Leandro Nole
email: leandronole@hotmail.com

Thierry Frédou

Alex Souza Lira

Lucas Vinícius

Santos Silva

Beatrice Padovani Ferreira

Arnaud Bertrand

Frédéric Ménard

Flávia Lucena

Length-Weight relationship of thirteen demersal fishes from the tropical Brazilian continental shelf

This study provides the length-weight relationship (LWR) for 13 demersal fish species belonging to 11 families and 8 orders. Data were collected in the northeast Brazilian continental shelf during two scientific surveys (2015 and 2017) using a bottom trawl net (side length of body mesh: 40 mm, side length of cod-end mesh: 25mm) at 35 stations between 15 and 60 m of depth. We provide novel LWRs for 4 species and expand the size range of 9 relationships previously established.

INTRODUCTION

Length-weight relationships (LWR) can be very important for stock differentiation, ecological modeling, to infer body condition indices, calculate biomass based on length frequency distributions, and for acoustic surveys (R. Froese, 2006;[START_REF] Vaz-Dos-Santos | Length-weight relationships of the ichthyofauna associated with the Brazilian sardine, Sardinella brasiliensis, on the Southeastern Brazilian Bight (22°S-29°S) between 2008 and 2010[END_REF]. However, despite its importance and the fact that these relationships are easily obtained, they are usually missing for several species, especially those that are not commercially important [START_REF] Freire | Length-weight relationships for fishes caught by shrimp trawl in southern Bahia, Brazil[END_REF].

Along the Brazilian coast, several studies have estimated fish LWRs parameters.

However, these studies mainly focused on the South (e.g. [START_REF] Catelani | Length-weight relationships of fishes from the estuary of the Macaé River, Southeastern Brazil[END_REF][START_REF] Vaz-Dos-Santos | Length-weight relationships of the ichthyofauna associated with the Brazilian sardine, Sardinella brasiliensis, on the Southeastern Brazilian Bight (22°S-29°S) between 2008 and 2010[END_REF][START_REF] Vianna | Length-Weight Relationship of Fish Caught As By-Catch By Shrimp Fishery in the Southeastern Coast of Brazil[END_REF] and Southeast (e.g. [START_REF] Freire | Length-weight relationships for fishes caught by shrimp trawl in southern Bahia, Brazil[END_REF][START_REF] Macieira | Length-weight relationships for rockpool fishes in Brazil[END_REF][START_REF] Passos | Weight-length relationship of 63 demersal fishes on the shallow coast of Parana, Brazil[END_REF] regions. In the continental shelf of northeast Brazil, an area of high biodiversity where many threatened and near-threatened species occur [START_REF] Eduardo | Identifying key habitat and spatial patterns of fish biodiversity in the tropical Brazilian continental shelf[END_REF], only a few LWR references are available for estuarine and shallow water (0-30m) species (e.g Aguiar-Santos, Sampaio, [START_REF] Aguiar-Santos | Length-weight relationships of six fish species from São Marcos Bay, Northeastern Brazil[END_REF][START_REF] Joyeux | Lengthweight relationships for Brazilian estuarine fishes along a latitudinal gradient[END_REF][START_REF] Viana | Length-weight relations of 70 fish species (Actinopterygii) from tropical coastal region of Pernambuco, Northeast Brazil[END_REF]. Here new LWR information is provided for 13 species of demersal fishes occurring along the Brazilian northeast continental shelf.

MATERIAL AND METHODS

The study area comprises the northeast Brazilian continental shelf, between the states of Rio Grande do Norte (5°0'S; 35°0'W) and Alagoas (9°0'S; 35°0'W). Data were collected during a scientific survey, the Acoustics along the BRAzilian COaSt (ABRACOS) expeditions, on board the IRD R/V ANTEA. Sampling was conducted during two cruises, from August 30 th to 20 th September 2015 and 9th April -6th May 2017, using a bottom trawl (side length of body mesh: 40 mm, side length of cod-end mesh: 25mm, entrance dimensions horizontal x vertical: 28 x10 m) at 35 stations. Hauls were performed between 15 and 60 m of depth, for about 5 minutes at 3.2 kt. Fish individuals were identified, measured (nearest 0.1 cm total length, TL) and weighed (nearest 0.01 g in total weight, TW). The LWR values were estimated using the equation: TW = a × TL b , where TW is the total weight (in g); TL is the total length (in cm); a is the intercept of the regression curve (intercept of TW when TL is zero or initial growth coefficient) and b is the regression slope (coefficient indicating isometric or allometric growth) (Rainer Froese, 2006;Rainer Froese, Tsikliras, & Stergiou, 2011).

Prior to calculation of the LWR, outliers for each species were graphically identified using TL vs. TW plots [START_REF] Froese | Empirical relationships to estimate asymptotic length, length at first maturity and length at maximum yield per recruit in fishes, with a simple method to evaluate length frequency data[END_REF] and removed. The fit of the model to the data was measured by the coefficient of determination r-squared (R²).

RESULTS

A total of 13 species belonging to 11 families and 8 orders were analyzed (Table 1). All regressions were highly significant (P < 0.01), with the coefficient of determination (r 2 ) ranging from 0.953 to 0.994 (Table 1). The intercept a varied between 0.00002 (Aulostomus maculatus) and 0.0119 (Haemulon squamipinna), while the value of b varied between 2.67 (Alphestes afer) and 3.58 in (Aulostomus maculatus).

DISCUSSION

This study provides novel LWRs for four species (Bothus ocellatus, A. afer, H. squamipinna and Scorpaena bergii) and expands the size range of nine other relationships (Table 1). For two species, Hypanus marianae and H. squamipinna, we also present record values of maximum total length. The LWR allometric coefficient (b) for all species were within the expected range of 2.5-3.5 (Rainer Froese, 2006), with exception of A. maculatus (b= 3.58). This positive allometric coefficient was obtained from a species with an unusual and elongated body shape. Further, factors as differences across populations, gonadal maturity, sample size, range of specimens size, and techniques of preservation might also have influenced the LWR parameters presented here (Rainer Froese, 2006).

In conclusion, this study provides new LWRs information for thirteen demersal fish species that may be a useful tool in future studies aimed at monitoring and understanding fish populations.

ACKNOWLEDGMENTS

We acknowledge the French oceanographic fleet for funding the at-sea survey ABRACOS 1 and 2 (http://dx.doi.org/10.17600/15005600 / http://dx.doi.org/10.17600/17004100) and the officers and crew of the R/V Antea for their contribution to the success of the operations. The present study could not have been done without the work of all participants from the BIOIMPACT Laboratory.

Thanks also to Michael Maia Mincarone (NUPEM) for species identification and deposition in the Fish Collection of NUPEM. We thank the CNPq (Brazilian National

Table 1 -

 1 Descriptive statistics and parameters of LWRs for 13 demersal fish species from the northeast Brazilian continental shelf. ( † †) Novel 0 length-weight relationships. 1

	Council for Scientific and Technological Development), which provided student
	scholarship to Leandro Nolé Eduardo and Alex Souza Lira and research grant for
	Thierry Frédou, Beatrice Padovani Ferreira and Flávia Lucena Frédou. This work is a
	contribution to the LMI TAPIOCA, program CAPES/COFECUB (88881.142689/2017-
	01), and PADDLE project, which has received funding from the European
	Union's Horizon 2020 research and innovation programme under grant agreement No
	73427.


Leandro Nolé
email: leandronole@hotmail.com

Michael Maia Mincarone

Teixeira Bárbara

Thierry Villarins

Alex Souza Frédou

Arnaud Lira

Flávia Lucena Bertrand

Leandro Frédou

Eduardo Nolé

Bárbara Villarins

Flávia Frédou

Bárbara Teixeira

Thierry Frédou

Alex Souza Lira

Arnaud Bertrand

Flávia Lucena Frédou

Length-weight relationships of eleven mesopelagic fishes from oceanic islands of the Southwestern Tropical Atlantic

Keywords: elongatus (Gonostomatidae), Argyropelecus aculeatus, Argyropelecus affinis, Argyropelecus sladeni, Sternoptyx diaphana, Sternoptyx pseudobscura

à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

INTRODUCTION

In the western Tropical Atlantic, the Fernando de Noronha Archipelago, Rocas Atoll and adjacent seamounts host a remarkable biodiversity [START_REF] Fiedler | Hyperiid amphipods around the seamounts and islands off northeastern Brazil[END_REF][START_REF] Hazin | Review of a small-scale pelagic longline fishery off northeastern Brazil[END_REF]. For this reason, the marine ichthyofauna of this large biogeographic unit categorized as Ecologically or Biologically Significant Marine Areas -EBSA [START_REF] Cbd | Ecologically or Biologically Significant Marine Areas (EBSAs). Special places in the world's oceans[END_REF] has been studied by many authors [START_REF] Dominguez | A pesca artesanal no arquipélago de fernando de noronha (PE)[END_REF][START_REF] Kikuchi | Atol das Rocas, litoral do Nordeste do Brasil -Único atol do Atlântico Sul Equatorial Ocidental[END_REF][START_REF] Oliveira | Population structure and growth of young lemon shark, Negaprion brevirostris (Poey, 1868), at the Atol das Rocas Biological Reserve, Brazil[END_REF]. However, most efforts focused on fishes living near to the surface (0-200 m) and few studies described the mesopelagic zone (200-1000 m depth) of this region, which is considered as one of the most understudied of the world ocean [START_REF] St | A dark hole in our understanding of marine ecosystems and their services: Perspectives from the mesopelagic community[END_REF].

The mesopelagic community is a key resource for higher trophic levels, maintaining part of the marine biodiversity and playing an important role in carbon sequestration and thus on the biological carbon pump [START_REF] Proud | Biogeography of the global ocean's mesopelagic zone[END_REF][START_REF] St | A dark hole in our understanding of marine ecosystems and their services: Perspectives from the mesopelagic community[END_REF]. To better account for the role of this community in the ecosystem structure and function, a prerequisite is to have the necessary biological information. One of such key basic knowledge concerns the length-weight relationships (LWR) that are one of the requisites for fisheries management and conservation [START_REF] Froese | Cube law, condition factor and weight-length relationships: history, meta-analysis and recommendations[END_REF][START_REF] Froese | Editorial note on weight-length relations of fishes[END_REF]. Indeed, LWRs are used to estimate body weight by length measurements, assess the condition factor or well-being of species of interest, as well as for the calculation of production and biomass of a fish stock [START_REF] Froese | Cube law, condition factor and weight-length relationships: history, meta-analysis and recommendations[END_REF]. Despite this, information on LWRs are still lacking for many deep-sea fishes. Here, we provide new LWRs for eleven mesopelagic fish species collected along the northeast Brazilian oceanic islands, in order to increase the biological data and general knowledge of these species.

MATERIAL AND METHODS

The study area comprises the northeast Brazilian oceanic islands, including Rocas Atoll (3°52'S, 33°49'W), Fernando de Noronha Archipelago (3°50'S, 32°25'W) and adjacent seamounts. Data were collected during the scientific survey ABRACOS (Acoustics along the BRAzilian COaSt) conducted on board the RV Antea, from 9th April to 6th May 2017. Mesopelagic sampling was conducted using a micronekton trawl (sidelength of body mesh: 40 mm, sidelength of cod-end mesh: 10 mm) at 35 stations from 0 to 1113 m depth. After capture, the material was fixed in a 4% formalin solution for one month and then preserved in a 70% alcohol solution for proximally six months before processing for length and weight. At the laboratory, species were identified, measured (nearest 0.1 cm of standard length, SL) and weighed (nearest 0.01 g of total weight, TW). All specimens were deposited in the Fish Collection of the Núcleo em Ecologia e Desenvolvimento Socioambiental de Macaé (NPM), Universidade Federal do Rio de Janeiro (NUPEM/UFRJ).

The parameters of the LWR were estimated through the equation: TW = a ×SL b , where TW is the total weight (g), SL is the standard length (cm), a is a constant being the initial growth index and b is the slope of the regression. Prior to the calculation of LWRs, the relationship plots were executed for visual inspection and removal of outliers [START_REF] Froese | Empirical relationships to estimate asymptotic length, length at first maturity and length at maximum yield per recruit in fishes, with a simple method to evaluate length frequency data[END_REF]. The significance of the regression was tested by ANOVA and the degree of association between TW and SL was calculated by the determination coefficient (r 2 ). We only included LWRs for species with n > 30, except for three species for which a wide fish-length range was available.

RESULTS

A total of 11 species belonging to five families and three orders were analysed (Table 1). All regressions were highly significant (P < 0.01), with the coefficient of determination (r 2 ) ranging from 0.9511 to 0.9862. The value of b varied between 2.66 for Sternoptyx pseudobscura and 3.22 for Sigmops elongatus, while the parameter a ranged between 0.0012 for Thysanactis dentex and 0.0250 for Ectreposebastes imus.

DISCUSSION

This work provides the first LWR for six species: S. pseudobscura, B. pedaliota, S. elongatus, T. dentex, M. zugmayeri, and E. imus. LWR information has been previously available for A. aculeatus, A. affinis, A. sladeni, S. diaphana, and M. niger, but it was based on a small length range, small sample size (<5) and/or without the descriptive statistics of the relationships [START_REF] Alpoim | Distribution and main characteristic of fish species on Flemish Cap based on the 1988-2002 EU-surveys in July[END_REF][START_REF] Davison | Mesopelagic fish biomass in the southern California current ecosystem[END_REF].

All species presented here but A. aculeatus and M. niger, have no LWRs available in FishBase. In addition, the highest standard-length values for Bonapartia pedaliota and Ectreposebastes imus are reported herein.

As established by [START_REF] Froese | Cube law, condition factor and weight-length relationships: history, meta-analysis and recommendations[END_REF], the allometric coefficients for all LWRs were within the expected range of 2.5-3.5. These values are reflection of intrinsic characteristics and process of adaptations of each species, as ontogenetic reproductive or environmental variations, mainly between sexes [START_REF] Froese | Cube law, condition factor and weight-length relationships: history, meta-analysis and recommendations[END_REF]. In addition, fixation in alcohol and formaldehyde can affect length and weight measurements through the shrinking and dehydration of specimens. For that reason, we recommend consider the LWRs presented here as being tentative.

Overall, this study increases the knowledge on mesopelagic fishes, providing basic biological information useful for further studies in ecology, conservation, and fisheries assessment.

Table 1 .

 1 Descriptive statistics and parameters of LWRs for 12 deep-sea fishes caught using a micronekton trawl at the northeast Brazilian oceanic 167 islands and seamounts, from 9th April to 6th May 2017. SL = Standard Length, TW = Total Weight, a = initial growth index, b =slope of the

	168
	169	regression and r2 = determination coefficient.
										170
		Taxa	n	SL (cm)	TW (g)	Regression parameters	r2
				Min Max Min Max	a	b (95% CL)
		Stomiiformes
		Gonostomatidae
		Bonapartia pedaliota Goode & Bean, 1896	85	3.7	7.5	0.4	2.7	0.0074 (0.0058-0.0094)	2.94 (2.80-3.08)	0.9571
		Sigmops elongatus (Günther, 1878)	35	4.9	25	0.2	28	0.0015 (0.0009-0.0023)	3.229 (3.07-3.39)	0.9814
		Sternoptychidae
		Argyropelecus aculeatus Valenciennes, 1850	49	3	8.2	0.8 20.9 0.0350 (0.0245-0.0496)	2.996 (2.77-3.21)	0.9529
		Argyropelecus affinis Garman, 1899	260	2.8	7.8 0.31 6.09 0.0218 (0.0183-0.0258)	2.807 (2.70-3.91)	0.9511
		Argyropelecus sladeni Regan, 1908	26	2	6.6 1.15 7.2	0.0425 (0.0257-0.0705)	2.703 (2.39-3.01)	0.9618
		Sternoptyx diaphana Hermann, 1781	600	1.2	4.3	0.1	4.3	0.0570 (0.0370-0.0770)	2.89 (2.79-2.99)	0.9275
		Sternoptyx pseudobscura Baird, 1971	51	1.3	5.6 0.24 6.6	0.0754 (0.0582-0.0970)	2.663 (2.45-2.88)	0.9655
		Stomiidae
		Malacosteus niger Ayres, 1848	33	6.3 18.1 1.5 34.4 0.0057 (0.0009-0.0030)	2.956 (2.74-3.17)	0.9635
		Thysanactis dentex Regan & Trewavas, 1930	35	4.3 14.5 0.1 10.6 0.0012 (0.0009-0.0012)	3.197 (3.07-3.33)	0.9868
		Gadiformes
		Melanonidae
		Melanonus zugmayeri Norman, 1930	20	6.4 19.1 1.06 32.31 0.0036 (0.0018-0.0071)	2.973 (2.68-3.26)	0.9623
		Scorpaeniformes
		Setarchidae
		Ectreposebastes imus Garman, 1899	25	5.2 23.4 3.43 290.3 0.0250 (0.0138-0.0482)	3.025 (2.81-3.24)	0.9728

ACKNOWLEDGEMENTS

We acknowledge the French oceanographic fleet for funding the at-sea survey ABRACOS (http://dx.doi.org/10.17600/17004100) and the officers and crew of the RV Antea for their contribution to the success of the operations. The present study could not have been done without the work of all participants from the BIOIMPACT (UFRPE) and LIZ (UFRJ) laboratories. We thank the CNPq (Brazilian National Council for Scientific and Technological Development) for providing student scholarship to LNE and ASL, and research grant for TF and FLF. This work is a contribution to the LMI TAPIOCA, CAPES/COFECUB program (88881.142689/2017-01), and PADDLE project (funding by the European Union's Horizon 2020 research and innovation programme -grant agreement No. 73427).


Michael Maia Mincarone
email: mincarone@macae.ufrj.br

Teixeira Bárbara

Leandro Villarins

Eduardo Nolé

Antunes Caires

Lucena Flávia

Thierry Frédou

Alex Souza Frédou

Arnaud Lira

Bárbara Bertrand

Bárbara Teixeira

Leandro Nolé

Rodrigo Antunes Caires

Flávia Lucena Frédou

Alex Souza Lira

Arnaud Bertrand

Deep-sea manefishes (Perciformes: Caristiidae) from oceanic islands and seamounts off northeastern Brazil, with comments on the caristiids previously reported in Brazilian waters

Keywords: Caristiidae, mesopelagic fish, western South Atlantic, Brazil

published or not. The documents may come

Introduction

Fishes of the family Caristiidae are rare deep-sea species with broad geographical distribution, occurring in all oceans [START_REF] Kukuev | Materials for the revision of the family Caristiidae (Perciformes ): 3 . Manefishes (Genus Caristius ) from moderate warm waters of the Pacific and Atlantic Oceans with a description of three new species from the Southeast Atlantic (C. barsukovi sp.n., C. litvinovi sp.n., C. walvisensis sp. n.)[END_REF][START_REF] Stevenson | Revision of the Manefish Genera Caristius and Platyberyx (Teleostei: Percomorpha: Caristiidae), with Descriptions of Five New Species[END_REF]. The family comprises four genera and 18 species commonly known as manefishes [START_REF] Stevenson | Revision of the Manefish Genera Caristius and Platyberyx (Teleostei: Percomorpha: Caristiidae), with Descriptions of Five New Species[END_REF].

These species present epipelagic larvae and juveniles, occurring from the surface to the mesopelagic zone, while adults have been reported at depths ranging from 100 to 2000 m [START_REF] Benfield | In Situ video observations of two Manefishes (Perciformes: Caristiidae) in the mesopelagic zone of the northern Gulf of Mexico[END_REF][START_REF] Stevenson | Revision of the Manefish Genus Paracaristius (Teleostei: Percomorpha: Caristiidae), with Descriptions of a New Genus and Three New Species[END_REF], 2013). The caristiids are characterized by having relatively short heads, steep snouts, large eyes, deep and strongly compressed bodies, very long and high dorsal fins and greatly elongated pelvic fins [START_REF] Benfield | In Situ video observations of two Manefishes (Perciformes: Caristiidae) in the mesopelagic zone of the northern Gulf of Mexico[END_REF][START_REF] Kukuev | Materials for the revision of the family Caristiidae (Perciformes ): 3 . Manefishes (Genus Caristius ) from moderate warm waters of the Pacific and Atlantic Oceans with a description of three new species from the Southeast Atlantic (C. barsukovi sp.n., C. litvinovi sp.n., C. walvisensis sp. n.)[END_REF][START_REF] Stevenson | Revision of the Manefish Genera Caristius and Platyberyx (Teleostei: Percomorpha: Caristiidae), with Descriptions of Five New Species[END_REF].

Studies on the taxonomy and distribution of caristiids were historically scarce and fragmented. However, a series of taxonomic revisions has been recently conducted [START_REF] Kukuev | Materials for the revision of the family Caristiidae (Perciformes). 2. Manefishes from the East Atlantic (Redescription of Platyberyx opalescens Zugmayer and description of two new species Platyberyx mauli sp. n. and Caristius andriashevi[END_REF][START_REF] Kukuev | Materials for the revision of the family Caristiidae (Perciformes ): 3 . Manefishes (Genus Caristius ) from moderate warm waters of the Pacific and Atlantic Oceans with a description of three new species from the Southeast Atlantic (C. barsukovi sp.n., C. litvinovi sp.n., C. walvisensis sp. n.)[END_REF][START_REF] Stevenson | Revision of the Manefish Genus Paracaristius (Teleostei: Percomorpha: Caristiidae), with Descriptions of a New Genus and Three New Species[END_REF], 2013) and the knowledge on the taxonomy and the distribution patterns was significantly improved. The family Caristiidae is currently divided into two distinctly pronounced groups: Paracaristiinae and Caristiinae. The Paracaristiinae comprises two genera (Neocaristius and Paracaristius) and five species usually known as "small-mouth" caristiids [START_REF] Stevenson | Revision of the Manefish Genus Paracaristius (Teleostei: Percomorpha: Caristiidae), with Descriptions of a New Genus and Three New Species[END_REF], while the Caristiinae, in turn, includes two genera (Caristius and Platyberyx) and 13 species referred to as "large-mouth" caristiids [START_REF] Stevenson | Revision of the Manefish Genera Caristius and Platyberyx (Teleostei: Percomorpha: Caristiidae), with Descriptions of Five New Species[END_REF].

In the current study, four species of Caristiidae are reported for the first time in Brazilian waters based on specimens collected around Rocas Atoll, Fernando de Noronha Archipelago, and sea mounts off Rio Grande do Norte. Meristic and morphometric data are provided for all specimens examined, and the identity of caristiids previously reported in Brazilian waters is further discussed.

Materials and Methods

The material examined in the current study is part of a large collection of mesopelagic invertebrates and fishes sampled during the ABRACOS expeditions (Acoustics along the BRAzilian COaSt), carried out in October 2015 and April 2017 and conducted by the French RV Antea off northeastern Brazil, including Rocas Atoll, Fernando de Noronha Archipelago, and seamounts off Rio Grande do Norte (Fig. 1). The extensive survey in 80 fishing stations from 0 to 1113 m depth resulted in the collection of 11 specimens of Caristiidae, of which seven where identified at species level. Sampling was conducted using micronekton (body mesh: 40 mm, codend mesh: 10 mm) and mesopelagic (body mesh: 30 mm, cod-end mesh: 4 mm) nets. Trawl depth was continuously recorded using a Scanmar depth sensor fitted on the upper part of the trawl mouth.

Measurements and counts were mostly taken according to Hubbs & Lagler (1947). In addition, "preorbital length" and "predorsal length" were measured along the body axis ("horizontal distance"), from the tip of the snout to a vertical line passing through the anterior margin of orbit (preorbital) and through the dorsal-fin origin (predorsal). This was necessary for comparison with data provided by [START_REF] Stevenson | Revision of the Manefish Genus Paracaristius (Teleostei: Percomorpha: Caristiidae), with Descriptions of a New Genus and Three New Species[END_REF], 2013) (Duane Stevenson & Christopher Kenaley, pers. comm.). Radiographs of specimens were taken using a Faxitron LX-60 to aid fin-rays and vertebrae counts. Specimens were identified according to the keys provided by [START_REF] Stevenson | Revision of the Manefish Genus Paracaristius (Teleostei: Percomorpha: Caristiidae), with Descriptions of a New Genus and Three New Species[END_REF] and [START_REF] Stevenson | Revision of the Manefish Genera Caristius and Platyberyx (Teleostei: Percomorpha: Caristiidae), with Descriptions of Five New Species[END_REF]. All specimens examined were deposited at NPM -Fish Collection of the Núcleo em Ecologia e Desenvolvimento Socioambiental de Macaé, Universidade Federal do Rio de Janeiro (Macaé, RJ, Brazil). Remarks. Morphometric and meristic data for the specimen reported herein are within the range to those recorded by [START_REF] Stevenson | Revision of the Manefish Genus Paracaristius (Teleostei: Percomorpha: Caristiidae), with Descriptions of a New Genus and Three New Species[END_REF] (Table I).

Results

Family Caristiidae

Genus

Genus Platyberyx Zugmayer, 1911

Platyberyx andriashevi [START_REF] Kukuev | Materials for the revision of the family Caristiidae (Perciformes). 2. Manefishes from the East Atlantic (Redescription of Platyberyx opalescens Zugmayer and description of two new species Platyberyx mauli sp. n. and Caristius andriashevi[END_REF] (Fig. 3a) Material Examined. NPM 4473 (1, 138 mm SL), RV Antea, ABRACOS #44A, Brazil, off eastern Fernando de Noronha Archipelago, 03°52'53"S, 32°17'33"W to 03°52'13"S, 32°26'28"W, 0-850 m depth, micronekton trawl net, 28 April 2017, 12:44-13:17h. NPM 4475 (2, 23-33 mm SL), RV Antea, ABRACOS #40B, Brazil, off northern Fernando de Noronha Archipelago, 03°31'12"S, 32°31'49"W to 03°31'03"S, 32°32'49"W, 0-230 m depth, micronekton trawl net, 26 April 2017, 12:14-12:37h. [START_REF] Stevenson | Revision of the Manefish Genera Caristius and Platyberyx (Teleostei: Percomorpha: Caristiidae), with Descriptions of Five New Species[END_REF], Platyberyx andriashevi may be distinguished from all congeners by the following combination of characters: 36 or more vertebrae, 31 or more dorsal-fin rays, and 20 or more anal-fin rays. Platyberyx andriashevi may be further distinguished from its congeners, except P. paucus and P. pietschi, by the presence of laterally flattened, bladelike ventral procurrent caudal rays, and an anteriorly directed hook-like process on the third posterior-most ventral procurrent caudal ray.

Diagnoses. According to

Distribution. Platyberyx andriashevi has been previously reported in the north and southeast

Atlantic, north and southwest Pacific, and Indian Ocean [START_REF] Stevenson | Revision of the Manefish Genera Caristius and Platyberyx (Teleostei: Percomorpha: Caristiidae), with Descriptions of Five New Species[END_REF][START_REF] Okamoto | Records of two manefishes, Platyberyx andriashevi and P. rhyton (Teleostei: Perciformes: Caristiidae), from off the Ogasawara Islands, Japan[END_REF]. The specimens reported around Fernando de Noronha Archipelago represent the first record of Platyberyx andriashevi in the western South Atlantic (Fig. 2).

Remarks. Considering the high meristics and rigidly fixed jaw teeth of P. andriashevi, which argue for placement within the genus Caristius, the species was first described as Caristius andriashevi [START_REF] Kukuev | Materials for the revision of the family Caristiidae (Perciformes). 2. Manefishes from the East Atlantic (Redescription of Platyberyx opalescens Zugmayer and description of two new species Platyberyx mauli sp. n. and Caristius andriashevi[END_REF]. However, due to the presence of a conspicuous lateral line, and its caudal skeleton similar to that of P. paucus and P. pietschi, [START_REF] Stevenson | Revision of the Manefish Genera Caristius and Platyberyx (Teleostei: Percomorpha: Caristiidae), with Descriptions of Five New Species[END_REF] placed the species into the genus Platyberyx.

Morphometric and meristic data for the specimens reported herein were within the range of those recorded by [START_REF] Stevenson | Revision of the Manefish Genera Caristius and Platyberyx (Teleostei: Percomorpha: Caristiidae), with Descriptions of Five New Species[END_REF], except for the number of pectoral-fin rays (19 vs. 17-18), and the peduncle length (8.5-13.0 vs. 12.0-18.9 %SL), respectively (Table I).

Platyberyx paucus Stevenson & Kenaley, 2013

(Fig. 3b) Material Examined. NPM 4474 (1, 85 mm SL), RV Antea, ABRACOS #44A, Brazil, off eastern Fernando de Noronha Archipelago, 03°52'53"S, 32°17'33"W to 03°52'13"S, 32°26'28"W, 0-850 m depth, micronekton trawl net, 28 April 2017, 12:44-13:17h. NPM 4511

(1, 97 mm SL), RV Antea, ABRACOS #35, Brazil, sea mounts off Rio Grande do Norte, 04°19'37"S, 35°29'52"W to 04°18'32"S, 35°32'20"W, 0-630 m depth, micronekton trawl net, 20 April 2017, 22:35-23:15h. NPM 4512 (1, 91 mm SL), RV Antea, ABRACOS #39, Brazil, off Rio Grande do Norte, 04°52'30"S, 34°35'23"W to 04°50'53"S, 34°51'05"W, 0-800 m depth, micronekton trawl net, 24 April 2017, 21:49-22:37h. [START_REF] Stevenson | Revision of the Manefish Genera Caristius and Platyberyx (Teleostei: Percomorpha: Caristiidae), with Descriptions of Five New Species[END_REF], Platyberyx paucus can be distinguished from all congeners by the following combination of characters: absence of palatine teeth and lower meristics (31 vertebrae, 24-26 dorsal-fin rays, and 15-16 anal-fin rays). It can be further distinguished from all congeners, except P. andriashevi and P. pietschi, by the presence of laterally flattened, bladelike ventral procurrent caudal rays, and an anteriorly directed hook-like process on the third posterior-most ventral procurrent caudal ray [START_REF] Stevenson | Revision of the Manefish Genera Caristius and Platyberyx (Teleostei: Percomorpha: Caristiidae), with Descriptions of Five New Species[END_REF].

Diagnoses. According to

Distribution. Platyberyx paucus is poorly known worldwide, reported from one specimen in the central North Pacific (Hawai'i, western O'ahu Island), and three specimens from the western Central Atlantic (off northern South America) [START_REF] Stevenson | Revision of the Manefish Genera Caristius and Platyberyx (Teleostei: Percomorpha: Caristiidae), with Descriptions of Five New Species[END_REF]. The current study reports the occurrence of three specimens off Rio Grande do Norte and around Fernando de Noronha Archipelago, which represent the first record of P. paucus in Brazilian waters (Fig. 2).

Remarks. Most of characters observed in our material (n=3) are within the ranges presented for the types of Platyberyx paucus (n=4). However, some measurements (head length, lower jaw length, prepectoral length, prepelvic length, and preanal length) of the specimens reported herein were smaller than those recorded by [START_REF] Stevenson | Revision of the Manefish Genera Caristius and Platyberyx (Teleostei: Percomorpha: Caristiidae), with Descriptions of Five New Species[END_REF] (Table I). Diagnoses. According to [START_REF] Stevenson | Revision of the Manefish Genera Caristius and Platyberyx (Teleostei: Percomorpha: Caristiidae), with Descriptions of Five New Species[END_REF], Platyberyx pietschi can be distinguished from its congeners, except P. andriashevi and P. paucus, by the presence of an anteriorly directed hook-like process on the third posteriormost ventral procurrent caudal ray. Platyberyx pietschi can be distinguished from P. andriashevi by having fewer dorsal-fin rays (30-31 vs. 31-37), anal-fin rays (18-19 vs. 19-22), and vertebrae (33-35 vs. 36-39); and from P. paucus by having greater number of dorsal-fin rays (30-31 vs. 24-26), anal-fin rays (18-19 vs. 15-16), pectoral-fin rays (17-18 vs. 16-17), and vertebrae (33-35 vs. 31), respectively.

Platyberyx pietschi

Distribution. Platyberyx pietschi is a poor known species, reported only from two specimens from the western Central Atlantic, one specimen from the central Pacific, and one from the western South Pacific (Australia). The specimen currently reported off Rio Grande do Norte represents the first record of P. pietschi in the western South Atlantic (Fig. 2).

Remarks. Morphometric and meristic data for the specimen reported herein were within the range of those recorded by [START_REF] Stevenson | Revision of the Manefish Genera Caristius and Platyberyx (Teleostei: Percomorpha: Caristiidae), with Descriptions of Five New Species[END_REF], except by its number of anal-fin rays (17 vs. 18-19), dorsal-fin base length (73.6 vs. 62.9-68.7 % SL), and lower jaw length (42.9 vs. 55.6-70.7 % HL), respectively (Table I).

Discussion

Among more than 7000 mesopelagic fish specimens caught during the two ABRACOS expeditions (October 2015 and April 2017), only 11 specimens of caristiids were collected, of which four could not be identified as they were in poor condition. Of the eighteen species of the family Caristiidae known to date, four have been reported for the first time in Brazilian waters:

Paracaristius nudarcus, Platyberyx andriashevi, Platyberyx paucus and Platyberyx pietschi.

In addition to the caristiids reported herein, a few specimens have been previously recorded off Brazilian coast. [START_REF] Caires | Registros novos e adicionais de teleósteos marinhos na costa brasileira[END_REF] recorded two specimens of Caristius collected off southern Brazil. The first one (MZUSP 93287) was identified as Caristius macropus (Bellotti, 1903), collected off State of Rio Grande do Sul, at 32°58'S, 50°35'W, 99 m depth; and the second (MZUSP 86699) was named as Caristius sp., collected off State of São Paulo, at 26°19'49"S, 45°57'00"W, 600 m depth. The authors, however, recognized the identification of both specimens was tentative due to the lack of taxonomic revisions available at that time. Based on the recent reexamination of the specimens reported by [START_REF] Caires | Registros novos e adicionais de teleósteos marinhos na costa brasileira[END_REF] Despite we consistently used two nets (micronekton and mesopelagic), specimens reported herein were caught only with the micronekton net, which has a greater mesh size and seems to have a higher fishing efficiency for caristiids. This has also been found in many mesopelagic studies (e.g. [START_REF] Pakhomov | PICES Scientific Report of the Advisory Panel on Micronekton Sampling Inter-calibration Experiment[END_REF][START_REF] Heino | Catchability of pelagic trawls for sampling deep-living nekton in the mid-North Atlantic[END_REF], where catch efficiency significantly differs among trawl types due to various influences from extrusion through meshes and net avoidance behavior [START_REF] Kaartvedt | Efficient trawl avoidance by mesopelagic fishes causes large underestimation of their biomass[END_REF]. Thus, we believe the diversity of Caristiidae species observed here is not only a consequence of biogeographic patterns of this group, but also reflects the selectivity of sample methods employed. Further, as most of the Brazilian deep waters remain unexplored the current knowledge on the diversity of Caristiidae occurring in the region is probably underestimated. Additional deep-water sampling over banks, continental slopes, seamounts, and near oceanic islands would likely uncover new information on species composition and distribution of the family Caristiidae.

  Material Examined. NPM 4476 (1 specimen, 165 mm SL), RV Antea, ABRACOS #41A, Brazil, off northern Fernando de Noronha Archipelago, 03°19'59"S, 32°24'42"W to 03°19'32"S, 32°25'05"W, 0-430 m depth, micronekton trawl net, 26 April 2017, 21:44-22:06h. Diagnoses. According to Stevenson & Kenaley (2011), Paracaristius nudarcus can be distinguished from P. aquilus and P. nemorosus by the absence of fingerlike papillae along the dorsal margin of the hyoid arch and at the interhyal-posterior ceratohyal articulation, as well as dorsal-fin rays (27-31 vs. 30-33) and anal-fin rays (17-20 vs. 15-18) counts. Paracaristius nudarcus can be distinguished of P. maderensis by the position of the dorsal-fin origin (above orbit vs. posterior to orbit) and by the arrangement of the jaw teeth (single row, except near symphyses vs. multiple rows). Distribution. Paracaristius nudarcus has been previously reported in the western North Atlantic, eastern South Atlantic, eastern Indian Ocean, and eastern and western Pacific (Stevenson & Kenaley, 2011). The specimen reported off northern Fernando de Noronha Archipelago represents the first record of the genus and species in the western South Atlantic (Fig 2).

  NPM 4510 (1, 72 mm SL), RV Antea, ABRACOS #35, Brazil, sea mounts off Rio Grande do Norte, 04°19'37"S, 35°29'52"W to 04°18'32"S, 35°32'20"W, 0-630 m depth, micronekton trawl net, 20April 2017, 22:35-23:15h.

  , Caristius macropus and Caristius sp. are herein reidentified as Platyberyx andriashevi and Platyberyx pietschi, respectively, extending the known distribution of both species to off southern Brazil. Carvalho-Filho et al. (2009) also reported another caristiid, named Caristius sp., in the stomach content of a tropical pomfret Eumegistus brevorti (Poey 1860) (Bramidae), caught off State of Bahia, northeast Brazil. Unfortunately, we did not have access to this material and some important characters that allow identification are not visible on the picture (fig. 5) of the halfdigested specimen.

FiguresFigure

  Figures

  Figure 1. Paracaristius nudarcus (NPM 4476, 165 mm SL). Scale = 10 mm.

Figure 2 .

 2 Figure 2. Distribution of fishes of the family Caristiidae around oceanic islands and seamounts off northeastern Brazil: Paracaristius nudarcus ( ), Platyberyx andriashevi ( ), Platyberyx paucus ( ), and Platyberyx pietschi ( ). RN -State of Rio Grande do Norte; RA -Rocas Atoll; FN -Fernando de Noronha Archipelago.

Figure 3 .

 3 Figure 3. A-Platyberyx andriashevi (NPM XXXX, XXX mm SL), B-Platyberyx paucus (NPM XXXX, XXX mm SL), and C-Platyberyx pietschi (NPM 4510, 72 mm SL). Scale = 10 mm.

Table I .

 I Proportions and counts for Paracaristius nudarcus, Platyberyx andriashevi, Platyberyx paucus and Platyberyx pietschi collected off northeastern Brazil (western South Atlantic) and compared with those reported in the literature.

Acknowledgment

We acknowledge the French oceanographic fleet for funding the at-sea survey ABRACOS (http://dx.doi.org/10.17600/15005600/ http://dx.doi.org/10.17600/17004100) and the officers and crew of the RV Antea for their contribution to the success of the operations. Thanks also to Dr. Paulo Eurico Travassos for the hard work in samples collection. The present study could not have been done without the work of all team members from BIOIMPACT (UFRPE) and LIZ (NUPEM/UFRJ) labs. We thank the CNPq (Brazilian National Council for Scientific and Technological Development), for providing student scholarship to LNE and ASL and research grant to FLF. This work is a contribution to the LMI TAPIOCA and to the PADDLE project, which has received funding from the European Union's Horizon 2020 research and innovation program (grant agreement 73427).

Species

Paracaristius nudarcus Platyberyx andriashevi Platyberyx paucus Platyberyx pietschi

Present study [START_REF] Stevenson | Revision of the Manefish Genus Paracaristius (Teleostei: Percomorpha: Caristiidae), with Descriptions of a New Genus and Three New Species[END_REF] Present study [START_REF] Stevenson | Revision of the Manefish Genera Caristius and Platyberyx (Teleostei: Percomorpha: Caristiidae), with Descriptions of Five New Species[END_REF] Present study [START_REF] Stevenson | Revision of the Manefish Genera Caristius and Platyberyx (Teleostei: Percomorpha: Caristiidae), with Descriptions of Five New Species[END_REF] Present study [START_REF] Stevenson | Revision of the Manefish Genera Caristius and Platyberyx (Teleostei: Percomorpha: Caristiidae), with Descriptions of Five New Species[END_REF]


Joao Bimbo

Claudio Pacchierotti

Nikos G Tsagarakis

Domenico Prattichizzo
email: domenico.prattichizzo@iit.itclaudio.pacchierotti@irisa.fr

Collision Detection and Isolation on a Robot using Joint Torque Sensing

As robotic systems become more flexible and intelligent, they must be able to move into environments with a high degree of uncertainty or clutter, such as our homes, workplaces, and the outdoors. In these unstructured scenarios, it is possible that the body of the robot collides with its surroundings. As such, it would be desirable to characterise these contacts in terms of their location and interaction forces. This paper addresses the problem of detecting and isolating collisions between a robotic manipulator and its environment, using only on-board joint torque and position sensing. The algorithm is based on a particle filter and, under some assumptions, is able to identify the contact location anywhere on the robot body. It requires the robot to perform small exploratory movements, progressively integrating the new sensing information through a Bayesian framework. The approach was tested and benchmarked in simulation, with respect to its accuracy and robustness. Validation using a robot with joint torque sensing in a real environment demonstrated the applicability of the method to real-world scenarios.

I. INTRODUCTION

A. Motivation

Going beyond the factory floor, robotic systems are nowadays addressing environments which are more and more unstructured, unpredictable, and cluttered. In these situations, collisions between parts of the robot and the environment are likely to occur. Indeed, cluttered and unstructured environments present several challenges, and extremely advanced perception capabilities as well as safety measures are required. Detecting collisions between the robot and its environment and immediately take appropriate safety measures is of the utmost importance when the robot is in close proximity with humans. However, in other circumstances it might be useful to explore and characterise the collision. In teleoperation settings, informing the user about the location of a contact between the robot and its environment might help him choose an appropriate action [START_REF] Bimbo | Teleoperation in cluttered environments using wearable haptic feedback[END_REF]. Other fields which rely strongly on contacts between the robot and its environment, such as grasping and locomotion, could greatly benefit from an accurate estimate of the contact location anywhere on the robot body. These capabilities can be useful in other fields such as the agri-food industry and search and rescue robots, where robots operate in highly unstructured and unpredictable environments. This paper addresses an issue which is present in many autonomous and teleoperated systems, specially those working in cluttered environments: detecting the location of collisions happening between a robot and its environment at any point of the robot, using only sensors that are already available in many robot arms, i.e., position and torque. This problem is known in the literature as collision detection and isolation.

B. Related Work

The problem of characterising a collision between a robot and the environment has been addressed in multiple ways, most of which employ additional sensing. An immediate way of obtaining the contact location and magnitude of the external force is to cover the robot body with tactile sensors [START_REF] Grice | Whole-arm tactile sensing for beneficial and acceptable contact during robotic assistance[END_REF], [START_REF] Jain | Reaching in clutter with whole-arm tactile sensing[END_REF], [START_REF] Cirillo | A conformable force/tactile skin for physical human-robot interaction[END_REF]. These can directly provide information about the collision location and the magnitude of the applied external force. This approach, besides costly, suffers from a number of drawbacks, such as the additional complexity, loosening, and the wear-and-tear of the tactile sensor surfaces. Another solution is to use vision systems to compute distances between the robot and its environment or between the robot and a user. External cameras can be used for collision avoidance [START_REF] Flacco | A depth space approach to human-robot collision avoidance[END_REF], for safe Human-Robot cooperation [START_REF] Ebert | Safe human-robot-cooperation: image-based collision detection for industrial robots[END_REF], and to obtain the contact location [START_REF] Magrini | Estimation of contact forces using a virtual force sensor[END_REF], which is then used to compute and handle the contact forces exchanged with a user. A force-torque sensor mounted at the robot base also enables this computation [START_REF] Buondonno | Combining real and virtual sensors for measuring interaction forces and moments acting on a robot[END_REF] if a pure force is assumed.

Out of the approaches that rely solely on the robot's proprioception, the work of Alessandro De Luca stands out as the source for most of the major contributions to the field [START_REF] Flacco | A depth space approach to human-robot collision avoidance[END_REF], [START_REF] Magrini | Estimation of contact forces using a virtual force sensor[END_REF], [START_REF] Buondonno | Combining real and virtual sensors for measuring interaction forces and moments acting on a robot[END_REF], [START_REF] De Luca | Sensorless robot collision detection and hybrid force/motion control[END_REF], [START_REF] De Luca | Collision detection and safe reaction with the DLR-III lightweight manipulator arm[END_REF], [START_REF] Haddadin | Collision detection and reaction: A contribution to safe physical humanrobot interaction[END_REF], [START_REF] Santis | An atlas of physical human-robot interaction[END_REF], [START_REF] Haddadin | Robot Collisions: A Survey on Detection, Isolation, and Identification[END_REF]. Climent Bigas [START_REF] Bigas | Proprioception for collision detection[END_REF] and Manuelli [START_REF] Manuelli | Localizing external contact using proprioceptive sensors: The contact particle filter[END_REF], [START_REF] Manuelli | Localizing external contact using proprioceptive sensors: The contact particle filter[END_REF] proposed probabilistic methods to address this problem. These approaches are considered in the next section.

C. Problem Presentation

This paper presents a method to estimate the contact state of a serial robot manipulator with its environment using only the robot's proprioceptive sensors (joint torque and position). The problem of finding the contact location is referred to in the literature as "collision isolation" [START_REF] Haddadin | Robot Collisions: A Survey on Detection, Isolation, and Identification[END_REF]. Without any additional external sensing this problem is not trivially solved, particularly when the contact happens near the base of the robot, i.e., when few joints are involved. In fact, Buondonno and De Luca [START_REF] Buondonno | Combining real and virtual sensors for measuring interaction forces and moments acting on a robot[END_REF] assert that a solution exists only if the contact is occurring after the sixth joint. This case allows the calculation of the external wrench, from which the collision point can be calculated by assuming an acting pure force, in a scheme similar to intrinsic contact sensing [START_REF] Bicchi | Contact Sensing from Force Measurements[END_REF]. For what concerns detecting contacts before the sixth link, most of the existing literature [START_REF] Haddadin | Robot Collisions: A Survey on Detection, Isolation, and Identification[END_REF] is limited to detecting the link in collision without estimating the exact contact point [START_REF] De Luca | Sensorless robot collision detection and hybrid force/motion control[END_REF]. This is usually done by measuring the external joint torques and identifying the last joint to have a non-zero additional torque. However, this approach may still lead to errors, as a contact force may exert zero torque at the joint(s) immediately before its point of contact. This information is nevertheless sufficient in most cases where safety is the only concern, since the robot can "bounce" away from the collision [START_REF] De Luca | Collision detection and safe reaction with the DLR-III lightweight manipulator arm[END_REF] or continue, to some extent, performing the desired task [START_REF] De Luca | Exploiting robot redundancy in collision detection and reaction[END_REF]. Existing approaches that rely on probabilistic methods can overcome some of the limitations above. Climent Bigas [START_REF] Bigas | Proprioception for collision detection[END_REF] implemented a probabilistic function to find probable contact locations on a robot body using torque measurements. He found that the information is often insufficient to fully determine the collision point, and depends on the contact point and configuration of the robot. Manuelli and Tedrake [START_REF] Manuelli | Localizing external contact using proprioceptive sensors: The contact particle filter[END_REF] used a particle filter to isolate collisions on the body of a humanoid robot. They solved a quadratic problem to determine whether a force at particular contact point and inside a friction cone could produce the measured torque. The proposed method is fast and accurate, but suffers from the same drawback as [START_REF] Bigas | Proprioception for collision detection[END_REF]: it is not able to detect the correct contact point when several combinations of contact locations and forces could be responsible for the same observed external torque. This problem is referred to as the identifiability of the method. Contacts happening near the robot's base produce forces that generate torques on only a few of the robot's sensors. This means that there are often several possible contact locations that satisfy the (limited) available information. This prevents the isolation of the contact point on the links closer to the robot base.

This paper shows that this limitation derives from not fully exploiting the capabilities of Bayesian Filtering, namely with respect to the chosen motion model. We propose a particle filter approach that, under some assumptions, is able to identify the contact location anywhere in the robot body. It requires the robot to perform small exploratory movements, progressively integrating the new sensing information using a Bayesian framework.

II. METHODS

A. Particle Filtering

A Particle Filter is a non-parametric Bayesian Filter that approximates a distribution of states by a set of particles. Each particle represents a possible state of the system. Modelling how the measurements match the state of the system and how these states change over time given a control action allows us to recursively narrow down the possible states until a single solution is found. This technique relies on the Markov property of a system, i.e., the current state depends only on the previous state and the last action, making the problem computationally tractable.

The implementation of a Bayesian Filter requires the following models:

• A measurement model that describes the likelihood of a measurement z given a state x,

p (z(t) | x(t)) . (1)
• A motion model (also known as update or actuation model), that describes the probability of transition to another state given the action performed u(t) ,

p(x(t) | u t , x(t -1)). (2)
The posterior belief of each state given all the previous measurements and actions can then be obtained using the recursion formula:

bel(x t ) = p(x t |u t , x t-1 ) bel(x t-1 )dx t-1 bel(x t ) = η • p(z t | x t ) bel(x t ) (3)
where x t = x(t), and η is a constant which normalises the beliefs such that they integrate to 1.

The Particle Filter presents a discretised version of the Bayesian Filter. Additionally, this filtering technique has a resampling step, where the weight of each particle is updated according to its likelihood, and a new set of particles is generated by resampling the existing particles according to their weight. Step by step, this allows the survival of the most likely estimates at the expense of the ones less probable.

B. Contact estimation

The contact state x that we intend to characterise consists of the point of contact p, the contact force F , and the stiffness of the contact K. In this work, we assume that the object in collision is convex, that there is a single contact region, and that the friction forces are negligible. We start by retrieving the triangular mesh describing the geometry of each link and calculate the normals of each triangle. Besides, the points generating the mesh are used to build a k-d tree to allow fast nearest neighbour searches [START_REF] Bentley | Multidimensional binary search trees used for associative searching[END_REF]. We randomly generate a high number of particles (N = 10000), where each particle defines a possible collision state. It contains the link number n, the index of the mesh triangle p, the force magnitude F , and the linear stiffness of the contact K.

1) Measurement Model:

We are interested in estimating the external torques τ ext , which result from the interaction of the robot with the collided object. Typically, these torques can be obtained from the manipulator equation:

τ ext = M (q)q + C(q, q) q + g(q) -τ m , (4)
where M (q) is the inertia matrix, C(q, q) q is the centripetal and Coriolis vector, and g(q) is the gravity vector. Note that other methods of estimating the external torque τ ext exist. Most notably, the residual method in [START_REF] De Luca | Collision detection and safe reaction with the DLR-III lightweight manipulator arm[END_REF] uses a generalised momentum observer, which avoids the typically noisy estimation of joint acceleration q and also works when q = 0. In this work, since we are collecting measurements when the robot is in contact, we assume that q ≈ 0. For further details, and other approaches to estimate τ ext see the survey in [START_REF] Haddadin | Robot Collisions: A Survey on Detection, Isolation, and Identification[END_REF].

Given the array of measured external torques τ ext , a likelihood function can be constructed from the difference between the measured torques and the torques τ , estimated from the contact state x,

p(z t | x t ) = e -α τ -τ ext , ( 5
)
where α is a design parameter that relates with the accuracy of the torque sensing and also how "greedy" we want the search to be. The estimated torques τ can be obtained using the robot Jacobian, calculated for contact point p and current joint configuration of the robot as

τ = J T p (q) • F c , (6)
where F c ∈ R 6×1 is the coordinate vector obtained from the contact force F and the normal direction n,

F c = F • n 0 T . (7)
Another simpler way of calculating joint torques is through the cross product of vectors i p and i F in the coordinate frame of the i-th joint, projected onto the joint axis.

2) Motion Model:

The motion or update model is the function that allows us to predict how the state will change given a control action, i.e., p(x(t) | u t , x(t -1)).

Consider a contact state x t = {n t , p t , F t , K t }, where n is the link in contact, p is the contact position, F is the contact force and K is the contact stiffness at time t. The control action is encoded by the kinematic postures of the robot at times t-1 and t. Here we take advantage of the assumptions that the surfaces in contact are locally convex and that the friction forces are negligible. Taking contact points p t-1 and p t , we assume that there is a constant curvature along the plane that passes through the two points and contains F t-1 . We sample a curvature radius r from a distribution uniform in the logarithmic space, and we obtain the centre of the curve c. p t is obtained from a nearest neighbour search from point c, and the force is obtained from

F t = F t-1 + (r -d t ) • K t , (8)
where d t is the distance p tc . Fig. 2. Reasoning for the motion model. As the robot (in orange) moves between t -1 and t instants, the possible contact locations between the robot and surfaces A and B are limited if the surfaces are convex. The new contact locations p A and p B will depend on the shape's curvatures. Given enough particles and sampled curvatures, this enables the algorithm to narrow down the right point of collision at time t.

Figure 2 illustrates the method and shows the result for two example curvatures (A and B). For surface A, the centre of the curve is at point c A and the contact point p t = p A . Surface B will have a different centre, and the contact point will change accordingly, i.e., p t = p B . Forces are calculated according to the distance between p t and the curve, multiplied by K. Finally, additional Gaussian noise w i ∼ N (0, σ 2 i ) was added to the particle's location, force, and stiffness.

The effectiveness of Particle Filters lies on a correct formulation of the motion model. Consider an example commonly used to explain Particle Filters [START_REF] Thrun | Probabilistic Robotics (Intelligent Robotics and Autonomous Agents)[END_REF], where the robot must locate itself in a map. If each measurement is considered individually, it is impossible to identify on which of the similar corridors the robot is currently at. Only through the correct updating of the particles, following a model of how the robot moves, all the possible robot locations can be narrowed down to a single point. Similarly, in this paper, only through a model of how the contact point and forces change when the robot performs small movements, the state can be correctly estimated.

Below, we compare the results of the proposed approach with two other motion models. One where the contact has zero velocity on the link frame, and another which assumes that the point of contact does not change with respect to an external frame.

III. RESULTS

A. System overview and implementation

The proposed method was implemented in C++ using the ROS platform [START_REF] Quigley | ROS: an open-source robot operating system[END_REF]. Robot dynamics were calculated using the KDL library [START_REF] Smits | KDL: Kinematics and Dynamics Library[END_REF], and the geometric operations relied on the PCL (Point Cloud Library) [START_REF] Rusu | 3D is here: Point Cloud Library (PCL)[END_REF]. The tested robot was a Kuka LBR iiwa, a 7 degree-of-freedom robot with joint torque sensing. Simulations were carried out using the Gazebo robot simulator [START_REF] Koenig | Design and use paradigms for gazebo, an open-source multi-robot simulator[END_REF].

B. Simulation

The simulated environment is shown in Fig. 1. The robot was made collide with a spherical object at different points. Ground truth values for contact location and force are obtained from the simulation allowing a quantitative evaluation of the algorithm. [START_REF] Manuelli | Localizing external contact using proprioceptive sensors: The contact particle filter[END_REF]. Red: zero-velocity on the global frame [START_REF] Manuelli | Localizing external contact using proprioceptive sensors: The contact particle filter[END_REF]. Yellow: method proposed in this paper.

As the robot contacted the object, the estimation process was started, setting a low value to α in ( 5) and a high standard deviation for the noise σ i in order to cover the search space. As the robot starts moving, we increase α and decrease σ i in order to narrow down the particles towards the correct solution. Figure 3 shows the progress of the algorithm for a contact happening at the third link of the robot. Initially, the particles with high likelihood (green dots) are scattered around links 2, 3, and also some on link 4. This is because there are possible forces at these locations that could generate the measured torque, requiring for instance a large force at link 2 or a lower force at link 4. The robot then makes small exploratory movements, narrowing down the possible contact locations. The bottom row of Fig. 3 shows the estimated force vs contact location. The small movements of the robots can be understood by the changes in the length of the true contact force (red arrow). See for example the decrease in Fig. 5. Performance of the algorithm when adding noise to the torque measurements. Mean position error on each link for added Gaussian noises with standard deviation of 0%, 5%, and 10%. These results show a good robustness to noise. contact force between the times E and F after a movement of the robot. These changes are correctly predicted by the particle filter, as can be seen from the shift of particles towards lower forces in last plot.

We compared the approach proposed in this paper with two alternative models described in [START_REF] Manuelli | Localizing external contact using proprioceptive sensors: The contact particle filter[END_REF]. One assumed that the contact location would remain approximately constant on the link frame, while the other one supposed that it would remain constant on a global coordinate frame.

We considered collisions at each robot link. As a metric, we evaluated the error between the estimated position of collision and the true one. Five trials were performed for each link and results are shown in Fig. 4. While there is no significant difference when collisions are happening on the sixth link, the advantages of the proposed approach become more and more visible as the contact takes place nearer to the robot base and less measures are available. For example, for a contact at link 3, the error of the proposed algorithm is around 1 cm, while the other approaches' exceed 5 cm. For collisions that happen on links 5 and 6, the motion model becomes less important, since these may only require a single measurement to unambiguously compute the contact location and force.

With respect to robustness to noise, Fig. 5 shows the result when Gaussian error is added to the torque measurements. A slight decrease in accuracy is visible when the standard deviation of noise is 10% of the measured signal, particularly for link 1. The effect of noise is mitigated for contacts happening further down the kinematic chain, achieving mean errors below 2 cm for every link and noise level after link 1. This result is expected and in line with the known ability of particle filters to deal with noisy measurements. Another result that is worth highlighting is the ability of the algorithm to deal with shapes which are not strictly convex. Figure 6 shows an example of a cubic obstacle, in contact with the robot at its edge. The system is still able to locate the contact with remarkable accuracy.

C. Real System

The results in simulation indicate that this method is suitable to be applied on a real robotic system with joint torque sensing capabilities. While the correct convergence of the algorithm requires accurate measurements and a good knowledge of the robot's dynamical properties, the method is, to some extent, robust to uncertainties.

An experimental trial was performed using a real Kuka LBR iiwa robot, and results are shown in Fig. 7. The robot collides laterally with a cylindrical pole. Initially, many possible contact locations along that side of the robot have similar likelihood. The robot is then commanded to perform small exploratory movements within the robot's null space, while maintaining contact with the obstacle. Although quantitative evaluation was not possible, we can see that the algorithm converges to the correct location (green dots on the lower left side of the figure). Other objects with different shapes and materials were tested, achieving similar results.

IV. CONCLUSIONS

A. Discussion

Results show that Bayesian Filtering can be used to estimate the contact location between a robot and an object anywhere on the robot body, under a few assumptions. These results showcase the effectiveness of particle filtering when used to estimate a state that is not observable from a single measurement. Having a model, even an approximate one, of how the state evolves given control actions allows us to sequentially narrow down likely states until a solution is found. In this paper we take advantage of simple yet useful concepts to increase the likelihood of finding the right contact location, such as (i) moving against a collision force is likely to increase it; (ii) collisions are typically not point contacts but surfaces; (iii) if they are convex and the robot link moves to the left the contact will probably move to its right. In fact, the Contact Particle Filter reported in [START_REF] Manuelli | Localizing external contact using proprioceptive sensors: The contact particle filter[END_REF], [START_REF] Manuelli | Localizing external contact using proprioceptive sensors: The contact particle filter[END_REF] uses no such model/assumptions and performs poorly when the problem is not identifiable. Using the same Kuka robot, it reports errors between 10 cm and 30 cm for contacts in links 1, 2, and 3. An additional force-torque sensor was added to cope with these cases. Another remarkable strength of particle filters lies in its "forgiveness" to noisy measurements, errors in the model, and simplified assumptions. This effect can be seen in the method's ability to detect the contact location using a real robot. In our experiment with the real robot, we used an imperfect model and noise was obviously present in the torque data. Most of the assumptions also did not hold: the object was not strictly convex, its stiffness was not linear and there was some friction; however, the estimation converged to an approximately correct result.

Nevertheless, the proposed approach has a significant limitation. If the robot collides with a concave object, there is no way of predicting the behaviour of the contact point as well as that of the forces. Consider, for example that the robot arm is inside a narrow tube. Any small movement by the robot might lead to moving the contact to the opposite side of the robot. This might render the method unable to find the contact location when the problem is not identifiable from a single measurement.

B. Concluding Remarks

This paper presents a probabilistic method to determine the contact location between a serial manipulator and an object in its environment. It uses only the robot's joint position and torque sensing, and it uses small exploratory movements to recursively estimate the location, force, and stiffness of the contact. The method assumes negligible friction forces, convex contact surfaces, and linear contact stiffness. Compared to existing approaches, it allows this detection to be carried in almost all the surface of the robot's body. We tested the proposed approach both in simulation and in a real environment. Experiments in simulation showed that our approach outperformed two other methods that made simpler assumptions. Experiments in a real environment using a robot with joint torque sensors showed the applicability of the method to real world scenarios and its ability to cope with situations where the algorithm's assumptions did not hold.

C. Future Work

Future work will focus on the actions of the robot when contact is detected. While in this work the exploratory movements of the robot were carried out manually, either arbitrarily or in the robot's null space, we would like to explore the different possibilities in terms of what movements can or should be performed. While some movements will allow a faster identification of the contact location, they might be dangerous (e.g., moving against the contact force). This demands for a trade-off between informative and safe actions that is worth being investigated. Another possibility is to use a similar method to blindly create a map of the robot's environment, and then plan the robot's movement within that sensed map. Finally, a possible research direction is to improve the current method to include friction and also the joint stiffness of the robot.

Fig. 1 .

 1 Fig. 1. Gazebo simulator environment with a 7-DoF Kuka iiwa robot and an object in collision.

Fig. 3 .

 3 Fig. 3. Progress of the algorithm for a collision on the third link. Upper row: likely particles on the robot body. The red arrow shows the true contact point and force vector. Lower row: particle distribution, plot of contact force vs. distance to base. Higher likelihoods in green, lower in red. Ground truth is represented by the yellow cross.

Fig. 4 .

 4 Fig.[START_REF] Cirillo | A conformable force/tactile skin for physical human-robot interaction[END_REF]. Estimation accuracy of the contact location algorithm for different motion models. Mean position error for each link is plotted. Blue: zerovelocity on the link frame[START_REF] Manuelli | Localizing external contact using proprioceptive sensors: The contact particle filter[END_REF]. Red: zero-velocity on the global frame[START_REF] Manuelli | Localizing external contact using proprioceptive sensors: The contact particle filter[END_REF]. Yellow: method proposed in this paper.

Fig. 6 .

 6 Fig. 6. Results in simulation when the robot is contacting a cubic object. Left: Simulated environment Right: Result of estimation (green dots show likely contact points).

Fig. 7 .

 7 Fig. 7. Results in the real-world environment. Top-left: initial steps of the estimation before moving. Bottom-left: result of the estimation. Right: collision state (the robot's third link is colliding with a cylindrical obstacle).

This research was funded by the European Union's Horizon 2020 Research and Innovation Programme, grant n. 645599 (SOMA).

1 J. Bimbo, N. Tsagarakis and D. Prattichizzo are with the Istituto Italiano di Tecnologia, Italy.