Hisao Hori
email: h-hori@kanagawa-u.ac.jp

Tomoki Ushio

Takuma Asai

Ryo Honma

Nadim Eid

Bruno Ameduri

-4-thia-perfluoro(2methyl)-1-dodecanoic acid, in superheated water induced by a combination of potassium permanganate and dioxygen

Keywords:

Efficient mineralization of a novel fluorotelomer surfactant, 2H,3H,3H,5H,5H,6H,6H

Introduction

Organofluorine compounds, which are thermally and chemically stable, show a high surface activity and do not absorb light [START_REF]Organofluorine Chemistry: Principles and Commercial Applications[END_REF][START_REF] Kirsh | Modern Fluoroorganic Chemistry: Synthesis, Reactivity, Applications. Second, Completely Revised and Enlarged Edition[END_REF]. Among them, compounds consisting of a perfluoroalkyl group (C n F 2n+1 -, where n = approx. 4 to 14) and an acid end group (COOH or SO 3 H) have been used as industrial surfactants in applications that involve severe chemical and thermal conditions, which are incompatible with conventional hydrocarbon agents [START_REF] Kissa | Fluorinated Surfactants and Repellents[END_REF][START_REF] Wang | Global emission inventories for C 4 -C 14 perfluoroalkyl carboxylic acid (PFCA) homologues from 1951 to 2030, Part I: production and emissions from quantifiable sources[END_REF]. While these chemicals are used as niche products, some of them showed environmentally negative features.

Representatively, perfluorooctanesulfonic acid and perfluorooctanoic acid (C 8 F 17 SO 3 H, PFOS and C 7 F 15 COOH, PFOA, respectively) and their derivatives, which had been used for several decades, exhibit high environmental persistence [START_REF] Houtz | Persistence of perfluoroalkyl acid precursors in AFFF-impacted groundwater and soil[END_REF][START_REF] Henry | A critical review of the application of polymer of low concern and regulatory criteria to fluoropolymers[END_REF][START_REF] Johansson | Global transport of perfluoroalkyl acids via sea spray aerosol[END_REF], bioaccumulation, and non-ignorable toxicity. Therefore, international regulations (including voluntary restraints) for their manufacturing, uses, export/import have been issued from the mid-2000s and it is still of concern [START_REF]Ninth Meeting of the Conference of the Parties to the Stockholm Convention[END_REF]. After the negative features of these compounds were revealed, over two hundred scientific reports that described decomposition methods of these compounds in water appeared, as summarized by recent review papers [START_REF] Merino | Degradation and removal methods for perfluoroalkyl and polyfluoroalkyl substances in water[END_REF][START_REF] Trojanowicz | Advanced oxidation/reduction processes treatment for aqueous perfluorooctanoate (PFOA) and perfluorooctanoate (PFOA) -a review of recent advances[END_REF][START_REF] Zhang | Nanotechnology in remediation of water contaminated by poly-and perfluoroalkyl substances: a review[END_REF].

Fluorochemical surfactants used in industry are not limited in such perfluorinated alkyl compounds [START_REF] Kissa | Fluorinated Surfactants and Repellents[END_REF][START_REF] Wang | Global emission inventories for C 4 -C 14 perfluoroalkyl carboxylic acid (PFCA) homologues from 1951 to 2030, Part I: production and emissions from quantifiable sources[END_REF][START_REF] Henry | A critical review of the application of polymer of low concern and regulatory criteria to fluoropolymers[END_REF][START_REF] Kostov | Original fluorinated surfactants potentially nonbioaccumulable[END_REF][START_REF] Krafft | Selected physicochemical aspects of poly-and perfluoroalkylated substances relevant to performance, environment and sustainability-part one[END_REF]. Derivatives with a perfluoroalkyl group that connects to ethylene unit (-CH 2 CH 2 -), i.e., compounds bearing C n F 2n+1 C 2 H 4group, are also used as surfactants for surface modification and other purposes. They are classified as fluorotelomer related products [START_REF]OECD/UNEP Global PFC Group, Synthesis paper on per-and polyfluorinated chemicals (PFCs)[END_REF], and any species containing C 8 F 17 , C 8 F 17 C 2 H 4or higher groups have been restricted by the Stockholm Convention in 2019 at the same time as PFOA because they have possibility to generate PFOA when they degrade [START_REF]Ninth Meeting of the Conference of the Parties to the Stockholm Convention[END_REF].

While many reports on the decomposition methods for PFOS and PFOA have been published, only a few ones focus on the decomposition of these fluorotelomers: by use of UV light irradiation [START_REF] Liu | Formation of perfluorocarboxylic acids from photogeneration of tetrahydroperfluorocarboxylic acids in water[END_REF], ball milling [START_REF] Lu | Mechanochemical mineralization of "very persistent" fluorocarbon surfactants-6:2 fluorotelomer sulfonate (6:2FTS) as an example[END_REF], heating with peroxodisulfate (persulfate, S 2 O 8 2-) [START_REF] Bruton | Treatment of aqueous film-forming foam by heat-activated persulfate under conditions representative of in situ chemical oxidation[END_REF],

oxidation with boron-doped diamond electrode [START_REF] Gomez-Ruiz | Boron doped diamond electrooxidation of 6:2 fluorotelomers and perfluorocarboxylic acids. Application to industrial wastewaters treatment[END_REF], advanced oxidation processes [START_REF] Yang | Stability of 6:2 fluorotelomer sulfonate in advanced oxidation processes: degradation kinetics and pathway[END_REF], TiO 2 photocatalyst [START_REF] Kutsuna | TiO 2 -induced heterogeneous photodegradation of a fluorotelomer alcohol in air[END_REF], and biodegradation [START_REF] Dinglasan | Fluorotelomer alcohol biodegradation yields poly-and perfluorinated acids[END_REF][START_REF] Dasu | Aerobic soil biodegradation of 8:2 fluorotelomer stearate monoester[END_REF][START_REF] Butt | Biotransformation pathways of fluorotelomer-based polyfluoroalkyl substances: a review[END_REF]. Furthermore, the majority of the previous studies were performed to investigate whether they could transform into PFOA in the environment and did not necessarily aim to achieve mineralization (i.e. decomposition to F -ions) of these compounds in view of the waste treatment. Although the hydrocarbon telomers seem to decompose readily compared to perfluorinated compounds because of the weak C-H bond (its dissociation energy is 337 kJ/mol, which is smaller than that of the C-F bond, 536 kJ/mol), their complete mineralization is still challenging.

Under the circumstances, development of an effective method to mineralize these compounds would be of interest. In addition, the generated F --containing solutions could be treated with Ca 2+

to generate harmless CaF 2 [START_REF] Aldaco | Calcium fluoride recovery from fluoride wastewater in a fluidized bed reactor[END_REF][START_REF] Garea | Improvement of calcium fluoride crystallization by means of the reduction of fines formation[END_REF]. CaF 2 is the raw material for producing hydrofluoric acid required for fluorination reactions. Because the global supply of mined high-purity fluorspar, the mineral form of CaF 2 , is limited (hugest reserves are in China, Mexico, and South Africa [START_REF] Survey | Mineral Commodity Summaries[END_REF]), such a treatment process would have the added benefit of recycling of fluorine element.

Hence, the objective of this study deals with the mineralization of 2H,3H,3H,5H,5H,6H,6H-4thia-perfluoro(2-methyl)-1-dodecanoic acid (FSC, Fig. 1), a novel fluorotelomer surfactant, in two different conditions: ⅰ ) in hot water (70-90 °C) with peroxodisulfate and ⅱ ) in superheated water (200-350 °C) with KMnO 4 . FSC is an alternative surfactant to PFOS and PFOA and is successfully used for preparing spherical wormhole-like mesoporous silica for applications in the field of catalysts [START_REF] Riachy | Investigation of a novel fluorinated surfactant-based system for the design of spherical wormhole-like mesoporous silica[END_REF].

Decontamination methods using peroxodisulfate is a powerful tool for the treatment of a broad range of organic compounds in water [START_REF] Wacławek | Chemistry of persulfates in water and wastewater treatment: a review[END_REF]. Indeed, PFOA and analogues were efficiently mineralized in hot water (80 °C) by addition of peroxodisulfate [START_REF] Hori | Efficient decomposition of perfluorocarboxylic acids and alternative fluorochemical surfactants in hot water[END_REF]. Superheated water (subcritical water, pressurized hot water) is a liquid state water at temperature ranging between 100 °C and 374 °C (the critical temperature). Reactions using superheated water are recognized to be environmentally benign [START_REF] Savage | Organic chemical reactions in supercritical water[END_REF][START_REF]Chemical Synthesis Using Supercritical Fluids[END_REF][START_REF] Knez | Chemicals and value added compounds from biomass using sub-and supercritical water[END_REF], because of water's high diffusivity, low viscosity, and high hydrolyzing power [START_REF] Tester | Supercritical water oxidation technology: process development and fundamental research[END_REF]. In view of water as a reaction medium, its nontoxicity and abundance are also attractive. Although reactions in superheated water can generate toxic COF 2 , it is readily transformed into CO 2 and HF under the reaction conditions, which is not the case for COF 2 generated during pyrolysis of fluorinated compounds. Furthermore, KMnO 4 , a harmless oxidizing agent, is employed at tap water manufacturing facilities to treat metal compounds, preventing undesired disinfection products (e.g., trihalomethanes) [START_REF]Drinking Water Treatability Database[END_REF]. So far, there have been only three reports that described KMnO 4 -induced superheated water treatment: destructions of acetic acid [START_REF] Chang | Supercritical water oxidation of acetic acid by potassium permanganate[END_REF], poly(vinylidene fluoride) [-(CH 2 CF 2 ) n -] [START_REF] Honma | Permanganateinduced efficient mineralization of poly(vinylidene fluoride) and vinylidene-fluoride based copolymers in low-temperature subcritical water[END_REF], and ionic liquids bearing perfluorinated anions [START_REF] Hori | Complete mineralization of fluorinated ionic liquids in subcritical water in the presence of potassium permanganate[END_REF].

Materials and methods

Materials

99.999% O 2 and 99.9% Ar for the degradation reactions and standard gas mixtures, 1.00 % CO 2 in N 2 and 0.971% trifluoromethane (or fluoroform, CF 3 H) in N 2 for the quantification of gas-phase products were supplied by Nissan Tanaka (Saitama, Japan). been maintained for the desired amount of time, the autoclave was immediately cooled to 25 °C.

The gas phase, which was recovered in a sampling bag, was subjected to GC and GC/MS. Then, the autoclave was opened, and the mixture inside was collected and centrifuged. The liquid was characterized by ion chromatography and HPLC/MS. The precipitate was dried overnight under vacuum at room temperature, and its X-ray diffraction pattern and X-ray photoelectron spectrum were measured. We also performed control reactions without KMnO 4 and reactions under Ar instead of O 2 .

Analytical procedures

The major gas-phase products were quantified on a GC 323 instrument (GL Sciences) with thermal conductivity detection (temperature, 130 °C). An activated carbon column (60/80 mesh, 2.17 mm i.d., 2 m length, the column oven temperature, 110 °C) was employed. The carrier gas was Ar, and the injection port was maintained at 150 °C. Minor gas-phase products were characterized by a GC/MS system (QP2010 SE, Shimadzu, Kyoto, Japan) equipped with a fusedsilica capillary column (Rt-Q-BOND; Restek, Bellefonte, PA, USA). The carrier gas was He, and the injection port was heated at 120 °C. The sample was injected in split mode (20/1), and the system was operated in full-scan mode. The temperature program was as follows: hold at An electrospray ionization MS system (in the absence of the column in the above-described HPLC/MS) was used to detect any species remaining in the reaction solutions, with methanol as the mobile phase (0.2 mL min -1 ). Selected sample solutions were subjected to another ion chromatography to detect short-chain perfluoroalkanoic acids (such as CF 3 COOH). For these analyses, the injection volume was 10 L, a TSKgel OApak-A (Tosoh) column was used, and the mobile phase was aqueous phthalic acid (10 mM) at 1.0 mL min -1 .

The F -and CO 2 yields were calculated by means of Eqs. 1 and 2, respectively:

F -yield (%) = [(moles of F -formed)/(moles of F atoms in initial FSC)] × 100 (1)
CO 2 yield (%) = [(moles of CO 2 formed)/(moles of C atoms in initial FSC)] × 100

Details of quantification conditions of major products, F -and SO 4 2-by ion-chromatography and CO 2 by gas-chromatography with thermal conductivity detection, are listed in Tables S-1 and S-2 in SM.

Results and discussion

Synthesis of FSC

First, FSC surfactant was prepared by a radical addition of the fluorinated mercaptan 3,3,4,4,5,5,6,6,7,7,8,8,8-tridecafluoro-1-octanethiol) onto 2-trifluoromethacrylic acid [START_REF] Riachy | Investigation of a novel fluorinated surfactant-based system for the design of spherical wormhole-like mesoporous silica[END_REF] (Scheme 1).

Reactions in hot water containing S 2 O 8 2-

The F -and CO

For a reaction in the presence of KMnO 4 under Ar, the F -yield was enhanced to 35% (entry 2), suggesting that in addition to the CF 3 group at C2, the C 6 F 13 group also decomposed partially.

The SO 4 2-yield increased to 88%, indicating that oxidative decomposition around the sulfur atom in FSC was accelerated. The CO 2 yield remained low (19%).

When FSC was decomposed under O 2 without any KMnO 4 , the pH of the resulting solution was 2.4; whereas for a similar reaction with KMnO 4 under Ar [initial pressure, 0.6 MPa (5.1

mmol)], it increased up to 8.0. Under the latter conditions, OH -ions were released (Eq. 4):

4KMnO 4 + 2H 2 O → 4MnO 2 + 3O 2 + 4KOH (4)
When the pH of the aqueous system was approximately 5-11, some of the CO 2 molecules existed in the form of HCO 3 -in water [START_REF] Wolf-Gladrow | Total alkalinity: the explicit conservative expression and its application to biogeochemical processes[END_REF]. Therefore, in these cases, the CO 2 yield calculated from the amount of gas-phase CO 2 did not accurately reflect the mineralization extent of the carbon atoms in FSC. As discussed in section 3.4, when pH is 3.8, the CO 2 amount in the reaction solution could be negligible, referring Henry's law constant and the dissociation constant.

Results of the reactions under O 2 without KMnO 4 and those with KMnO 4 (0.50 mmol) under

Ar are compared at several reaction temperatures (Fig. 2). For both conditions, F -, SO 4 2-and CO 2 amounts were similar at each temperature. However, at all tested temperatures, the reactions with KMnO 4 (0.50 mmol) under Ar (Figs. 2c and2d) gave higher F -and SO 4 2-amounts and yields than those released from reactions under O 2 in the absence of KMnO 4 (Figs. 2a and2b).

Reaction of FSC with KMnO 4 under O 2 produced the highest F -yield (52 ± 1%) at 300 °C (Table 2, entry 3). This finding demonstrates that not only the CF 3 group at C2 but also the C 6 F 13 group began to decompose. Under these conditions, the SO 4 2-yield was 100%, indicating that the sulfur atom in FSC was quantitatively mineralized. The pH value of the solution was 7.7

while the CO 2 yield increased to 31 ± 1%.

Because the combination of KMnO 4 and O 2 effectively mineralized FSC, we examined this mixture in more details as described in section 3.4. In all reactions listed in Table 2, trace amounts of 1H-perfluoroalkanes were detected in the gas phase (Table 2). It was of interest to optimize the reaction conditions to achieve a high mineralization efficiency while suppressing the formation of 1H-perfluoroalkanes, which are quite stable, some of them having high global warming potentials [START_REF] Mcculloch | Fluorocarbons in the global environment: a review of the important interactions with atmospheric chemistry and physics[END_REF]. For example, CF 3 H has a global warming potential of 12400 (for one hundred years) [START_REF] Hodnebrog | Global warming potentials and radiative efficiencies of halocarbons and related compounds: a comprehensive review[END_REF] and emissions of such a gas in East Asia have been gradually increasing since 2010 [START_REF] Fang | Multiannual topdown estimate of HFC-23 emissions in East Asia[END_REF].

Reactions in superheated water containing both KMnO 4 and O 2

The first experiments used FSC (initial amount, 34.8 mol) at 350 °C for 6 h under O 2 (13.6 mmol, ca 391-fold excess of FSC) while varying the initial KMnO 4 amount (Fig. 3). These experiments revealed that the F -amount increased as the KMnO 4 amount increased up to 0.50 mmol (ca. 14-fold molar excess of FSC), after which the F -amount remained essentially unchanged (Fig. 3a). When the KMnO 4 amount was 1.0 mmol, the F -content was 422 mol, or a 76% F -yield. CO 2 was the major gas-phase product, and the amount increased as the initial KMnO 4 amount was increased (Fig. 3a). Small 1H-perfluoroalkane amounts were also found in the gas phase (Fig. 3b). It is worth noting that increasing the KMnO 4 amount from 0.25 mmol to 1.0 mmol reduced the CF 3 H amount, which reveals that CF 3 H could be decomposed in such a present reaction system. A reaction without any KMnO 4 was also performed. The released F -, CO 2 , and SO 4 2-amounts were 160, 199, and 17.0mol, which correspond to 29, 48, and 49% yields, respectively (Table 3, entry 1). The mineralization of FSC did not proceed effectively in the absence of KMnO 4 .

Next, we explored the effect of the O 2 amount on the F -, SO 4 2-, and CO 2 formations during reactions of FSC with 0.50 mmol KMnO 4 (ca. 14-fold molar excess of FSC) for 6 h (Figs. 4a and4b). These experiments revealed that F -and CO 2 formation was elevated when the O 2 amount was increased. When the initial O 2 amount was 13.6 mmol, the F -content was 417 ± 20 mol (entry 2 in Table 3), which corresponds to 75 ± 4 % yield. Under the same conditions, the CO 2 content in the gas phase reached 308 ± 28 mol, which corresponds to 74 ± 7 % yield. The pH of the solution at the end of the reaction was 3.8. Under the conditions, we estimated the CO 2 amount present in the reaction solution as follows. The Henry's law constant (H) of CO 2 is 3.3 × 10 -4 mol m -3 Pa -1 [START_REF] Sander | Compilation of Henry's law constants (version 4.0) for water as solvent[END_REF]. The CO 2 partial pressure [P(CO 2 )] of the collected gas after the autoclave was released to normal pressure was 2.85 ± 0.21 kPa (= 1.01 × 10 5 Pa × (2.82 ± 0.21) × 10 -2 ; the CO 2 concentration in the collected gas phase was 2.82 ± 0.21 % by gas chromatography).

Therefore, the CO 2 concentration in the reaction solution was 0.94 ± 0.07 mM [= H × P(CO 2 )].

This concentration and the reaction solution volume (10 mL) indicated that the CO 2 amount present in the reaction solution was 9.4 ± 0.7 mol. This value was only ca. 3% of the CO 2 amount (308 ± 28 mol) present in the gas phase. Furthermore, the pKa (6. Therefore, the presence of CO 2 in the reaction solution could be quasi-negligible, relative to that in the gas phase.

The SO 4 2-content was 32.6 ± 1.0 mol (entry 2 in Table 3), which indicated the yield was almost quantitative (94 ± 3%). Small amounts (0.1~15 mol) of 1H-perfluoroalkanes were also detected (Fig. 4c). The CF 3 H content gradually decreased when that of O 2 increased to 13.6 mmol.

Fig. 5a exhibits time courses of the formation of F -and SO 4 2-and CO 2 , when FSC was heated with 0.50 mmol KMnO 4 under O 2 (13.6 mmol) at 350 °C. The F -and CO 2 amounts were enhanced by time. The F -and SO 4 2-ions efficiently formed from the initial period such as 2 h.

After 18 h, these amounts were 459 and 33.6 mol, corresponding to 82 and 97% yields, respectively. This F -yield is the highest value among those tested in the present study. The released CO 2 gradually increased with increasing time, and reached 349 mol after 18 h, corresponding to 84% yield. In the gas phase, 1H-perfluoroalkane traces were detected (Fig. 5c), reaching maxima at ca. 6 h, and then decreased after prolonged time. The fluorine recovery-[(total moles of F atoms in F -and 1H-perfluoroalkanes after reaction)/(moles of F atoms in FSC before reaction)]-at 18 h was calculated to 96% (See Mass balance calculations in SM). The carbon recovery-[(total moles of C atoms in CO 2 and 1H-perfluoroalkanes after reaction)/(moles of C atoms in FSC before reaction)]-was 91% (See Mass balance calculations in SM). That is, most of the fluorine and carbon contents in the initial FSC could be accounted for F -, CO 2 , and 1H-perfluoroalkanes. The carbon recovery (91%) was lower than the fluorine recovery (96%).

Sulfur recovery was almost quantitative (97%, See Mass balance calculations in SM). The reaction solution after 18 h was analyzed by ion-chromatography, but did not reveal any shortchain perfluoroalkanoic acids such as CF 3 COOH. However, when the reaction solution was characterized by electrospray ionization mass spectrometry, which is more sensitive than the above technique, a peak with a m/z signal of 131, corresponding to [CF 3 COO + H 2 O] -, was detected (Fig. 6), indicating the presence of traces of CF 3 COOH.

Proposed reaction mechanism

To monitor the fate of KMnO 4 , X-ray diffraction was achieved on the precipitates recovered after the reaction of FSC containing 0.50 mmol KMnO 4 under O 2 (initial amount, 13.6 mmol) at 350 °C for 2, 6 and 18 h (Fig. 7). The patterns did not display any diffraction peaks originating from KMnO 4 , while peaks assigned to MnO 2 only were detected. This result is unsurprising because reports on the decomposition of persistent chemicals by treatment with KMnO 4 in superheated water [START_REF] Chang | Supercritical water oxidation of acetic acid by potassium permanganate[END_REF][START_REF] Honma | Permanganateinduced efficient mineralization of poly(vinylidene fluoride) and vinylidene-fluoride based copolymers in low-temperature subcritical water[END_REF][START_REF] Hori | Complete mineralization of fluorinated ionic liquids in subcritical water in the presence of potassium permanganate[END_REF] have indicated that KMnO 4 is converted to MnO 2 (Eq. 4), which then acts as the oxidizing agent. In the present system, it had been unclear whether most of the MnO 4 was transformed into MnO 2 before the FSC starts to decompose, because large amounts of F - ions formed even after short reaction periods (such as 2 h, Fig. 5a). Nevertheless, during the period when the 1H-perfluoroakane amounts decreased (after 6 h, Fig. 5b), KMnO 4 had already been converted into MnO 2 . To clarify the role of the in situ formed MnO 2 on the mineralization of FSC in more detail, a two-stage reaction was performed. i) First, aqueous KMnO 4 (0.50 mmol in 10 mL) without FSC was heated at 350 °C for 2 h with O 2 (initial amount 13.6 mmol). This reaction period was enough to convert KMnO 4 into MnO 2 (Fig. 7a). ii) After the autoclave was cooled, FSC (37.5 mol) was added to the reaction mixture in the autoclave. The vessel was then pressurized with O 2 (13.6 mmol) and reacted at 350 °C for 6 h. This two-stage operation efficiently released F -(475 mol, 72 % yield), SO 4 2-(35.3mol, 94% yield), and CO 2 (353 mol, 78% yield) (Table 3, entry 3). These yields were similar to the corresponding yields obtained from the reaction where both FSC and KMnO 4 were charged initially, pressurized with O 2 (13.6 mmol), and then heated at 350 °C for 6 h (Table 3, entry 2). This result clearly indicates that the in situ formed MnO 2 dominantly acts as the oxidizing agent for the FSC mineralization.

The observed high fluorine (96%) and sulfur (97%) recoveries mentioned above indicate that the F -and SO 4 2-concentrations in the reaction solution do not meaningfully decrease by the adsorption of these ions on the in situ formed MnO 2 surface. Of course, it is not surprising that traces of the fluorine component are detected on the formed MnO 2 surface by means of a sensitive analytical method. In fact, after 18 h-reaction, the collected precipitate was analyzed by X-ray photoelectron spectroscopy and the F(1s) spectrum displayed a peak around 684 eV, which corresponds to F -(Fig. S-4 in SM). In contrast, the spectrum did not show any peak assigned to carbon-fluorine bond (if the bond was present, the peak would appear at ~689 eV).

This result is consistent with the fact that FSC was efficiently mineralized by this treatment.

On the basis of our observations of the products generated under the reactions described herein, as well as from the literature, FSC decomposes according to the suggested process displayed in Scheme 2.

When FSC was heated in superheated water containing KMnO 4 under an excess O 2 , the thioether bond (C-S-C) in the non-fluorinated moiety can be oxidized to give a sulfone structure (C-SO 2 -C). This transformation is supported by the oxidation of common thioethers with electrophilic oxygen such as H 2 O 2 [START_REF] Cremlyn | An Introduction to Organosulfur Chemistry[END_REF]. Further oxidation around S atom is likely to lead to a fluorotelomer sulfonate, C 6 F 13 CH 2 CH 2 SO 3 -. Actually, the formation of fluorotelomer sulfonate from sulfone homologue is reported in the electrochemical degradation for fluorotelomers [START_REF] Gomez-Ruiz | Boron doped diamond electrooxidation of 6:2 fluorotelomers and perfluorocarboxylic acids. Application to industrial wastewaters treatment[END_REF].

The sulfonate derivative induced desulfonation, which releases C 6 F 13 • radical, SO 4 2-, and CO 2 .

The degradation steps of FSC until here seem to proceed easily because the SO 4 2-yield in the present system reached almost 100% as described above.

While the non-fluorinated moiety decomposes, a CF

The sequence of these steps results in the CF 3 COOH formation, the shortest perfluoroalkanoic acid which was consistently detected by electrospray ionization mass spectrometry. The stepwise degradation of perfluoroalkanoic acid via the formation of shorter-chain analogues as shown here has been frequently described in the literature [START_REF] Trojanowicz | Advanced oxidation/reduction processes treatment for aqueous perfluorooctanoate (PFOA) and perfluorooctanoate (PFOA) -a review of recent advances[END_REF][START_REF] Zhang | Nanotechnology in remediation of water contaminated by poly-and perfluoroalkyl substances: a review[END_REF][START_REF] Gomez-Ruiz | Boron doped diamond electrooxidation of 6:2 fluorotelomers and perfluorocarboxylic acids. Application to industrial wastewaters treatment[END_REF][START_REF] Hori | Efficient decomposition of perfluorocarboxylic acids and alternative fluorochemical surfactants in hot water[END_REF][START_REF] Hori | Efficient decomposition of environmentally persistent perfluorocarboxylic acids by use of persulfate as a photochemical oxidant[END_REF].

According to the same mechanism, CF 3 COOH decomposes into CO 2 and HF via the formation of CF 3 OH. The CF 3 • radical, released from C2 also reacts onto O 2 and H 2 O to generate CF 3 OH that is further transformed into CO 2 and HF via COF 2 . Recently, decomposition of persistent chemicals in superheated water in the presence of alkali reagent was reported [START_REF] Wu | Rapid destruction and defluorination of perfluorooctanesulfonate by alkaline hydrothermal reaction[END_REF][START_REF] Xiu | DEHP degradation and dechlorination of polyvinyl chloride waste in subcritical water with alkali and ethanol: a comparative study[END_REF]. When such a system is applied to perfluoroalkanesulfonic acids, the perfluoroalcohol formation seems to be accelerated [START_REF] Wu | Rapid destruction and defluorination of perfluorooctanesulfonate by alkaline hydrothermal reaction[END_REF]. If the reaction solution is highly basic, such a possibility should be accounted.

In addition to the above decomposition processes, which produce the major products, processes that form the minor products, the 1H-perfluoroalkanes, may also occur. The released C 6 F 13 • radical reacts with H 2 O to yield C 6 F 13 H. The formation of 1H-perfluoroalkanes during reactions of perfluorinated compounds in superheated water was reported, where the hydrogen atoms in 1H-perfluorolkanes arise from water [START_REF] Hori | Efficient decomposition of perfluorocarboxylic acids and alternative fluorochemical surfactants in hot water[END_REF][START_REF] Hori | Decomposition of perfluorinated ion-exchange membrane to fluoride ions using zerovalent metals in subcritical water[END_REF]. When KMnO 4 and O 2 were present, C 6 F 13 H could be transformed into C 6 F 13 OH, which decomposed into C 5 F 11 COF as described above. Likewise, the shorter-chain 1H-perfluoroalkanes (C 5 F 11 H to CF 3 H) could be produced as byproducts after carbon-carbon bond cleavage between the perfluoroalkyl and the carboxyl groups. This is consistent with a previous study reporting that heating PFOA at ~300 °C in a glass tube underwent decarboxylation to form CO 2 and 1H-perfluoroalkanes [START_REF] Krusic | Gas-phase NMR studies of the thermolysis of perfluorooctanoic acid[END_REF].

There have been several reports on the superheated water decomposition of perfluorinated surfactants [START_REF] Wu | Rapid destruction and defluorination of perfluorooctanesulfonate by alkaline hydrothermal reaction[END_REF][START_REF] Hori | Efficient decomposition of environmentally persistent perfluorooctanesulfonate and related fluorochemicals using zerovalent iron in subcritical water[END_REF][START_REF] Hori | Iron-induced decomposition of perfluorohexanesulfonate in sub-and supercritical water[END_REF][START_REF] Hori | Oxygen-induced efficient mineralization of perfluoroalkylether sulfonates in subcritical water[END_REF][START_REF] Hori | Iron-induced efficient mineralization of a cyclic perfluoroalkyl surfactant in subcritical and supercritical water[END_REF][START_REF] Hori | Efficient decomposition of a new fluorochemical surfactant: perfluoroalkane disulfonate to fluoride ions in subcritical and supercritical water[END_REF]. Among them, the destruction that proceeded by oxidative way has been quite rare [START_REF] Hori | Oxygen-induced efficient mineralization of perfluoroalkylether sulfonates in subcritical water[END_REF]. On the other hand, to our knowledge, the present report on the oxidative decomposition of FSC is the first example for the degradation of fluorotelomer surfactant in superheated water. Direct comparison on the reactivity of the present FSC and perfluorinated molecules is difficult because of a few examples. Accumulation of the data for superheated water reactions of both perfluorinated and fluorotelomer surfactants is thus desired, as further investigations.

Conclusions

A fluorotelomer surfactant (FSC) was involved in reactions in hot water (70-90 °C) with yields in the reaction solution and that of CO 2 in the gas phase reached 82, 97, and 84%, respectively. These are optimized conditions to release F -ions. In addition to these major products, gas-phase 1H-perfluoroalkanes (C n F 2n+1 H, n = 1~6) were also produced. After reaction of FSC for 18 h, the carbon, fluorine, and sulfur recoveries were calculated to be 91, 96, and 97%, respectively. Accompanying the reactions, MnO 4 -was converted into MnO 2 , and the in situ formed MnO 2 dominantly acts as the oxidizing agent for the mineralization of FSC.

S
Extension of this methodology (superheated water reaction in the presence of both KMnO 4

and O 2 ) to other organofluorine compounds and surfactants and scale-up of the reaction system are further planned in our laboratory. a Two-stage reaction. i) An aqueous solution of KMnO 4 (0.50 mmol in 10 mL) without FSC was heated at 350 °C for 2 h in the presence of O 2 (initial amount 13.6 mmol). ii) After the autoclave was cooled, FSC was added to the reaction mixture, and the autoclave was pressurized with O 2 (13.6 mmol) and then heated at 350 °C for 6 h.

  30 °C for 5 min, ramp to 200 °C at 20 °C min -1 , and hold at 200 °C for 20 min. An ion chromatograph (IC-2001; Tosoh, Tokyo, Japan) equipped with an analytical column (Tosoh TSKgel Super IC-Anion, the column oven temperature, 40 °C) was employed to quantify the amounts of F -and SO 4 2-in the reaction solutions. The mobile phase was an aqueous solution composed of 6 mM sodium tetraborate, 15 mM boric acid, and 0.2 mM sodium hydrogen carbonate; and flowed at 0.8 mL min -1 . HPLC/MS enabled us to quantify FSC in the reaction solutions. The instrument was an LCMS-2010 EV (Shimadzu) equipped with an analytical column (TSKgel ODS-100H, Tosoh). The mobile phase was 60:40 (volume ratio) MeCN/pure water at 0.8 min -1 . A typical mass chromatogram (m/z = 519, corresponding to [C 6 F 13 C 2 H 4 SCH 2 CH(CF 3 )COO] -, i.e., deprotonated FSC) and a calibration curve based on the peak intensity are shown in Fig. S-3 in SM.

  35, first dissociation step) [45] and the pH (3.8) indicated that most CO 2 molecules are not dissociated in the reaction solution ([HCO 3 -]/([H 2 CO 3 ] + [CO 2 ]) = 4.47 × 10 -7 ).

Fig. 1 .Fig. 2 .

 12 Fig. 1. Structure of 2H,3H,3H,5H,5H,6H,6H-4-thia-perfluoro(2methyl)-1-dodecanoic acid (FSC)

Fig. 3 .

 3 Fig. 3. Effect of initial KMnO 4 amount on (a) F -and SO 4 2-amounts formed in the reaction solution and CO 2 amount released in the gas phase and (b) their corresponding yields and (c) 1H-perfluoroalkane amounts in the gas phase upon reaction of FSC (initial amount, 34.8 mol) at 350 °C for 6 h under O 2 (13.6 mmol). Error bars at the initial KMnO 4 0.50 mmol were obtained from two reactions under the same conditions.

Fig. 4 .

 4 Fig. 4. Effect of initial O 2 amount on (a) F -and SO 4 2-amounts formed in the reaction solution and CO 2 amount produced in the gas phase and (b) their corresponding yields (c) amounts of 1H-perfluoroalkanes in the gas phase upon reaction of FSC (initial amount, 34.8 mol) at 350 °C for 6 h containing KMnO 4 (initial amount, 0.50 mmol). Error bars at the initial O 2 13.6 mmol were obtained from two reactions under the conditions.

Fig. 5 .

 5 Fig. 5. Effect of reaction time on (a) F -and SO 4 2-amounts formed in the reaction solution and CO 2 amount released in the gas phase and (b) their corresponding yields and (c) amounts of 1H-perfluoroalkanes in the gas phase upon reaction of FSC (initial amount, 34.8 mol) at 350 °C containing KMnO 4 (initial amount, 0.50 mmol) under O 2 (initial amount, 13.6 mmol). Error bars at 6 h were obtained from two reactions under the same conditions.

Fig. 6 .

 6 Fig. 6. Electrospray ionization mass spectrum of solution obtained by reaction of FSC (initial amount, 34.8 mol) at 350 °C in the presence of KMnO 4 (initial amount, 0.50 mmol) under O 2 (initial amount, 13.6 mmol) for 18 h.

Fig. 7 .

 7 Fig. 7. X-ray diffraction patterns for precipitates collected after reactions of FSC (initial amount, 34.8 mol) in the presence of KMnO 4 (initial amount, 0.50 mmol) under O 2 (initial amount, 13.6 mmol) at 350 °C for (a) 2, (b) 6, and (c) 18 h.

  2 amounts produced by reactions of FSC in hot water containing 50 mM K 2 S 2 O 8 at 70, 80, and 90 °C are listed in Table1. We previously reported that C5-C9 perfluoroalkanoic acids such as PFOA effectively decompose into F -and CO 2 at around 80 °C[START_REF] Hori | Efficient decomposition of perfluorocarboxylic acids and alternative fluorochemical surfactants in hot water[END_REF]. For example, when C 6 F 13 COOH in 50 mM aqueous K 2 S 2 O 8 is heated at 80 °C with 50 mM K 2 S 2 O 8 for 6 h, F - and CO 2 are obtained in 75.7 and 77.9% yields, respectively. In this previously reported system, 80 °C was suitable to achieve efficient mineralization of these compounds because at this The F -and CO 2 amounts formed by reactions of FSC at 300 °C for 6 h in superheated water under several combinations between coexisting gas (either O 2 or Ar, initial amount, 5.1 mmol) and KMnO 4 (initial amount, 0.50 mmol) are summarized in Table2. In all cases, no FSC remained. For the reaction under O 2 without any KMnO 4 , the F -and CO 2 yields were both 20% (entry 1). This result suggests that the decomposition of FSC was almost limited to the CF 3 group at C2 and adjacent non-fluorinated moiety. Compared to these yields, the SO 4 2-yield (Eq.

	FSC little mineralized, S 2 O 8 2-was consumed. Although we did not quantify S 2 O 8	2-in the
	reaction solution because S 2 O 8 2-cannot be detected by conventional ion-chromatography, S 2 O 8	2-
	and SO 4	2-are known to be the only stable sulfur species and the total S atom content [moles of
	(S 2 O 8 2-× 2 + SO 4 2-)] was constant and the same as the initial value (moles of initial S 2 O 8 2-× 2) 3; each FSC molecule contains one sulfur atom. Note: the calculation of the SO 4 2-yield is
	during the decomposition of perfluoroalkanoic acids in water [39]. Therefore, 34% SO 4 different from that using S 2 O 8 2-as described above) was higher (55%, entry 1), indicating that 2-yield
	suggested that 66 % of the initial S 2 O 8 2-remained. Rising the reaction temperature to 80 °C the carbon-sulfur bond in FSC was cleaved more easily.
	increased the F -and CO 2 yields to 16 and 6 %, respectively (Table 1, entry 2). However, the
	SO 4 SO 4	2-amount was 766 mol, which corresponds to 77% yield, suggesting that the remaining 2-yield (%) = [(moles of SO 4 2-formed)/(moles of S atom in initial FSC)] × 100
	temperature, S 2 O 8 S 2 O 8 22 O 8 2-decomposes to two sulfate anion radicals (2SO 4 • In the current study, we have found that when FSC was treated with hot water containing 50 2-is likely the poor solubility of FSC in water.
	mM K 2 S 2 O 8 at 70 °C for 6 h, virtually no mineralization proceeded. The F -and CO 2 yields were
	only 1 and 2%, respectively (Table 1, entry 1). At this temperature, the SO 4 3.3. Reactions in superheated water	2-amount was 336
	mol, which corresponds to 34% [= 336/(500 × 2)] of the sulfur atoms in the initial S 2 O 8 2-
	amount (0.50 mmol) [note that although each FSC molecule contains one sulfur atom, the
			2 O 8 2-]. That is, while

-), which have high oxidizing ability. The SO 4 • -radical is reduced to SO 4 2-, and the perfluoroalkanoic acid undergoes oxidation accompanied by a carbon-carbon bond cleavage between the perfluoroalkyl group and carboxyl group, in a process similar to Kolbe electrolysis

[START_REF] Hori | Efficient decomposition of perfluorocarboxylic acids and alternative fluorochemical surfactants in hot water[END_REF][START_REF] Kutsuna | Rate constants for aqueous-phase reactions of SO 4 with C 2 F 5 C(O)Oand C 3 F 7 C(O)Oat 298 K[END_REF]

. In contrast, at higher temperature, the mineralization extent decreases because SO 4 • -is consumed by other reactions, such as reaction with water. In both thermal-

[START_REF] Hori | Efficient decomposition of perfluorocarboxylic acids and alternative fluorochemical surfactants in hot water[END_REF]

and photochemical

[START_REF] Hori | Efficient decomposition of environmentally persistent perfluorocarboxylic acids by use of persulfate as a photochemical oxidant[END_REF]

reactions, 50 mM was the most desired K 2 S 2 O 8 concentration to mineralize perfluoroalkanoic acids in water: K 2 S 2 O 8 is not fully soluble at further higher concentration. amount (29.7 mol) was much lower than that (1000 mol) in the initial S -percentage was only 23%. At 90 °C, the CO 2 yield increased to 12% but the F -yield did not increase (14%) (entry 3). These yields suggest that a CF 3 group on C2 position and adjacent non-fluorinated moiety decomposed (if the CF 3 group decomposed into F -, the yield should be 19% (= 3/16; one FSC molecule has 16 fluorine atoms). However, the SO 4

2-amount at 90 °C was 974 mol, which means 97% of the sulfur atoms in the initial S 2 O 8 2-amount. This result indicates that the majority of S 2 O 8 2-was consumed (the remaining ratio was estimated to be 3% only). Therefore, we concluded that no further increase in FSC mineralization could be expected under these conditions, Hence, it was of interest to explore reactions of FSC in superheated water containing KMnO 4 . One reason for the low reactivity against S

  3 • radical is also released from C2. The C 6 F 13 • radical likely reacts with O 2 and water to form C 6 F 13 OH. Because perfluoroalcohols are unstable[START_REF] Cheburkov | [END_REF][START_REF] Saint-Loup | Synthesis and properties of novel fluorotelechelic macrodiols containing vinylidene fluoride, hexafluoropropene and chlorotrifluoroethylene[END_REF], C 6 F 13 OH releases into HF and C 5 F 11 COF acid fluoride (Eq. 5), which can be hydrolyzed to produce the corresponding C 5 F 11 COOH perfluoroalkanoic acid[START_REF] Chambers | Fluorine in Organic Chemistry[END_REF] (Eq. 6).

	C 6 F 13 OH → C 5 F 11 COF + HF	(5)
	C 5 F 11 COF + H 2 O → C 5 F 11 COOH + HF

  2 O 8 2-anions or in superheated water with KMnO 4 . This examination is the first report on the degradation of FSC. Hot water under the former conditions was not efficient to mineralize FSC.Decomposition of FSC molecule occurred only around CF 3 group at C2. FSC was only slightly soluble in aqueous K 2 S 2 O 8 and its low solubility of FSC in water may be the reason for its low reactivity. In contrast, under the latter conditions, the mineralization moiety was extended to C 6 F 13 group, and it mineralized greater by increasing the O 2 amount. Specifically, when FSC was treated with 0.50 mmol KMnO 4 under O 2 (13.6 mmol) at 350 °C for 18 h, the F -and SO 4

	2-

Table 1

 1 Product yields of obtained by reaction of FSC in hot water with S 2 O 8 Initial FSC amount, 29.7 mol; reaction solution volume, 10 mL; initial K 2 S 2 O 8 amount, 0.50 mmol (50 mM as concentration); reaction time, 6 h. b Based on the sulfur amount (1000 mol) in the initial S 2 O 8 2-. Although FSC molecule contains one sulfur atom, the amount (29.7 mol) was much lower than the amount (1000 mol) from S 2 O 8 2-. Even if the initial sulfur atom of FSC is included in the yield calculation, the SO 4 2-yields become almost similar values. Note: the calculation of the SO 4 2-yield is different from that using KMnO 4 as described in the later sections.

	2-a

a

Table 2

 2 Products obtained by reaction of FSC under several combinations between O 2 , KMnO 4 and Ar (300 °C, 6 h)

	Entry	Initial	Coexisting	Initial	F -(mol)	CO 2 (mol)	SO 4 2-(mol)	1H-perfluoroalkanes in
		KMnO 4	gas (mmol)	FSC				the gas phase (mol)
		(mmol)		(mol)	[yield (%)]	[yield (%)]	[yield (%)]
								CF 3 H (0.7), C 2 F 5 H (0.3),
	1	none	O 2 (5.1)	30.1	95.4 [20]	71.4 [20]	16.5[55]	C 3 F 7 H (1.3), C 4 F 9 H (1.1), C 5 F 11 H (1.3),
								C 6 F 13 H (0.5)
								CF 3 H (15.2), C 2 F 5 H
	2	0.50	Ar (5.1)	34.2	193 [35]	78.0 [19]	30.2[88]	(4.0), C 3 F 7 H (0.8), C 4 F 9 H (4.1), C 5 F 11 H
								(2.4), C 6 F 13 H (0.1)
								CF 3 H (14.8 ± 0.9),
	3	0.50	O 2 (5.1)	35.4	293 ± 2 [52 ± 1]	132 ± 4 [31 ± 1]	35.3 ± 0.2 [100]	C 2 F 5 H (2.7 ± 1.3), C 3 F 7 H (1.0), C 4 F 9 H (4.9 ± 0.2), C 5 F 11 H (2.3 ±
								0.3), C 6 F 13 H (0.1)

Table 3

 3 Products obtained by reactions of FSC in the presence of O 2 (13.6 mmol) at 350 °C for 6 h

	Entry	Initial	Initial	F -(mol)	CO 2 (mol)	SO 4 2-(mol)	1H-perfluoroalkanes in the gas
		KMnO 4	FSC				phase (mol)
		(mmol)	(mol)	[yield (%)]	[yield (%)]	[yield (%)]
							CF 3 H (1.3), C 2 F 5 H (1.6),
	1	none	34.8	160 [29]	199 [48]	17.0 [49]	C 3 F 7 H (2.7), C 4 F 9 H (6.3),
							C 5 F 11 H (5.1), C 6 F 13 H (1.6)
	2	0.50	34.8	417 ± 20 [75 ± 4]	308 ± 28 [74 ± 7]	32.6 ± 1.0 [94 ± 3]	CF 3 H (9.5 ± 1.5), C 2 F 5 H (3.1 ± 0.5), C 3 F 7 H (1.1 ± 0.2), C 4 F 9 H (3.6), C 5 F 11 H (4.4 ± 0.6), C 6 F 13 H (0.4)
	3 a	0.50	37.5	475	353	35.3	CF 3 H (1.8), C 2 F 5 H (2.3), C 3 F 7 H (2.2), C 4 F 9 H (4.6),
				[72]	[78]	[94]	C 5 F 11 H (4.7), C 6 F 13 H (0.7)

Acknowledgments

The authors thank the Japan Society for the Promotion of Science for a grant (JSPS KAKENHI no. JP18H03402) and Elf Atochem and Tosoh Finechem Corp. for supplying free reactants.

Declarations of interest

None.

Appendix A. Supplementary data

Supplementary data ( 1 H and 19 F NMR spectra, quantification conditions of major products, mass chromatogram of FSC solution, calibration curve for the quantification of FSC, mass balance calculations, and XPS spectrum) associated with this article can be found, in the online version, at https://doi.org/10.1016/jcej.

FSC


Hassan Nehme
email: h.nehme@sitia.fr

Clément Aubry

Thomas Solatges

Xavier Savatier

Romain Rossi

Rémi Boutteau

LiDAR-based Structure Tracking for Agricultural Robots: Application to Autonomous Navigation in Vineyards

Keywords: Agricultural robotics, Autonomous navigation, Structure tracking, LiDAR

Autonomous navigation is a key defining feature that allows agricultural robots to perform automated farming tasks. Global navigation satellite system (GNSS) technology is providing autonomous navigation solutions for current commercial robotic platforms that can achieve centimeter-level accuracy when real-time kinematic (RTK) corrections are available. However, GNSS-based solutions are expensive and require a long preparation phase where the field has to be surveyed with a GNSS rover to collect waypoints for the navigation path. An alternative navigation approach can be provided by Local perception sensors, such as LiDAR scanners, by tracking geometric features in the perceived scene. This paper presents a robust LiDAR-based solution for structure tracking along vine rows. The proposed method does not require prior field surveying, and it is insensitive to crop characteristics such as row width and spacing. Moreover, the proposed algorithm identifies and builds an online regression model of the structure. This is done by applying the Hough transform with a parameterization and search method motivated by a practical interpretation of point cloud statistics. The proposed method was tested on a commercial robotic platform in two configurations of vineyards. The experiments show that the proposed algorithm achieves consistent and accurate row tracking, which was validated against a reliable RTK-GNSS ground truth.

Introduction

Increasing demands for food production, lack of workforce, and new environmental regulations regarding the use of chemicals are raising the interest in automated agricultural machinery as a way to improve production means. Indeed, autonomous agricultural robots offer an entirely new approach to performing automated agricultural tasks. In order to perform these tasks efficiently and safely without damaging the crops, a robot has to navigate along crop rows with a considerable level of accuracy. Global Navigation Satellite System (GNSS) technology provides robot navigation solutions that can achieve centimeter-level accuracy when Real-Time Kinematic (RTK) corrections are available. However, these solutions require a prior definition of a global path from a set of waypoints which can be collected by surveying the field using a GNSS rover. In this regard, a reliable GNSS-based solution is costly in terms of materials invested and time consumed preparing the task. This drawback has motivated a research interest in developing alternative navigation solutions based on local perception sensors.

In a local perception navigation paradigm, sensor data such as images and 3D point clouds are analyzed in order to identify and track local features in the scene. This approach has been applied to on-road autonomous driving by tracking local features such as lane marking [START_REF] Aly | Real time detection of lane markers in urban streets[END_REF][START_REF] Pan | Spatial as deep: Spatial cnn for traffic scene understanding[END_REF] or road boundaries [START_REF] Ort | Autonomous vehicle navigation in rural environments without detailed prior maps[END_REF]. In agricultural fields, crop rows represent a geometrical structure that can be exploited as a navigation clue. Crop rows vary in features across different types of cultures, ranging from small plants in market gardening to dense canopies in viticulture. Hence, feature identification can be challenging in agricultural environments due to their open and changing nature and extreme lighting conditions. In this regard, LiDAR sensors are often preferred over cameras in these situations due to their accuracy and insensitivity to lighting conditions. Common local navigation approaches require a prior 3D map of the environment [START_REF] Merriaux | Robust robot localization in a complex oil and gas industrial environment[END_REF] or a prior measurement model [START_REF] Hiremath | Laser range finder model for autonomous navigation of a robot in a maize field using a particle filter[END_REF][START_REF] Tipaldi | Lifelong localization in changing environments[END_REF] that incorporates crop-specific characteristics such as spacing width and periodicity. This makes them less suitable for versatile robots intervening on different crops with different characteristics. Hence the interest in structure tracking methods that are indifferent to specific crop characteristics and require no prior map of the environment.

This paper presents a robust LiDAR-based solution for structure tracking along vine rows. The proposed solution consists of two main steps. The first step consists of the identification of the navigation clues provided by the vine row structure as an estimation of the overall heading and the lateral position of each row. This is done by applying Hough transform on the perceived point clouds with a parameterization and a search method motivated by a practical interpretation of point cloud statistics. In the second step, frame-to-frame structure estimations are used along with the robot's motion in order to build and maintain, in real-time, a persistent regression model for each row. Finally, tracking data are provided in the form of relative localization information, i.e., lateral and angular deviations, with respect to the regression model of the row to follow. The proposed method was tested on a commercial robotic platform in two configurations of vineyards. The experiments show that the proposed algorithm achieves consistent and accurate row tracking, which was validated against a reliable RTK-GNSS ground truth. The main contributions of this paper are:

-A LiDAR-based solution to provide autonomous tracking in vineyards, which is considered as a perceptually challenging environment due to the irregular canopy shape and high vegetation density. -The proposed solution does not require prior field surveying, and it is insensitive to crop characteristics such as row width and spacing. This reduces the effort and time invested in task preparation. -The proposed method was implemented and tested in real conditions on production sites. The evaluation with respect to a reliable GNSS-based solution showed very high robustness and consistency, even when some vines were missing. This suggests that the proposed method can be implemented as an alternative to GNSS-based tracking or as a part of a hybrid navigation solution, which reduces the cost and accuracy requirements of the GNSS system.

The remainder of the paper is organized as follows. Section 2 presents some related work. Section 3 states the problem and describes the different elements of the proposed method for structure tracking along vine rows. Section 4 presents the experimental results and the validation against a reliable ground truth in production sites. Finally, Section 5 concludes the paper and provides some ideas for future work.

Related work

This paper proposes a navigation approach based on the perception and identification of a geometric structure in the scene. Crop rows provide this structure in the majority of cases where an agricultural robot has to intervene. In this setting, the problem discussed here is related to the field of crop/weed detection and discrimination in the computer vision literature. Crop rows detection is generally a first step where its outputs are used for further analysis in order to provide solutions for weed detection [START_REF] Bah | Weeds detection in uav imagery using slic and the hough transform[END_REF], modeling plant characteristics [START_REF] Rabab | A template-free machine visionbased crop row detection algorithm[END_REF], or autonomous navigation [START_REF] Basso | A uav guidance system using crop row detection and line follower algorithms[END_REF]. Hence, the discrimination accuracy and distinctiveness requirements of a crop rows detection algorithm varies depending on the application. Mature results have been presented in the literature with the use of deep convolutional neural networks [START_REF] Bah | Crownet: Deep network for crop row detection in uav images[END_REF] with the objective of increasing detection accuracy and reducing the fault rate for weeding applications and offline planning. On the other hand, for autonomous navigation applications, crop rows are identified as a local feature in a framework that takes the inaccuracy of feature extraction as an input to a model matching and filtering step [START_REF] Basso | A uav guidance system using crop row detection and line follower algorithms[END_REF][START_REF] Nagham | A review of autonomous navigation systems in agricultural environments[END_REF]. In such a framework, a trade-off between accuracy and efficiency takes place. Therefore, high discrimination accuracy and distinctiveness of the algorithm, which comes at the expense of increased computational cost, is not necessarily crucial for this task, and a computationally efficient accurate-enough feature extraction technique is often preferred. Classical vision-based navigation approaches in agricultural environments implement line fitting techniques in order to identify the underlying parallel line structure of crop rows from image data. Common line fitting techniques include linear regression [START_REF] Søgaard | Determination of crop rows by image analysis without segmentation[END_REF], RANSAC [START_REF] Reiser | Crop row detection in maize for developing navigation algorithms under changing plant growth stages[END_REF] and Hough transform [START_REF] Rovira-Más | Hough-transform-based vision algorithm for crop row detection of an automated agricultural vehicle[END_REF]. Hough transform is a mathematical transformation between a feature space (often the image space) and a parameter space called Hough space. It is used as a pattern recognition technique to identify a parametric model such as a line through a voting procedure in the Hough space. Hough transform is preferred over linear regression due to its robustness against outliers and its ability to be generalized to identify curves and complex patterns. A common approach is to apply line fitting on a binary image obtained after a segmentation, done by thresholding appearance features such as color indices [START_REF] Hamuda | A survey of image processing techniques for plant extraction and segmentation in the field[END_REF], aiming to separate pixels belonging to the crops from other elements in the scene: Hough transform was applied in [START_REF] Rovira-Más | Hough-transform-based vision algorithm for crop row detection of an automated agricultural vehicle[END_REF] after the image was binarized by thresholding grey values and in [START_REF] Gée | Crop/weed discrimination in perspective agronomic images[END_REF] after thresholding excess green index (ExG). The simple application of the Hough transform to detect a single line reaches a limitation in situations with significant presence of weed or high vegetation density. To deal with such situations, search techniques in the Hough space that exploit prior hypotheses about the field were introduced. Row spacing was used in [START_REF] Åstrand | A vision based row-following system for agricultural field machinery[END_REF] to search for parallel lines in the Hough space. Row parallelism was exploited in [START_REF] Jones | Modelling agronomic images for weed detection and comparison of crop/weed discrimination algorithm performance[END_REF][START_REF] Gée | Crop/weed discrimination in perspective agronomic images[END_REF], and the authors concluded that, in Hough space, the peaks corresponding to parallel lines are aligned around the overall orientation.

A different pattern analysis algorithm was proposed in [START_REF] English | Vision based guidance for robot navigation in agriculture[END_REF]. The authors proposed a segmentation-free image-based method to extract the heading of parallel crop rows by analyzing the texture in a grayscale image. In this method, the image is first wrapped into an overhead view. Then, the image is iteratively skewed, and the variance of the sum of grey values for each column is computed at each iteration. Finally, the overall heading of the structure is considered to be the angle that maximizes the computed variance. This method was completed in [START_REF] English | Learning crop models for visionbased guidance of agricultural robots[END_REF] with a learning method to learn a crop model that was used to calculate the lateral deviation.

The preprocessing steps in a typical image-based pipeline perform color analysis in order to find a set of keypoints on which line fitting will be applied. Other operations are required in order to project the keypoints in a 3D metric space relative to the guided vehicle. These operations introduce challenges such as dealing with variable appearance due to seasonal changes and light conditions. LiDAR sensors, on the other hand, provide precise measurements directly in that space, and through a simple preprocessing (e.g., height thresholding), the set of keypoints to be used to detect crop rows can be found. This was applied in [START_REF] Hamner | Improving orchard efficiency with autonomous utility vehicles[END_REF], where the Hough transform was applied on data points acquired by two laser scanners in order to guide a vehicle between tree rows in an orchard. In [START_REF] Reiser | Crop row detection in maize for developing navigation algorithms under changing plant growth stages[END_REF], the RANSAC algorithm was applied on 2D laser-scan measurements to detect crop rows at different growth stages. A common keypoints extraction method was discussed in [START_REF] Winterhalter | Crop Row Detection on Tiny Plants With the Pattern Hough Transform[END_REF] for LiDAR and vision measurements by thresholding the height for point clouds and a color index for images. Furthermore, the Hough transform was extended in [START_REF] Winterhalter | Crop Row Detection on Tiny Plants With the Pattern Hough Transform[END_REF] to fit a pattern of parallel equidistant lines parametrized by a common orientation, an offset, and spacing. Such parameterization improved the detection, and it requires less prior knowledge about the structure since it includes the spacing in the parameter space. The drawback of this method is that it increases the computation complexity by adding a third dimension to the parameter space.

In this work, LiDAR point clouds are used as the perception modality in order to identify and track a parallel structure. The proposed algorithm applies Hough transform with a parameterization motivated by a practical interpretation of point cloud statistics. Furthermore, a search strategy in Hough space is applied in order to estimate the overall structure heading inspired by the ideas from [START_REF] Gée | Crop/weed discrimination in perspective agronomic images[END_REF][START_REF] English | Vision based guidance for robot navigation in agriculture[END_REF] without adding the third dimension to the search space. Eventually, to provide complete and reliable navigation in challenging environments with high vegetation density, a model matching and filtering algorithm is developed to deal with the inaccuracy and faults during the feature extraction step.

Materials and methods

The method described in this paper is designed and tested on Trektor1 , a 3 tons versatile agricultural robot developed by SITIA. The robot, shown in two vineyard configurations in Figure 1, is designed to intervene on different crops with their variety of features, ranging from tiny plants in market gardening to dense small trees in viticulture. The robot can also adjust its width to adapt to different vineyard configurations: wide and narrow vineyards. A parallel structure is common in all of these fields, whether it is provided by crop rows or man-made structures (e.g., wheel tracks). Thus, it is worthy to investigate a structure tracking solution based on local perception. This section explains the motivation and development of the LiDAR-based structure tracking method.

Problem Statement and overview of the proposed solution

One of the main applications of our robotic platform is autonomous navigation in vineyards. The current solution implemented onboard requires a global GNSS path covering the entire field. Hence, the robot is equipped with an accurate global navigation system based on the fusion of RTK-GNSS and high accuracy inertial navigation systems. Leveraging this accuracy in practice requires the global path to be in high resolution, meaning that several waypoints along the vine rows need to be collected using a GNSS rover, which requires a significant effort in the task preparation phase. Hence comes the motivation for a local perception navigation method that exploits the navigation clues provided by the crop row structure. In this setting, the accuracy and resolution requirements of the global path are significantly reduced: only the start and endpoints of the desired rows need to be surveyed in order to create the global path that handles the transition between rows while leaving accurate row tracking for the local perception algorithm.

Local perception for this task is provided by a 16-channel 3D LiDAR sensor (Ouster OS1-16) mounted on top of the robot, as shown in Figure 2. The design decision behind such positioning is to allow several rows to be perceived in different vineyard configurations as well as in various types of cultures. In this setting, vine rows will be perceived from the top, resulting in the structure profile illustrated in Figure 3. The goal of the proposed approach is to identify this structure from 3D LiDAR point clouds as an overall heading ∆γ and the lateral positions y i of each perceived row. Hence, crop rows are assumed to be locally parallel in the considered range of measurement of the LiDAR sensor (it was set to 10 meters in experimentation). Consequently, the method builds a model for each row that will serve as a reference path to follow. The final outputs of the method are the relative localization information: the lateral deviation ∆l and the angular deviation ∆γ. This information is suitable for tracking control laws that are designed for car-like mobile robots. We refer the reader to the approach proposed in [START_REF] Lenain | Adaptive and predictive non linear control for sliding vehicle guidance: Application to trajectory tracking of farm vehicles relying on a single rtk gps[END_REF] for a complete explanation of the control law implemented on our robotic platform. The tracking control law is beyond the scope of this paper since the main focus here is on the perception part of the problem. A schematic overview of the proposed solution is provided in Figure 4 with three major blocks:

-Preprocessing: the operations in this step are tailored by the target culture and sensor choice. The aim here is to extract a set of representative keypoints to be used by the pattern analysis algorithm. In the case of vineyards perceived with a 3D Lidar, downsampling and height thresholding is sufficient to eliminate the ground and extract representative keypoints.

-Structure identification: this is the step where frame-to-frame rows detection occurs. The proposed algorithm, based on Hough transform and point cloud histograms, extracts row positions and a common heading from the set of keypoints.

-Model matching: this step takes the outputs from the identification step and performs data aggregation and filtering in order to construct a persistent model of each row of the structure.

The remainder of this section explains in detail the different steps of the proposed solution.

Fig. 3: Illustration of the structure profile to be identified. Tracking is provided by calculating the lateral ∆l and angular ∆γ deviations with respect to the reference row.

Fig. 4: Overview of the proposed solution.

Structure identification

The goal here is to identify a set of parallel rows from input point clouds after preprocessing through height thresholding and voxel grid downsampling [START_REF] Rusu | 3D is here: Point Cloud Library (PCL)[END_REF].

Heading estimation with iterative skewing

Figure 5a shows an example of an input point cloud acquired in a narrow vineyard (configuration shown in Figure 17a). The core of the proposed structure identification method is the estimation of a common heading by analyzing the entire input point cloud: Figure 5 shows the concept behind heading estimation. The first row shows illustrations in the x-y plane of the same point cloud except that in Figure 5b, the point cloud is rotated in a way to be aligned with the x-axis. The second row shows the corresponding y-histograms of the point clouds. It is clear that the histogram of the corrected point cloud has peaks that can identify each row, while the histogram of the original point cloud is more flattened, and the rows cannot be separated. Hence, the information about the heading can be resumed in the y-histogram: the variance of histogram values is maximized when the point cloud has zero heading [START_REF] English | Vision based guidance for robot navigation in agriculture[END_REF]. The method used here to maximize this variance, and thus, finding the common heading, is the one originally proposed in [START_REF] English | Vision based guidance for robot navigation in agriculture[END_REF] for images where the equivalent of y-histogram was the sum along the columns of a grayscale image. This method, named iterative skewing, consists of iteratively rotating the cloud about the z-axis while computing the y-histogram along with its variance in each iteration. Finally, the heading is considered to be the angle that maximizes the variance.

Relation to the Hough transform

Looking into the iterative skewing algorithm, the relationship between the coordinates of a point in the rotated cloud and the original cloud is the following:

y rot =x 0 sin γ + y 0 cos γ (1)
=x 0 cos θ + y 0 sin θ, γ = π 2 -θ, (2)
where γ is the heading rotation angle, y rot is the ordinate of a point in the rotated cloud, and (x 0 , y 0 ) are the coordinates of the corresponding point in the original cloud. Equation 2, when generalized to any (x, y) tuple, is the representation of a line according to the normal parameterization using the normal angle θ and a signed distance y rot which is the standard representation of a candidate line in Hough transform [START_REF] Duda | Use of the hough transformation to detect lines and curves in pictures[END_REF]. Therefore, computing the histogram of y rot for iterative values of γ is equivalent to computing the Hough transform of the point cloud through a 2D voting procedure. Indeed, Hough transform maps input points from their 2D metric space (x, y) to the parameter space (i.e., the Hough space) (y rot , γ). A point (x 0 , y 0 ) in the input point cloud is mapped to a sinusoid in the Hough space (y rot , γ) that is defined in Equation 2. This sinusoid defines the parameter of all the possible lines that pass through the point (x 0 , y 0 ). Thus, each point votes for the parameter of candidate lines. After considering all points, the Hough representation (also called the Hough accumulator) of the input cloud is a heatmap in the 2D parameter space where the coordinates of high heat define the most likely model candidates. In this setting, each column of the resulting Hough accumulator is the y-histogram of the point cloud rotated by a heading γ.

Such an interpretation gives a formal understanding of the iterative skewing algorithm as a search method in Hough space that estimates the heading angle by finding the column with maximal variance. This search method finds the common heading of a pattern of parallel lines without integrating it in the search space. Therefore, the search space remains limited to only two parameters: (y rot , γ). This provides a considerable advantage in terms of computational time by not adding a third dimension to the search space as in other pattern fitting methods [START_REF] Winterhalter | Crop Row Detection on Tiny Plants With the Pattern Hough Transform[END_REF]. Figure 6 illustrates the heading estimation method: the Hough accumulator for γ ∈ [-20 • , 20 • ]. The plot of column variance with respect to the heading angle is shown in the second row along with the estimated pattern heading.

Detecting lateral row positions

Once the heading is estimated, each row in the structure must be located (position on the y-axis) in order to complete the crop profile. This is done through 1D peak detection on the accumulator column corresponding to the estimated heading. This column is the y-histogram of the corrected point cloud in Figure 5b and thus finding its peaks would locate each row on the y-axis. To this end, a simple peak detection method is proposed to complete the detection. The proposed peak detection method is efficient and does not require prior knowledge about the structure details such as spacing and row width (these are often required in standard peak detection methods such as mean shift [START_REF] Cheng | Mean shift, mode seeking, and clustering[END_REF] or k-means). Figure 7 shows the principle of the algorithm. First, a thresholding step is performed on Fig. 6: Illustration of the heading estimation method in Hough space. First row: the hough accumulator of the input point cloud. Second row: the column variance with respect to the heading angle. The heading is estimated as the angle that maximizes the variance.

histogram values (using their mean as the threshold) to find histogram segments that represent interval estimation of the position of each row. Then, a position is estimated from each interval as the mean of its values. Since the input point cloud corresponds to the crop's canopy, the exact position of the tree trunk is not directly observable and thus needs to be estimated. The mean of histogram values provides a reasonable estimate of the trunk's position as the center of the perceived canopy row. The results of peak detection are presented in Figure 6 as white dots in the Hough accumulator. In summary, the structure identification step applies Hough transform with a custom search method in the parameter space in order to identify a common heading along with the position of each row. Imperfections in the detection could occur, such as discontinuity and inaccuracy of row position estimation due to high vegetation pressure in the discussed case. The discretization resolution of the parameters in Hough space also produces some inaccuracy. This is not ideal for accurate navigation since the tracking algorithm requires continuous and smooth lateral and angular deviations. Therefore, a model matching and filtering step is required in order to construct a consistent and robust model to be used as a reference path.

Model matching

At each time step and as the robot moves forward, structure identification estimates, for each point cloud, an overall heading γ and a set of row positions. Thus providing local observations as a set of points

O t = {(x i , y i , γ i ), i : 1 → n} (3)
where x i and y i represent the coordinates of a detected row center, γ i is the corresponding estimated heading, and n is the number of rows detected per input frame (point cloud). These observations are not consistent in their representation of the actual structure elements (crop rows): discontinuity occurs in these observations due to gaps in the vegetation, which is common in old production sites, or due to detection failures. Figure 8 illustrates the general idea behind the model matching step in such situations. The goal here is to make sense of the local observations by associating them with a unique model of each row that is persistent across all the frames. The models constructed in this step are linear regression models representing line equations in a relative frame. Thus, an odometry localization is needed to provide this relative frame.

A detailed diagram of the operations in the model matching step is provided in Figure 9. The first set of observations is used to initialize line models. After that, the existing models are used to associate the frame-to-frame centers. Data association here means attributing each center (x i , y i , γ i ) to a unique model (l (id) ). Finally, the associated centers are used to update the existing models and create new ones if needed. These three operations are explained in detail below.

Initialization: The initialization step is crucial since data association and model updating are highly dependent. A poor initialization could lead to failure in the following operations. Here it is simply supposed that the algorithm will be activated in front of the structure2 so that the first observation O 1 would be reliable. Once the first set of observations O 1 is perceived, row models are initialized accordingly. A row model (l (id) ), defined with the parameters w (id) 0 and w

(id) 1 , is initialization per each (x i , y i , γ i ) data point in O 1 as follows: (l (id) ) : y = x tan γ i + y i -x i tan γ i := w (id) 1 x + w (id) 0 . ( 4
)
Fig. 8: Illustration of the goal of model matching. Three cases are presented to show that local observations are not necessarily consistent with their representation of the actual rows: a missing detection, a gap, or a row that appears after several time steps. The detected row centers (red dots) are to be used to build a regression model for each row in a relative frame.

Fig. 9: A detailed diagram of the model matching step. Frame-to-frame row centers are used to initialize and build regression models. This is done through a cycle of associating centers with existing models and updating the models using the associated centers.

In the case of Figure 3, five models would be initialized according to Equation (4) as five lines placed at rows positions (x i , y i ) and oriented with the common heading γ i .

Data association: After row models initialization, tracking begins by calculating lateral and angular deviations with respect to the selected row model to follow. As the robot moves forward, row centers from frame-to-frame profiles are mapped in the relative frame and should be assigned to row models in order to update them. The assignment is done using a simple zone rule based on the distance d ij , between frame-to-frame row centers (x i , y i ) and existing models (l (j) ), and a row spacing s that is inferred as the median of the differences between successive intercepts of existing models. A greedy approach is considered; therefore, the best candidate model for the input (x i , y i ) is the model (l (j min ) ) with the lower distance. The following zone rule is used to decide whether center (x i , y i ) has to be assigned to (l (j min ) ), rejected, or used to initialize a new model:

     d ij < 0.4s ⇒ assign 0.4s < d ij < 0.5s ⇒ reject outlier d ij > 0.5s ⇒ initialize new model
Updating models with regularized regression: Data points in the data association step are assigned to the buffer of the corresponding row model as a set of (x i , y i , γ i ) points. A data buffer is used to update a row model using linear regression. Linear regression is formalized as follows:

(l (id) ) : Y = XW (id) (5)
where

Y =    y 1 . . . y n    , X =    1 x 1 . . . . . . 1 x n    and W (id) = w (id) 0 w (id) 1 .
As mentioned in the explanation of the structure identification step, rows centers (x i , y i ) estimation is not as accurate as heading γ i estimation. Thus, in the early steps of tracking, when there are only a few data points along row directions, classic linear regression would lead to false lines and therefore, data association would fail, leading to a failure in tracking.

In order to initialize robust regression models, the heading-which represents strong information about the row direction-is added as a regularization term for the linear regression. The heading is integrated as the regularization term of the following loss function3 :

L = n i=1 y i -x T i W 2 + α n i=1 | -→ n . -→ γ i | 2 (6) = n i=1 y i -x T i W 2 + α n i=1 (tan γ i -w 1 ) 2 (7) = ||Y -XW|| 2 + α||Γ -aW|| 2 , (8)
where

Γ = [tan γ 1 . . . tan γ n ] T , a = 0 . . . 0 1 . . . 1
T and α is the regularization parameter. Minimizing the loss function L leads to:

Ŵ = (X T X + αa T a) -1 (X T Y + αa T Γ ). (9)
The regularization term

n i=1 | -→ n . -→ γ i | 2
is the dot product of the normal vector of the solution -→ n = (-w 1 1) and the vector -→ γ = (1 tan γ) oriented along the Fig. 10: Effect of using the heading as a regularization term in linear regression using (x i , y i , γ i ) data points. Only diamond-shaped points (x i , y i ) are used in the regression, the small arrows represent the heading γ i ; blue points are points belonging to the same row and are unseen at the time of regression. heading angle γ. This regularization penalizes the solutions that are not coherent with the estimated heading. Figure 10 shows the effect of the regularization term on the results. In the presented case and the subsequent experimentations, an aggressive regularization was chosen (α = 1.5). This regularization has the most impact after initialization since it ensures that the row model is oriented along the estimated heading γ i and mitigates the effect of lateral imprecisions due to the estimation of row positions (x i , y i ) from a discretized histogram. However, this regularization will have less impact in the later stages of tracking with the accumulation of (x i , y i ) data points along the row direction, which provides more reliable information about the row's direction.

To summarize the overall solution: Point clouds are perceived and preprocessed at the input of the identification step that provides frame-to-frame local observations of the structure. These observations are mapped in the relative frame, and the model matching step build row models from the local observation. Tracking is done by sending lateral and angular deviations with respect to the reference model. Figure 11 shows the results of the combined components of the proposed algorithm. Data association is shown as the color assigned to each center (a unique color per row), and the linear regression models are plotted as the lines representing each row.

Experimental evaluation

The proposed algorithm was tested on a vineyard production site in the two configurations presented in Figure 1: wide and narrow vineyards. The baseline solution Fig. 11: Mapping of LiDAR frames along with the detected row centers and the corresponding models in a relative frame. The robot is shown in a position where there is a missing tree in the row, showing that tracking continues with respect to the model.

for the navigation task is provided via a reliable GNSS-based localization and navigation system. This solution consists of creating a global path by manually defining geo-referenced points along the rows using a reliable GNSS rover (Septentrio Altus NR3). Figure 12 shows the satellite image of the narrow vineyard (provided by google earth) along with the geo-referenced points and the reference path. In the following, the ground truth for the structure algorithm is considered to be the global GNSS path. The goal here is to validate the feasibility of the proposed local navigation approach in this perceptually challenging environment. Perception challenges in vineyards come from the irregular shape and density of the perceived canopy. Hence, the experiments were conducted with the goal of validating the consistency and reliability of the proposed algorithm's estimates against those of the baseline GNSS-based solution. To this end, the autonomous tracking was provided by the ground truth GNSS-based algorithm, and the structure-based algorithm was run as an observation in real-time during the experiments. In order o deal with the overhead turns and the transition from one row to another, a global planner was used to define two sub-portions of the path: an in-row portion and an overhead turn portion. The structure-based observations were only activated in the in-row portion of the path, which was shifted 3 meters before the start and end of each row in order to adapt to the measurement range of the LiDAR sensor.

The configuration and parameters were considered in experimentation: point clouds were acquired using a 16-channel LiDAR sensor (Ouster OS1-16) at a frequency of 10 Hz. Preprocessing consisted of cropping the point clouds in the range of [-4m, 4m] along the y-axis in the robot's frame (Figure 3) followed by a voxel grid downsampling with a voxel size of 0.15m. Y-histograms for heading estimation using iterative skewing were computed by discretizing the [-4m, 4m] interval into 100 bins. For model matching and linear regression, a buffer size of 50 was used with a regularization parameter α = 1.5.

Validation on the wide vineyard

The first experiment consisted of navigating in the wide vineyard (Figure 17b). The navigation was done on eight rows characterized by an inter-row spacing of 1.9m and a row length of approximately 120m. The robot speed was 1 m/s in the in-row zone. A more detailed view of the results on one row can be found in Figure 14, with the lateral and angular deviations estimated by the structure algorithm and the ground truth GNSS algorithm. By considering the GNSS-based algorithm as the ground truth of the experiment, the absolute difference between the deviations of the two algorithms is, therefore, the total error of the structure algorithm with respect to the ground truth. In the case presented in Figure 14, the redundancy of the two algorithms can be concluded with a slight lateral offset. The root mean square error (RMSE) characterizing the lateral offset of the algorithm on all the rows is summarized in Table 1. The average RMSE for this experiment is 0.107m which is reasonable compared to 1.9m row spacing. This lateral offset is investigated in the next experiment presented in the following section.

Validation on the narrow vineyard

The same experiment was repeated on seven rows of the narrow vineyard (Figure 17a). The RMSE lateral error for this experiment is reported in Table 2 with slightly higher values than the first experiment. To get an insight into the repeatability of the results and to understand the higher RMSE on some rows, a second experiment was conducted on one row of the narrow vineyard and consisted of repeating the navigation five times on the same row. Figure 15 shows the concatenation of the point clouds from each frame along with the GNSS reference and the estimated structure path for all five passages. It can be concluded from the figure that the estimated structure path follows the perceived vegetation, which is the vine canopy. The position and shape of the canopy with respect to the trunks varies depending on the tree. In some situations, it is wider and can be shifted on one side of the trunk, as it is shown in the middle of the concerned row in Figure 15. This can be further noticed in Figure 16 that shows the lateral error between the estimated structure path and the ground truth GNSS path of all five passages. The lateral error is plotted with respect to the time offset since each observation was activated on the same location at the beginning and with the same speed profile. The path estimation of each run starts with a lateral error of approximately 0.20m that decreases afterward to under 0.05m. This offset at the beginning is justified since only a few noisy frame-to-frame observations were received, and the regression model is less reliable with fewer data at the start. This can also be seen in the standard deviation of the offset across all the runs that decreases as the regression model gathers more data (the height of the 1-std range shown on the figure); a lower standard deviation indicates the repeatability of the algorithm. The lateral offset increases again towards the end; however, by comparing this offset with the results reported in Figure 15, this can be interpreted by the shift and width of the perceived canopy with respect to the ground truth. Figure 17 shows two photos of the canopy taken by an onboard camera on the robot during the experiment: one of a regular canopy and another of a wide canopy that scored an offset of 0.20m with respect to the ground truth. Finally, the performed experiments demonstrate a redundant behavior of the proposed structure-based algorithm with respect to a reliable GNSS-based algorithm. The peak lateral offset in the most challenging cases remained under 0.2m; this ensures satisfying autonomous navigation in real scenarios knowing that the inter-row separation of the vineyard structure is between 1.5 and 1.9 meters. The main practical advantage of the proposed algorithm is that it does not require a prior manually defined global path and provides robust and similar tracking as the GNSS-based tracking. A practical approach that reduces the effort in the task preparation phase is to integrate the proposed algorithm in a hybrid approach with a GNSS-based solution that defines only the row limits and the overhead turns and uses the structure-based algorithm to navigate along the rows of the crop.

Conclusion and perspectives

This paper presents a robust LiDAR-based method for autonomous structure tracking in vineyards; which is one of the most challenging structure tracking scenarios in precision agriculture due to the wide and dense vine canopy. The proposed method does not require prior field surveying, and it is insensitive to crop-specific characteristics such as row width and spacing. In fact, the proposed method is based on the identification of the navigation clues provided by crop row structures. This allowed the proposed algorithm to be suitable for a versatile robot that intervenes in different types of cultures. Indeed, it was shown that the proposed method provides accurate and robust tracking in two vineyard configurations: wide and narrow vineyards. This was achieved by exploiting a practical interpretation of point cloud histograms to extract local structure observations from Hough space that are used to build an online crop model as the robot moves forward in the field. A key challenge while building an online model is proper initialization. Hence, robust heading estimation used as a regularization term provides a strong initialization for linear regression models.

Experimental validation was conducted on vineyards. The experiments confirm a robust structure tracking that is redundant with a reliable GNSS-based solution while significantly reducing the requirements of the fastidious task preparation phase (only the row limits were used to handle the transition from one row to another). Moreover, the proposed method can reduce the accuracy requirements, and thus the cost, of the GNSS subsystem since it provides accurate tracking relative localization with respect to the perceived structure.

A future work direction is to study the behavior of the proposed algorithm on different types of cultures, such as greenhouses and open fields. The idea is to consider wheel tracks as negative rows after extracting the ground plane from the point cloud using a random sample consensus algorithm. Hence, further analysis is required to study the consistency of the proposed algorithm in such fields and to define suitable conditions for applicability such as minimum plant height or wheel track depth. By doing so, the proposed approach could contribute to providing full autonomy on various production sites, including areas with poor precision GNSS coverage.

  (a) Narrow vineyard. (b) Wide vineyard.

Fig. 1 :

 1 Fig. 1: SITIA's Trektor: the robotic platform used in the experimentation.

Fig. 2 :

 2 Fig. 2: LiDAR sensor's positioning.

Fig. 5 :

 5 Fig. 5: The top view of two point clouds along with the corresponding y-histograms. (a) A point cloud with initial heading with respect to the robot's frame and its y-histogram. (b) The corrected point cloud after iterative skewing (zero heading) and its y-histogram. The y-histogram of the corrected point cloud has a maximal variance.

Fig. 7 :

 7 Fig. 7: Illustration of the peak detection algorithm used to find the y-coordinate of each row.

Fig. 12 :

 12 Fig. 12: Satellite image of the vineyard test field along with the geo-referenced points used to create the ground-truth path.

Figure 13

 13 Figure 13 offers a global view of the results of the navigation on eight rows. It shows the ground truth predefined GNSS global path along with the path estimated by the structure-based algorithm. Row limits are also shown on the figure to indicate where the structure algorithm was activated/deactivated. Such illustration on the global scale shows that the path estimated from local structure perception remained consistently available and reliable on the whole covered area.

Fig. 13 :

 13 Fig. 13: The ground truth GNSS path and the estimated structure path. The rows do not have the same length. The black dots indicate the positions on which the structure tracking algorithm was activated/deactivated.

Fig. 14 :

 14 Fig. 14: The lateral and angular deviations estimated by both the proposed structure-based and the baseline GNSS-based algorithms. The absolute difference between the deviations along with the root mean square error is noted on each graph.

Fig. 15 :

 15 Fig. 15: The estimated structure path of the repeated navigation along with the ground truth GNSS path and the concatenated point clouds.

Fig. 16 :

 16 Fig.16:The lateral error between the estimated structure path and the ground truth of each of the individual runs along with their mean curve and the 1-std range.

Fig. 17 :

 17 Fig. 17: Photos taken by an onboard camera on the robot in the narrow vineyard. (a) a regular vine canopy, (b) a wider vine canopy that caused the estimated structure path to shift 0.20m from the ground truth.

Table 1 :

 1 Root mean square lateral errors on each row of the wide vineyard.

	Row number	r1	r2	r3	r4	r5	r6	r7	r8	average
	RMSE lateral (cm)	6.6	14.4	4.6	13.4	7.9	16.7	10.7	10.9	10.7

Table 2 :

 2 Root mean square lateral errors on each row of the narrow vineyard.

	Row number	r1	r2	r3	r4	r5	r6	r7	average
	RMSE lateral (cm)	6.4	13.3	13.1	12.6	7.5	20	11.2	12

www.sitia.fr/en/innovation-2/trektor/

Since the presence of a structure in the perceived point cloud is a base assumption for the proposed algorithm; a global planner is needed to ensure this condition at row starts, as will be discussed in section 4.

The superscript(id) is omitted in the following since the same optimization is done per row model.

Acknowledgements This work is partially supported by the Agence Nationale de la Recherche ANR through the ROSE challenge, ANR-17-ROSE-0002-01 and by the Association Nationale de la Recherche et de la Technologie ANRT through the CIFRE PhD, ANRT CIFRE N • 2018/0792.

Availability of data and material : None.

Code availability : None.

Declarations

Funding This work is partially supported by the Agence Nationale de la Recherche ANR through the ROSE challenge, ANR-17-ROSE-0002-01 and by the Association Nationale de la Recherche et de la Technologie ANRT through the CIFRE PhD, ANRT CIFRE N • 2018/0792.

Conflicts of interest :

The authors have no conflicts of interest to declare that are relevant to the content of this article.

Authors' contributions : All authors contributed to the study's methodology, conception and design. Formal analysis: Hassan Nehme; Software and experimental validation: Hassan Nehme, Clément Aubry, Thomas Solatges; Resources: Hassan Nehme, Clément Aubry, Thomas Solatges; Writing: The first draft of the manuscript was written by Hassan Nehme and all authors commented on previous versions of the manuscript, all authors read and approved the final manuscript; Supervision and administration: Clément Aubry, Romain Rossi, Rémi Boutteau; Funding acquisition: Thomas Solatges, Xavier Savatier.

Ethics approval : Not applicable.

Consent to participate : Informed consent was obtained from all participants in the study.

Consent for publication : Participant consented to the submission of this article to the journal.