SLS) model.

Fig. 9 :Algorithm 1 4 : 5 : 6 : 7 :

 914567 Fig. 9: Comprehensive diagram for modeling piezoresistive sensors.

Fig. 12 :

 12 Fig. 12: Both NARX network architectures: (a) Series-parallel architecture; (b) Parallel architecture.

1 :

 1 Load data ⊲ Resistance and angle measurement 2: Normalize data 3: Prepare data ⊲ Convert the normalized data into "tonndata" format 4: Choose training function 5: Create NARX network ⊲ Use the "narxnet" function 6: Prepare data for training and simulation ⊲ Use the "preparets" function 7: Set up data division ⊲ Outlined in Table I 8: Train the network ⊲ Use the "train" function to train the network 9: Evaluate the performance of the trained model and analyze its predictions ⊲ Using equations 5 and 6.TABLE I: Parameters used in MATLAB Programming for proposed model.

Fig. 14 :

 14 Fig. 14: Static characterization of the conductive textile, Resistance vs. strain in the weft and the warp direction.

Fig. 15 :

 15 Fig. 15: Dynamic characterization of the conductive textile weft resistance as a function of time: (1) rest position; (2) mechanical bending (90°); (3) maximum bending (135°), where 𝑅 𝑓 𝑖𝑙𝑡𝑒𝑟 𝑒𝑑 is filtered with a low-pass filter of order 2 and a cut-off frequency of 0.3Hz.

Fig. 16 :

 16 Fig. 16: Resistance vs. Mechanical Bending Angle (𝜃) for the Piezoresistive Sensor (with error bars representing minimum and maximum values) .

Fig. 17 :

 17 Fig.17: The response of sensor to decreasing and increasing angle, as well as hysteresis trends.

Fig. 18 :Fig. 19 :

 1819 Fig.18:The mechanical bending 𝜃 measured by the test bench and the dynamic resistance R vs. time.

Fig. 20 :Fig. 21 :

 2021 Fig. 20: Parallel architecture NARX model, where x is the electrical resistance and y is the estimated mechanical angle.

Fig. 22 :

 22 Fig. 22: Histogram of normalized data errors of both viscoelastic and NARX models.

AKNOWLEDGMENT

The authors express their sincere gratitude to Ms. Rozenn Jodin for her invaluable technical assistance in prototyping the integrated textile sensors.

These

This study was funded by the ANR within the framework of the PIA EUR DIGISPORT project (ANR-18-EURE-0022) Abdo-Rahmane Anas Laaraibi and Florence Razan are with OASIS, IETR

Corentin Depontailler born in Troyes, France, earned Bachelor's degrees in Electronics, Electrical Energy and Automation (EEEA) and Science for Engineering (SPI) from the Mechatronics Department of the Ecole Normale Sup érieure of Rennes in 2022. He is currently pursuing a Master's degree in Sciences for the Engineer and Applications (SPIA) at the same institution and has conducted extensive research on the development and evaluation of textile piezoresistive sensors. This research involved fabricating and characterizing the sensors, designing a smart wearable garment that incorporates these sensors, and integrating them into the garment. Additionally, Corentin has investigated the energy consumption of the system and explored the sensors' ability to detect human motion. Through this work, he has gained a deep understanding of the capabilities and limitations of textile-based piezoresistive sensors and their potential applications in wearable technology.

Gurvan JODIN received the B.S. in both mechanical engineering and electrical engineering, from Rennes 1 University, France, in 2011. He received the M.Ed in mechatronics from Ecole Normale Sup érieure de Rennes, and was major of the 2013 "agr égation" teacher competitive recruitment of Industrial Science for Engineering. He received the Ph.D. degree from Polytechnic National Institute of Toulouse, France, in electrical engineering and aerodynamics. After postdocs at Mechanical Engineering Department at Massachusetts Institute of Technology, Boston, MA, USA, and at Ecole Normale Sup érieure de Rennes, he is currently associate professor with SATIE laboratory at Ecole Normale Sup érieure de Rennes, France. His research interests are in eco-co-design complex mechantronics systems. This includes topics in experimental approach, mechatronics, hydrodynamics, sensors, power electronics and smart grids.

Damien HOAREAU received the B.S. degree in both mechanical engineering and electrical engineering, from Rennes 1 University, France, in 2017. He received the M.S and M.Ed degree in mechatronics from Ecole Normale Sup érieure de Rennes in 2018 and 2019. He received the Ph.D. degree from Ecole Normale Sup érieure de Rennes, France, in electrical engineering in 2023. His research interest includes the development of sensing system for sport science and signal processing to monitor athlete parameters to improve performance.

Nicolas BIDEAU was born in France in 1978. He received the bachelor degree in Mathematics from the University of Brest, France, the applied mathematics degree and the mechanics degree from the university Rennes 1. He received the PhD degree in Mechanics from the University Rennes 1, France, in 2009. In 2009 he joined the University of Technology of Compi ègne, France as a postdoctoral researcher in biomedical engineering. Since 2011, he is an assistant professor in biomechanics at the department of sports sciences from the University Rennes 2. His current research interests, as member of the Movement, Sports and Health (M2S) laboratory, include movement analysis, modeling end experimental biomechanics with applications to sports sciences. His main applications focus on biomechanical analysis of the musculoskeletal system from optoelectronic or IMU based motion capture as well as the analysis of the athlete's material and environmental interactions.

Florence RAZAN received a master in physic and electronic in 2002 and a PhD in microsystems of Bordeaux University (France) in 2005. From 2006 to 2020, she was an associate professor with the mechatronic department at ENS Rennes and in SATIE laboratory. She is currently professor at ENS Rennes and IETR group. Her teams interest concerns the development of autonomous biosourced microsystems for movement characterization. Her current work focuses on the development of autonomous and biosourced embedded communicating systems as an interface between humans or humanoid robots and their environment. The main challenges concern the system architecture, the design of autonomous sensors, the integration of an energy recuperator and the development of low-power electronics. Her main research interests focuse on the development of piezoelectric transducers.