Lin Chao

Yanyan Liu

Grégoire T Freschet

Weidong Zhang
email: wdzhang@iae.ac.cn

Xin Yu

Wenhui Zheng

Xin Guan

Qingpeng Yang

Longchi Chen

Feike A Dijkstra

Silong Wang
email: slwang@iae.ac.cn.

Litter carbon and nutrient chemistry control the magnitude of soil priming effect

1. Plant litter inputs can promote the decomposition of soil organic matter (OM) through the priming effect (PE). However, whereas leaf litter chemistry has long been identified as the primary driver of litter decomposition within biomes worldwide, little is known about how litter chemical traits influence the occurrence and strength of the PE.

2. Here, we studied the effects of 15 co-occurring C 3 leaf litters of contrasting chemistry on C 4 soil respiration by analyzing changes in 13 C natural abundance during early and later stages of litter decomposition (up to 125 days).

3. Besides an apparent PE of 16% in the first three days, soil C respiration was increased by 24% on average with leaf litter addition in the initial stage of decomposition (426 d) and by 8% at later stages (27125 d). Most interestingly, soil PE related well to initial litter chemistry and the dominant factors influencing the magnitude of the PE changed with decomposition stage. In the early stage of decomposition, litter leachate C content and litter hemicellulose concentration were positively correlated with the strength of the PE, whereas tannin concentration was negatively associated with soil PE. Together, tannin and hemicellulose explained half of the observed variation in the PE (R 2 = 0.58). In the later phase of decomposition, lignin and lignin:N ratios were negatively related to the PE, whereas Ca, K and Mg concentrations were positively related to the PE; lignin alone gave the best prediction of the PE (R 2 = 0.58) at later decomposition stages. 4. Our findings provide evidence that the magnitude and direction of the PE is influenced by the chemistry of organic matter inputs and suggest that, as decomposition proceeds differently among litter of contrasting chemistry, litters can also have variable effect on soil PE through

Introduction

Soils contain the largest reservoir of carbon (C) in terrestrial ecosystems [START_REF] Lin | Decadally cycling soil carbon is more sensitive to warming than faster-cycling soil carbon[END_REF], the size and stability of which depend on the balance between C inputs from plant litter and C outputs from soil organic C (SOC) mineralization [START_REF] Averill | Ectomycorrhizal fungi slow soil carbon cycling[END_REF]. SOC mineralization is influenced by microbial activities, which are usually nutrient or energy limited in most soils. Leaf litter inputs to soil can release this limitation and stimulate SOC mineralization rates [START_REF] Kuzyakov | Priming effects: interactions between living and dead organic matter[END_REF][START_REF] Wang | Response of organic carbon mineralization and microbial community to leaf litter and nutrient additions in subtropical forest soils[END_REF], a phenomenon known as "the priming effect (PE)" [START_REF] Kuzyakov | Priming effects: interactions between living and dead organic matter[END_REF]Zhang & Wang, 2012).

Plant litter decomposition plays an important role in regulating C and nutrient cycling in soil systems [START_REF] Cornwell | Plant species traits are the predominant control on litter decomposition rates within biomes worldwide[END_REF]Freschet et al., 2013). Litter decomposition is determined by three main factors: climate, litter quality and decomposer organisms [START_REF] Bradford | A test of the hierarchical model of litter decomposition[END_REF][START_REF] Coûteaux | Litter decomposition, climate and liter quality[END_REF][START_REF] García-Palacios | The importance of litter traits and decomposers for litter decomposition: a comparison of aquatic and terrestrial ecosystems within and across biomes[END_REF]. Whilst it is well accepted that climate is the predominant factor controlling litter decomposition at the global scale [START_REF] Aerts | Climate, leaf litter chemistry and leaf litter decomposition in terrestrial ecosystems: a triangular relationship[END_REF][START_REF] Makkonen | Highly consistent effects of plant litter identity and functional traits on decomposition across a latitudinal gradient[END_REF]Zhou et al., 2008), litter quality, which generally varies with plant species, was viewed as the critical factor in determining litter decomposition within biomes [START_REF] Cornwell | Plant species traits are the predominant control on litter decomposition rates within biomes worldwide[END_REF]. Litter chemistry correlates broadly with initial rates of litter decomposition [START_REF] Melillo | Nitrogen and lignin control of hardwood leaf litter decomposition dynamics[END_REF][START_REF] Schmidt | Persistence of soil organic matter as an ecosystem property[END_REF]. Leaf litter chemical

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properties that stimulate decomposition rates include low lignin concentrations, high concentrations of nitrogen (N) and cations (potassium: K, calcium: Ca and magnesium: Mg) and low tannin concentrations [START_REF] Hättenschwiler | Leaf traits and decomposition in tropical rainforests: revisiting some commonly held views and towards a new hypothesis[END_REF][START_REF] Makkonen | Highly consistent effects of plant litter identity and functional traits on decomposition across a latitudinal gradient[END_REF][START_REF] Paudel | Quantifying the factors affecting leaf litter decomposition across a tropical forest disturbance gradient[END_REF]Zhang, Hui, & Luo, 2008).

The importance of plant litter for SOC decomposition has long been recognized [START_REF] Broadbent | The effect of quantity of plant material added to soil on its rate of decomposition[END_REF][START_REF] Sparling | Effect of barley plants on the decomposition of 14C-labelled soil organic matter[END_REF]. Over the past several decades, empirical evidence has been growing that the PE plays a crucial role in regulating SOC decomposition and in predicting the responses of soil ecological processes to global change (Fontaine, Bardoux, Abbadie, & Mariotti, 2004;[START_REF] Sullivan | Evaluation of mechanisms controlling the priming of soil carbon along a substrate age gradient[END_REF]. However, the strength, direction and duration of the PE can be controlled by multiple factors, including soil physico-chemical properties, the amount and quality of organic substances present in the soil, and microbial community structure and activity [START_REF] Blagodatskaya | Mechanisms of real and apparent priming effects and their dependence on soil microbial biomass and community structure: Critical review[END_REF][START_REF] Kuzyakov | Priming effects: interactions between living and dead organic matter[END_REF][START_REF] Luo | Fresh carbon input differentially impacts soil carbon decomposition across natural and managed systems[END_REF]. Owing to difficulties associated with disentangling all these influences, the response of SOC decomposition to litter addition remains controversial. Divergent results have been reported, with stimulatory [START_REF] Luo | Fresh carbon input differentially impacts soil carbon decomposition across natural and managed systems[END_REF]Zhang and Wang, 2013), inhibitory [START_REF] Kuzyakov | Sources and mechanisms of priming effect induced in two grassland soils amended with slurry and sugar[END_REF][START_REF] Potthast | Impact of litter quality on mineralization processes in managed and abandoned pasture soils in Southern Ecuador[END_REF] or no effects [START_REF] Nottingham | Soil priming by sugar and leaf-litter substrates: a link to microbial groups[END_REF][START_REF] Wang | Response of organic carbon mineralization and microbial community to leaf litter and nutrient additions in subtropical forest soils[END_REF]Zhang, Wang, & Wang, 2013) on SOC decomposition rates. Several hypotheses have been proposed to explain these inconsistent PEs associated with the input of litter [START_REF] Blagodatskaya | Mechanisms of real and apparent priming effects and their dependence on soil microbial biomass and community structure: Critical review[END_REF]Fontaine, Mariotti, & Abbadie, 2003;[START_REF] Kuzyakov | Review of mechanisms and quantification of priming effects[END_REF]. Generally, positive PEs could be induced due to increased microbial biomass and associated microbial production of extracellular enzymes, whereas negative PEs might be caused by the toxic effects of litter to microorganisms and preferential litter utilization by microorganisms [START_REF] Kuzyakov | Review of mechanisms and quantification of priming effects[END_REF]Zhang, Wang, Wang, 2013;[START_REF] Xiao | Priming of soil organic matter decomposition scales linearly with microbial biomass response to litter input in steppe vegetation[END_REF]. More specifically, the balance in microbial competition between microorganism communities specialized in the decomposition of easily degradable organic compounds and those feeding on polymerized SOC may

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This article is protected by copyright. All rights reserved. further explain differences in soil PE (Fontaine, Mariotti, & Abbadie, 2003). In this context, the chemical composition of fresh litter inputs could be a critical driver of SOC degradation by regulating the balance between different functional types of soil microbial communities (Fanin, Hättenschwiler, & Fromin, 2014;[START_REF] Fang | Microbial mechanisms of carbon priming effects revealed during the interaction of crop residue and nutrient inputs in contrasting soils[END_REF]. Despite this, the relationship between litter chemistry and PEs remains largely unexplored.

Although several studies have assessed the effect of litter addition on SOC decomposition, prior PE studies utilized a small number of plant litters [START_REF] Kuzyakov | Priming effects: interactions between living and dead organic matter[END_REF][START_REF] Wang | Response of organic carbon mineralization and microbial community to leaf litter and nutrient additions in subtropical forest soils[END_REF]. Commonly tested litters were typically 13 C-labeled plant materials such as ryegrass, wheat straw, and green leaves instead of actual plant litters [START_REF] Blagodatskaya | Mechanisms of real and apparent priming effects and their dependence on soil microbial biomass and community structure: Critical review[END_REF]Fontaine, Mariotti, & Abbadie, 2003) and poorly represented the global diversity of litter chemistry.

Consequently, to the best of our knowledge, no studies have yet directly investigated the influence of contrasting litter chemistry on the magnitude and direction of the PE. Additionally, as litter decomposition processes change with time [START_REF] Berg | Plant litter: decomposition, humus formation, carbon sequestration[END_REF][START_REF] Bray | Temporal dynamics of microbial communities on decomposing leaf litter of 10 plant species in relation to decomposition rate[END_REF], the influence of the decomposing litter on microbial communities also changes (Fanin, Hättenschwiler, Chavez Soria, & Fromin, 2016), with likely effects on the magnitude of the PE [START_REF] Luo | Fresh carbon input differentially impacts soil carbon decomposition across natural and managed systems[END_REF]. Therefore, it is crucial to gain a better understanding of the dynamics of the PE and the dominant factors controlling the PE at different stages of decomposition (García-Palacios, Maestre, Kattge, & Wall, 2013;[START_REF] Yue | Degradation of lignin and cellulose during foliar litter decomposition in an alpine forest river[END_REF].

The overall objective of this study was to determine the influence of leaf litter chemistry on the strength of the PE at both the initial and intermediate stages of litter decomposition. To do so, we studied the 13 C isotopic signature of CO 2 respired from microcosms where leaf litters of 15 C 3 plant species with contrasting chemical composition were added to a C 4 soil. We hypothesized that the magnitude of the PE would vary with the chemistry of litter species and differ among decomposition stages. Specifically, assuming that the nutritional competition and balance between microbial communities control the PE (Fontaine et al., 2003), we further hypothesized that litters with high

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concentrations of easily degradable C compounds (e.g., litter C leachates, cellulose and hemicellulose) would mostly induce increases in PE in the initial stages of decomposition, as they are likely to stimulate micro-organisms specialized in degrading easily degradable SOC; whereas litters with high recalcitrant compound content (e.g., lignin) would increase the PE in later stage of decomposition, as they are more likely to stimulate micro-organisms specialized in degrading recalcitrant SOC. Alternatively, following the co-metabolism concept, we hypothesized that the rate of litter decomposition and therefore the access of microbial communities to litter compounds would essentially drive the PE, leading to similar prediction of a positive relationship between easily degradable C compounds and PE in the initial stage of decomposition but negative relationship between the concentration of recalcitrant compounds and the PE at later stages of decomposition.

Materials and methods

Sampling of soil and leaf litter

The soil used in this study was collected from the plow layer (020 cm) of an agricultural site that has been planted with a C 4 maize crop for over 20 years at the experimental station of Heilongjiang Academy of Agricultural Science (45°69' N, 126°62' E), near Harbin, Heilongjiang Province, northeast China. Local mean annual temperature is 4.5 ºC and annual precipitation is 569 mm. The soil is a clay loam (43% sand, 22% silt, 35 % clay) with a pH of 6.9. Soil C and N concentrations were 17.3 g kg -1 and 1.5 g kg -1 , respectively, corresponding to a C:N ratio of 11.6. The δ 13 C value of C 4 maize soil was -15.8‰. The soil was air-dried, thoroughly homogenized and passed through a 2 mm mesh sieve. Visible plant debris and stones were carefully removed by hand.

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We collected freshly senesced leaf litter from 15 common and relatively abundant tree species in a subtropical forest characterized by a wide range of life strategies, carbon chemistry (Table 1) and nutrient content (Supporting Information Table S1) at the Huitong Natural Research Station of Forest Ecosystem (26°40'27°09'N, 109°26'110°08'E) in the Hunan province, central China. Local mean annual temperature and precipitation are 16.5 ºC and 1200 mm. Only freshly senesced, undamaged leaf litter was picked, whereas leaves with visible signs of herbivory, abrasions, fungal attacks or leaves that were still green were excluded. The litter was pooled by species and dried at 35 ºC immediately after collection.

Experimental setup and soil incubation

We used the natural abundance difference in δ 13 C values of C 3 plant leaf litters and C 4 soil to separate leaf-derived CO 2 from soil-derived CO 2 . The equivalent of 150 g dry soil was weighed into a 1 L Mason jar, and adjusted to 60% water-holding capacity by adding distilled water. Leaf litter samples were ball-milled into fine powder and homogenized by passing through a 0.25 mm mesh sieve. We added ground litter rather than chopped litter, because we were mostly interested in differences in litter chemistry, rather than in aspects of litter morphology, size or anatomy that could (i) affect the homogeneity of litter distribution within the soil in the microcosms and create non-optimal contact between soil and litter, and (ii) interact with litter chemistry in a non-systematic way and thereby obscure the potential effect of litter chemical compounds on soil PE. Prior to litter addition, all soils were pre-incubated at 25 ºC for 10 days.

After pre-incubation, litter powder was added to the soil and throughly mixed. The amount of added litter C was calculated separately for each species so as to represent 5% of the SOC concentration (corresponding to 0.25 -0.43 g of litter material, Supporting Information Table S2).

The amount of litter C added to the soil (75 g C m -2 yr -1 , considering a soil depth of 10 cm)

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corresponded to a realistic yearly input of litter in local tree plantations (e.g. Cunninghamia lanceolata forest; [START_REF] Ning | Litterfall production and dynamic for twenty years of a successive replanting Cunninghamia lanceolata plantation at Huitong, Hunan[END_REF]. Three analytical replicates were included for each leaf litter. Soils without litter addition were also included as controls. Two holes were punched in the Mason jar lids and installed with bulkhead connectors (SMC, KQ2E06-00A; Singapore). Polyurethane tubes (TU-0604; SMC, USA) were used for linking the bulkhead connectors with a manual valve (VHK2-06F-06F; SMC, Japan). The manual valve remained open during incubation, but was kept closed between sampling periods. All incubations were conducted in a laboratory incubator (SPX-500; Jiangnan, Ningbo, China) at a constant temperature of 25 ºC for 125 days.

Analysis of CO 2 fluxes

Gas samples were sampled from jars on day 1, 3, 7, 10, 15, 26, 61, 90, and 125 after the incubation began. To make sure that there was no CO 2 at the start of the CO 2 flux measurements, we removed CO 2 inside each jars before gas sampling by circulating CO 2 free air, which was generated using an air compressor (ACO-318; Hailea, Guangdong, China) pumped through a soda lime column for 2 minutes. Then, jars were immediately sealed by closing the manual valve. Due to the faster CO 2 release from soil in the initial stages of decomposition than at later stages, gas was collected 12 (early stage) or 24 h (later stage) after sealing using a portable gas sampling pump (01 L-D; Delin, Dalian, China) and stored in a pre-evacuated gas sampling bag (LB-201-0.2; Delin, Dalian, China). The CO 2 concentration and δ 13 C were analyzed by a High-precision Isotopic CO 2 Cavity Ring-Down Spectrometer (CRDS) (Picarro G2131-i Analyzer, Picarro, Inc., Santa Clara, CA, USA).

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Measurement of litter chemistry

The ground leaf litter was analyzed for C, N, phosphorus (P), litter C leachates, lignin, hemicellulose, cellulose and tannin using standard methods. Briefly, C and N concentrations were determined using a CN elemental analyzer (ElementarVario, Hanau, Germany). To determine litter C leachates, 2 g litter powder samples were extracted with 60 ml deionized water, by shaking them on a reciprocal shaker for 30 min. The resulting solution was filtered, then analysed using a TOC analyzer (Vario TOC cube, Elementar Analysis system GmbH, Langenselbold, Germany). Lignin, hemicellulose and cellulose (300 mg litter samples) were measured according to the National Renewable Energy Laboratory Procedure [START_REF] Sluiter | Determination of structural carbohydrates and lignin inbiomass[END_REF]. In brief, we used a two-step acid hydrolysis to fractionate the litter into easily quantified forms. The hydrolysis liquid was used to quantify the cellulose and hemicellulose by high-performance liquid chromatography (HPLC) (Agilent-1260, Agilent Technologies, Santa, Clara, CA, USA). Two fractionate forms of lignin (acid insoluble material and acid soluble material) were measured by UV-Vis spectroscopy (Lambda 25, PerkinElmer, Singapore).

Tannins were determined by an acid-butanol assay as described by [START_REF] Hagerman | The Tannin Handbook[END_REF]. The initial total P, Ca, K, Mg and Mn concentrations were measured using inductively coupled plasma mass spectroscopy (ICP-MS) (Elan DRC-e; PerkinElmer, Norwalk, CT, USA) after acid digestion of litter samples with H 2 SO 4 and HClO 4 solution.

Calculations and statistical analysis

CO 2 -C efflux was calculated as follows:

where R is the CO 2 -C efflux (µg C g 1 soil day 1 ); C is the measured CO 2 concentration (ppm); V is the effective volume of a 1 L Mason jar (L); M is the molar mass of C (12 g mol 1 ); 22.4 (L) is the

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This article is protected by copyright. All rights reserved. molar volume of an ideal gas at 1 atm and 273.15 K. W is the gram dry weight of the soil; t is the time of CO 2 accumulation (days); and T is the incubation temperature (25 ºC).

Mass balance equations were used to separate leaf-derived CO 2 from soil-derived CO 2 :

Where C t is the total CO 2 -C from soil respiration (C t =C L +C S ) during the considered time period, C L is the amount of C derived from C 3 litter, C S is the amount of C derived from C 4 soil, δ t is the δ 13 C value of CO 2 emitted from jars containing soil-litter mixtures, and δ L and δ s are the δ 13 C values of C 3 litter material and C 4 soil, respectively. Soil cumulative production of CO 2 (T, mg C kg 1 soil) at early and later stages of decomposition was calculated by the following equation:

where R i and R i+1 are soil CO 2 efflux at i th and (i+1) th incubation time (mg C kg 1 day 1 ), respectively, t i+1 t i is the interval between the i th and (i+1) th incubation time (day), and n is the number of incubation times.

Mean daily soil CO 2 production (mg C kg 1 soil d -1 ) at early and later stages of decomposition was then calculated by dividing T by the number of days in each stage.

The proportion of litter C decomposition (L d , %) was calculated using the following equation:

where T d is the cumulative CO 2 (mg C kg 1 ) efflux from litter during the incubation period and M d is the amount of litter C added to soil (mg C kg 1 ).

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The early stage of litter decomposition was defined here as the phase presenting a sharp decrease in CO 2 efflux with time (i.e., for all litters, from the first to the 26 th days after the start of the incubation), whereas the late phase of decomposition was characterized by relatively stable, lower CO 2 efflux rates (as observed for all litters 61, 90, and 125 days after the start of the incubation). This trend was highly conserved across all 15 species allowing the delineation of the same early versus later phase of decomposition for all 15 litters (Supporting Information Figure S1).

It is generally considered that the initial flush of CO 2 occurring during the first three days after new C input mainly results from an increased turnover or pool substitution of soil microbial biomass [START_REF] Blagodatskaya | Mechanisms of real and apparent priming effects and their dependence on soil microbial biomass and community structure: Critical review[END_REF][START_REF] Kuzyakov | Priming effects: interactions between living and dead organic matter[END_REF]. This 'apparent' PE occurring during the first three days of incubation was therefore omitted from PE calculations for the early stage of decomposition (0-26 days) so as to consider only the 'real' PE. The PE induced by litter addition on SOC decomposition was expressed as the % change compared to CO 2 C released from the control.

The magnitude of PE during the considered time period (t) was calculated using the following equation:

where CO 2 -C treatment is the accumulated amount of total emitted CO 2 derived from C 4 soil in the litter-amended soil, and CO 2 -C control is the amount of CO 2 emitted from the control soil. The absolute change in decomposition of SOC following addition of litter was also calculated by subtracting

CO 2 -C control from CO 2 -C treatment .
The difference in PE between early and later phases of decomposition was tested across all litter species using paired t-tests. A correlation analysis was carried out, to test collinearity among litter traits. To determine how well variation in multiple aspects of litter chemistry explained variation in the PE, the relationships between leaf litter chemical properties, litter decomposition and the PE were assessed using hierarchical multiple linear regressions. The introduction of 'added

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litter mass' as a covariate with precedence in hierarchical multiple linear regression analyses was necessary to correct for the potentially confounding influence of variable added litter mass (litter input was based on a similar total litter C addition across species). Models with lowest Akaike information criterion (AICc) were retained. All data met the requested assumptions of these parametric tests. Statistical analyses for all data were carried out using SPSS version 16.0 (SPSS Inc., Chicago, Illinois, USA).

Results

Litter decomposition and relationship with litter chemistry

The 15 common species used in this study exhibited a broad range of leaf litter chemistry properties (Table 1, Table S1). Lignin and lignin:N ratio (r=0.86, P < 0.001), P and K (r=0.78, P < 0.001), Ca and Mg (r=0.74, P < 0.01) were highly correlated (Supporting Information Table S3). At the initiation of the experiment, these litters all displayed a high carbon decomposition rate (i.e. high litter-derived CO 2 fluxes) that decreased quickly and markedly in the initial stages of litter decomposition (0-26 d) and then remained low during later stages of litter decay (27-125 d) (Figure 1, Supporting Information Table S4). The fraction of added litter-C decomposed over the entire incubation period was 24% averaged across all 15 species with the lowest for Phoebe bournei (15%) and the highest for Machilus Pauhoi litter (41%) (Figure 2). On average, 65% of the decomposition occurred in the early stage. Initial litter chemistry properties related only poorly to early and later stage leaf litter decomposition (Table 2). Whether in univariate or multivariate analyses, only Mn concentration explained some variation in litter decomposition in the early stage (negative relationship; R 2 = 0.33, P = 0.03), whereas N concentration explained some variation in litter decomposition in the later stage (negative relationship; R 2 = 0.28, P = 0.04) (Table 2,3).

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CO 2 production and PE

Over the 125 days incubation period, mean daily CO 2 production from the control soil was 4 mg C kg -1 soil d -1 , but 8 mg C kg -1 soil d -1 from the soil with leaf litter. This ranged from 6 mg C kg -1 soil d -1 (Phoebe zhennan) to 11 mg C kg -1 soil d -1 (Machilus pauhoi) (Figure 3).

Across the 15 species, the magnitude of PE (c. 1 mg C kg -1 soil d -1 ) at the early stage of decomposition was significant higher than the later stage (c. 0.2 mg C kg -1 soil d -1 ; P < 0.001). Overall, in the first 26 days, added leaf litters significantly stimulated the decomposition of SOC by 24 % on average, which was threefold higher than in the 27125 day period (8% on average). Leaf litter addition induced additional SOC decomposition as compared to the control soil for all 15 species in the early stage of incubation (426 d) and all but two species in the later stage (27125 d) (Figure 3).

Nevertheless, the magnitude of this PE varied strongly among treatments. The PE ranged from 4% to 51% in the early stage of incubation and from a 7% reduction to a 25% enhancement in the later stage of incubation (Figure 3).

Relationships between PE and leaf litter chemistry

Initial leaf litter chemistry and PE were significantly related, although these relationships differed among earlier and later stages of decomposition (Table 2). In the early stage of litter decomposition, the PE was positively related to the amount of litter C leachates and litter hemicellulose concentration, and related negatively to tannin concentration (Table 2, Figure 4). In the later stage of litter decomposition, lignin and to a lesser extent the lignin:N ratio was related negatively to the PE, whereas K, Ca and Mg concentrations were positively related to the PE (Table 2, Figure 4). However, the PE was not related to initial N or P concentrations in either the early or later stage of decomposition. Additionally, the added litter mass only had a marginally significant effect on early PE (R 2 = 0.20, P = 0.09) and no significant effect on later PE (R 2 = 0.00, P = 0.82). Considering

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all litter traits together, the combination of tannin and hemicellulose concentrations appeared most relevant to explain the PE in the early stage of decomposition (R 2 = 0.58, P = 0.006), whereas lignin concentration was the single best explanatory variable in the later stage (R 2 =0.58, P = 0.001) (Table 3).

Relationships between litter decomposition and PE

Leaf litter decomposition rate was positively related with the PE during the early stage of litter incubation (R 2 =0.29, P = 0.04; Figure 5a), i.e. when the largest part of the PE occurred (76% averaged across all species), but there was no relationship between decomposition rates and PE in the later stage (P = 0.28; Figure 5b). Over the entire period of decomposition, litter decomposition rate was positively related with the PE (R 2 = 0.32, P = 0.03; Figure 5c).

Discussion

Our findings provide evidence that the magnitude and direction of the PE is influenced by the chemistry of organic matter inputs. In particular, the relative proportion of different C compounds in litter input, such as litter C leachates, hemicellulose, lignin and tannins, can have substantial influence on the soil PE. Importantly, as decomposition proceeds differently among litters of contrasting chemistry, litters can also have variable effects on soil PE over time. In this context, our results also suggest that in the medium term, litter compounds unrelated to the C resource, such as cation content (Ca, K, Mg), might also influence the magnitude of the soil PE.

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Variation in soil PE with litter addition and decomposition stages

In line with previous studies showing that different kinds of substrates can trigger PE to different extents [START_REF] Blagodatskaya | Mechanisms of real and apparent priming effects and their dependence on soil microbial biomass and community structure: Critical review[END_REF][START_REF] Luo | Fresh carbon input differentially impacts soil carbon decomposition across natural and managed systems[END_REF] we demonstrated here that different litters with contrasting chemistry also trigger variable PEs. The addition of leaf litter generally stimulated the decomposition of native SOC although in a few instances we also observed inhibiting effects or no effect of inputs on native SOC mineralization rates [START_REF] Blagodatskaya | Mechanisms of real and apparent priming effects and their dependence on soil microbial biomass and community structure: Critical review[END_REF][START_REF] Kuzyakov | Priming effects: interactions between living and dead organic matter[END_REF][START_REF] Wang | Response of organic carbon mineralization and microbial community to leaf litter and nutrient additions in subtropical forest soils[END_REF]Zhang & Wang, 2012).

While the PE is generally defined as a short-term change in the turnover of soil organic matter caused by comparatively moderate treatment of the soil [START_REF] Kuzyakov | Review of mechanisms and quantification of priming effects[END_REF], the temporal dynamics of the PE has been rarely estimated [START_REF] Kuzyakov | Priming effects: interactions between living and dead organic matter[END_REF]. In a recent meta-analysis, [START_REF] Luo | Fresh carbon input differentially impacts soil carbon decomposition across natural and managed systems[END_REF] observed significant positive PEs that strongly decreased over time but persisted up to 100 days after adding complex C substrates (such as plant litter) to soil. Our results support this and other results (Fontaine et al., 2011;Zhang & Wang, 2012) showing long-term effects of complex substrate additions on the soil PE. They further confirm across a range of litters with contrasting chemistry that the magnitude of the PE generally decreases predictably with time [START_REF] Luo | Fresh carbon input differentially impacts soil carbon decomposition across natural and managed systems[END_REF]Zhang, Wang & Wang, 2013). Among litter species, the significant relationship between litter decomposition and soil PE may suggest that faster litter decomposition rates trigger larger C accessibility to microorganisms and therefore increase the PE. For all litters, the much faster decomposition rate in the initial compared to the later stages of decomposition also relates to the much stronger PE observed in the first 26 d of litter incubation. Previous studies have indeed shown that, as litter decomposition proceeds, labile fractions are quickly exhausted and recalcitrant C compounds like lignin and cellulose remain [START_REF] Bray | Temporal dynamics of microbial communities on decomposing leaf litter of 10 plant species in relation to decomposition rate[END_REF][START_REF] Wickings | The origin of litter chemical complexity during decomposition[END_REF][START_REF] Yue | Degradation of lignin and cellulose during foliar litter decomposition in an alpine forest river[END_REF]. The C return on investment in lignolytic enzymes is hypothesized to be low [START_REF] Talbot | Interactions among lignin, cellulose, and nitrogen drive litter chemistry-decay relationships[END_REF], therefore limiting the growth and activity of microbial

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communities feeding on lignin and potentially explaining the decrease in soil PE occurring in the later stage of decomposition.

Leaf litter chemistry control on soil PE

In support of our overarching hypothesis, leaf litter chemistry strongly influenced the magnitude of the soil PE. The positive relationship between soil PE and the concentrations of litter C leachates and hemicellulose in the initial stages of decomposition may be mainly explained by the co-metabolism concept, resulting from stimulated microbial growth and enzyme production induced by the utilization of litter easily degradable C compounds (i.e. C leachates and hemicellulose), with consequences for both the decomposition of litter and native SOC [START_REF] Kuzyakov | Review of mechanisms and quantification of priming effects[END_REF][START_REF] Qiao | Labile carbon retention compensates for CO 2 released by priming in forest soils[END_REF][START_REF] Xiao | Priming of soil organic matter decomposition scales linearly with microbial biomass response to litter input in steppe vegetation[END_REF]. While lignin has conventionally been considered as a recalcitrant compound that protects hemicellulose and cellulose from degradation by microbes [START_REF] Austin | Dual role of lignin in plant litter decomposition in terrestrial ecosystems[END_REF][START_REF] Hall | Lignin decomposition is sustained under fluctuating redox conditions in humid tropical forest soils[END_REF][START_REF] Talbot | Interactions among lignin, cellulose, and nitrogen drive litter chemistry-decay relationships[END_REF], unshielded hemicellulose is generally abundant in the early stages of decomposition. Therefore, this unshielded hemicellulose may have provided microbial communities with an easily accessible C source and thereby stimulated the soil PE in the early stage of decomposition, until the unshielded portions were exhausted. In contrast, the concentration of tannins was negatively associated with the PE in the early decomposition stage, possibly resulting from the inhibitory effect of tannins on soil enzyme activity, thus impeding SOC mineralization [START_REF] Chomel | Plant secondary metabolites: a key driver of litter decomposition and soil nutrient cycling[END_REF][START_REF] Liu | Labile carbon input determines the direction and magnitude of the priming effect[END_REF], before tannin compounds were further degraded by soil microbial communities in the later stage of decomposition [START_REF] Joanisse | Soil enzyme inhibition by condensed litter tannins may drive ecosystem structure and processes: the case of Kalmia angustifolia[END_REF][START_REF] Makkonen | Highly consistent effects of plant litter identity and functional traits on decomposition across a latitudinal gradient[END_REF][START_REF] Ushio | Effects of condensed tannins in conifer leaves on the composition and activity of the soil microbial community in a tropical montane forest[END_REF].

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In support for our alternative hypothesis, a negative relationship between lignin and the PE was observed in the later stage of litter decomposition. As litter decomposition proceeds, the chemical composition of litter changes; labile C compounds are exhausted whereas recalcitrant litter compounds such as lignin tend to accumulate [START_REF] Berg | Plant litter: decomposition, humus formation, carbon sequestration[END_REF][START_REF] Coûteaux | Litter decomposition, climate and liter quality[END_REF][START_REF] Hall | Lignin decomposition is sustained under fluctuating redox conditions in humid tropical forest soils[END_REF]. A large proportion of lignin in litter would therefore correspond to a lower amount of decomposition byproducts in the form of accessible C substrate at later stages of decomposition that may explain the lower soil PE. The substantial PE observed in the later stage of decomposition suggests nonetheless that other complex C sources may still be available for microbial communities [START_REF] Luo | Fresh carbon input differentially impacts soil carbon decomposition across natural and managed systems[END_REF] or that additional mineralization of SOC by the microbial community induced by earlier inputs persist after all easily accessible C substrate have been used (Fontaine et al., 2011).

Interestingly, the lack of a relationship between the soil PE and initial leaf litter N and P concentrations contrasts with previous studies that suggested that high soil N and P availability can decrease the soil PE (Fontaine et al., 2011;[START_REF] Wang | Response of organic carbon mineralization and microbial community to leaf litter and nutrient additions in subtropical forest soils[END_REF]. This lack of effect could be due to the already high availability of N (inorganic N = 132 mg kg -1 ) and P (available P = 70 mg kg -1 ) in the (chemically fertilized) agricultural soil used in our experiment, preventing any effect of additional N and P from litter on microbial stoichiometry and therefore on litter decomposition (Freschet, Aerts, & Cornelissen, 2012) and the PE [START_REF] Luo | Fresh carbon input differentially impacts soil carbon decomposition across natural and managed systems[END_REF]. In contrast, we found a strong positive influence of several cation concentrations (Ca, K and Mg) on the soil PE in the later stage of litter decomposition. The positive influence of these cations could be linked to their role in relieving a potential deficiency of our experimental soil in such elements, thereby favoring long-term microbial growth, activity and litter decomposition [START_REF] Cornelissen | Functional leaf attributes predict litter decomposition rate in herbaceous plants[END_REF] and stimulating SOC decomposition rates. However, given the strong correlation between Ca and Mg, their relative influence on later PE cannot be disentangled.

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Finally, we acknowledge that our work, using only one homogeneous sample of litter per species, demonstrates the effect of between-species litter chemistry effects and does not represent the natural variability of within-species litter chemistry effects on soil PE, which precludes comparisons among species. Additionally, the use of ground litter was not entirely representative of the effect of typical litter input on soil PE and may have increased PE as compared to entire or coarsely chopped litter. For example, [START_REF] Nottingham | Soil priming by sugar and leaf-litter substrates: a link to microbial groups[END_REF] found that chopped and ground maize added to soil caused similar increases in the soil CO 2 efflux, but that ground maize caused a larger PE than chopped maize. Nonetheless, our methodological choice allowed us to establish important links between litter chemical quality and PE.

Conclusions

We demonstrated here that leaf litter chemical traits (litter C leachates, hemicellulose, tannin and lignin, or even Ca, K and Mg) and litter decomposition rate strongly influence the magnitude and direction of the PE. Additionally, the dominant factors that control soil PE were different during contrasting stages of decomposition. While the lack of data on microbial biomass and community composition does not allow us to draw conclusions about the mechanisms behind the observed patterns, we note that these results are consistent with the idea that the access of microbial communities to litter-derived compounds (as controlled by litter decomposition rate) plays a role in driving the PE at early and intermediate stages of decomposition. A potential positive effect of high concentrations of recalcitrant compounds in litter, such as lignin, on the PE at later stages of decomposition was not observed. However, our results did not cover the entire period of litter decomposition and do not exclude that microbial competition (e.g. the balance between different functional types of soil microbial communities mediated by litter chemistry effects) could become dominant at the latest stages of decomposition and eventually persist after the complete disappearance of litters (Fontaine et al., 2011). While this study demonstrated the potentially

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important effect of litter chemistry on the PE, further experiments using temporally explicit approaches are critically needed to explore the role of microbial biomass and community composition in mediating these effects. Moreover, soils with different properties should also be considered to further strengthen the validity of such experimental results across a range of soils and ecosystems.

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Figure Captions Figure 1 .

 Captions1 Figure Captions

Figure 2 .

 2 Figure 2. Cumulative fraction of added plant litter released as CO 2 during two stages of

Figure 3 .

 3 Figure 3. Mean daily SOM-derived CO 2 (gray bar), leaf litter-derived CO 2 (white bar) and CO 2

Figure 4 .

 4 Figure 4. Relationships between priming effect and litter chemistry at early stage (a) and later stage (b) of decomposition. Strength (R 2 ) and significance (P) of linear regressions are displayed when

Figure 5 .

 5 Figure 5. Relationships between litter decomposition and priming effect in the day 0-26 (a), day 27-125 (b) and day 0-125d (c). Strength (R 2 ) and significance (P) of linear regressions are displayed

Table 1

 1 Initial litter chemistry of the fifteen subtropical tree species incubated in this study.

Table 2

 2 Strength (R 2 ) and significance (P) of linear regressions between initial leaf litter chemical traits and leaf litter decomposition and priming effect during two decomposition stages.

			Early stage			Later stage
	Trait	Litter decomposition Priming effect	Litter decomposition	Priming effect
		R 2 (+/-) P-value R 2 (+/-) P-value	R 2 (+/-)	P-value	R 2 (+/-)	P-value
	Litter C leachates	0.078 (+)	0.078	0.298 (+)	0.035	0.049 (-)	0.429	0.241(+)	0.063
	Lignin	0.038 (+)	0.489	0.139 (-)	0.171	0.016 (-)	0.656	0.584 (-)	0.001
	Cellulose	0.009 (+)	0.734	0.254 (+)	0.056	0.006 (+)	0.782	0.235 (+)	0.067
	Hemicellulose	0.193 (+)	0.094	0.342 (+)	0.022	0.268 (+)	0.060	0.166 (+)	0.132
	Tannin	0.108 (-)	0.233	0.361 (-)	0.012	0.008 (-)	0.746	0.102 (-)	0.246
	Lignin:N	0.000 (-)	0.960	0.006 (-)	0.786	0.022 (+)	0.595	0.389 (-)	0.013
	N	0.102 (-)	0.246	0.190 (-)	0.104	0.284 (-)	0.041	0.021 (+)	0.604
	P	0.017 (+)	0.644	0.006 (+)	0.791	0.068 (-)	0.347	0.234 (+)	0.068
	Ca	0.219 (+)	0.08	0.042 (+)	0.466	0.035 (+)	0.506	0.354 (+)	0.019
	K	0.001 (-)	0.922	0.004 (-)	0.821	0.130 (-)	0.187	0.312 (+)	0.031
	Mg	0.06 (+)	0.371	0.022 (+)	0.602	0.001 (+)	0.773	0.396 (+)	0.012
	Mn	0.331 (-)	0.025	0.085 (-)	0.293	0.135 (-)	0.178	0.238 (-)	0.065

Table 3

 3 Outcome of determination of stepwise regressions between initial litter chemical properties and litter decomposition and priming effect at two decomposition stages. The strength (R 2 ) and significance (P) of models with lowest AICc are displayed.

		Model
		Early stage			Later stage
		Traits	R 2	P	Traits	R 2	P
	Litter
	decomposition	Mn	0.331 0.025	N	0.284 0.041
	Priming effect	Tannin	0.361 0.018	Lignin	0.584 0.001
		Tannin; Hemicellulose 0.575 0.006

Acknowledgements

We are grateful to the editor and two anonymous reviewers for their many useful and constructive comments on this manuscript. We also thank Yakov Kuzyakov for his constructive comments on previous versions of the manuscript. This research was funded by the National Key Research and Development Program of China (2016YFA060080203), the key research program of Frontier Sciences of the Chinese Academy of Sciences (QYZDB-SSW-DQC002-03), the National Natural Science Foundation of China (41630755) and the Youth Innovation Promotion Association of the Chinese Academy of Sciences (2017239). Lin Chao was further supported by the Youth Talent Exchange and Cooperation Foundation of the Key Laboratory of Forest Ecology and Management of the Chinese Academy of Sciences to work at the CEFE in Montpellier (France).

DATA ACCESSIBILITY

The data associated with this paper are available from the Dryad Digital Repository http:// DOI: doi:10.5061/dryad.b4s71jj (Chao et al., 2018).

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Fanin, N., Hättenschwiler, S., & Fromin, N. (2014). Litter fingerprint on microbial biomass, activity, and community structure in the underlying soil. Plant & Soil, 379,[79][80][81][82][83][84][85][86][87][88][89][90][91] https://doi.org/10.1007/s11104-014-2051-7 Fanin, N., Hättenschwiler, S., Chavez Soria, P. F., & Fromin, N. (2016). (A)synchronous availabilities of N and P regulate the activity and structure of the microbial decomposer community. Frontiers in Microbiology, 6(e49990), 1507. http://doi.org/10.3389/fmicb.2015.01507 Fontaine, S., Bardoux, G., Abbadie, L., & Mariotti, A. (2004). Carbon input to soil may decrease soil carbon content. Ecology Letters, 7, 314-320. https://doi.org/10.1111/j.1461-0248.2004.00579.x Fontaine, S., Henault, C., Aamor, A., Bdioui, N., Bloor, J. M. G., … Maire, V. ( 2011). Fungi mediate long term sequestration of carbon and nitrogen in soil through their priming effect. Soil Biology & Biochemistry, 43, 86-96. https://doi.org/10.1016/j.soilbio.2010.09.017 Fontaine, S., Mariotti, A., & Abbadie, L. (2003). The priming effect of organic matter: a question of microbial competition? Soil Biology & Biochemistry, 35, 837-843. https://doi.org/10.1016/S0038-0717(03)00123-8 Freschet, G. T., Aerts, R., & Cornelissen, J. H. C. (2012). A plant economics spectrum of litt er decomposability. Functional Ecology, 26(1), 56-65. https://doi.org/10.1111/j.1365-2435.2 011.01913.x Freschet, G. T., Cornwell, W. K., Wardle, D. A., Elumeeva, T. G., Liu, W., Jackson, B. G., … Cornelissen, J. H. C. (2013). Linking litter decomposition of above-and below-ground organs to plant-soil feedbacks worldwide. Journal of Ecology, 101, 943-952. http://doi.org/10.1111/1365-2745.12092

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García-Palacios, P., Maestre, F. T., Kattge, J., & Wall, D. H. (2013). Climate and litter quality differently modulate the effects of soil fauna on litter decomposition across biomes. Ecology

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Zhang, D., Hui, D., Luo, Y., & Zhou, G. (2008). Rates of litter decomposition in terrestrial ecosystems: global patterns and controlling factors. Journal of Plant Ecology, 1, 85-93. https://doi.org/10.1093/jpe/rtn002 Zhang, W., & Wang, S. (2012). Effects of NH 4 + and NO 3 -on litter and soil organic carbon decomposition in a Chinese fir plantation forest in South China. Soil Biology &Biochemistry, 47,116-122.http://doi.org/ 10.1016/j.soilbio.2011.12.004 Zhang, W., Chao, L., Yang, Q., Wang, Q., Fang, Y., & Wang, S. (2016). Litter quality mediated nitrogen effect on plant litter decomposition regardless of soil fauna presence. Ecology, 97, 2834-2843. http://doi. org/10.1002/ecy.1515 Zhang, W., Wang, X., & Wang, S. (2013). Addition of external organic carbon and native soil organic carbon decomposition: a meta-analysis. Plos One, 8, e54779. http://doi.org/10.1371/journal.pone.0054779 Zhou, G., Guan, L., Wei, X., Tang, X., Liu, S., Liu, J., … Yan, J. (2008). Factors influencing leaf litter decomposition: an intersite decomposition ex-periment acr oss China. Plant & Soil, 311, 61-72. http://doi.org/10.1007/s11104-008-9658-5

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SUPPORTING INFORMATION

Additional supporting information may be found online in the Supporting Information section at the end of the article.

How


M Lesellier

M Gouttefarde

A Bounding Volume of the Cable Span for Fast Collision Avoidance Verification

Keywords: Cable-Driven Parallel Robot, Cable, Span, Collision

The problem of verifying the absence of collision between a cable and the mobile part(s) of a device located on-board the mobile platform of a Cable-Driven Parallel Robot (CDPR) is addressed. The set of all positions taken by one cable of the CDPR for all the poses of the mobile platform in a prescribed workspace is called the cable span. A simple bounding volume approximation of the cable span is proposed in this paper. This bounding volume is a polyhedron and the characterization of the faces of this polyhedron is discussed. Using this polyhedron as a bounding volume of the cable span allows to accelerate computations related to collision avoidance checking.

Introduction

Cable-Driven Parallel Robots (CDPRs) consist of a mobile platform driven by cables. Using cables instead of rigid links gives CDPRs interesting characteristics such as a potentially very large workspace, large payload-to-weight ratio, and high dynamics capabilities.

However, one of the major drawbacks of CDPRs is their low stiffness due to the use of cables. This low stiffness may be the cause of vibrations affecting the platform positioning accuracy. Several techniques can be used to damp these vibrations: input shaping [START_REF] Montgomery | Suppression of cable suspended parallel manipulator vibration utilizing input shaping[END_REF], modal space control [START_REF] Weber | Active vibration canceling of a cable-driven parallel robot in modal space[END_REF], or active damping by creating a transient wrench to compensate the vibrations. This wrench can be created by additional actuated stabilizing mechanical devices placed on board the mobile platform [START_REF] Rushton | Vibration control in cable robots using a multi-axis reaction system[END_REF][START_REF] Weber | Active vibration canceling of a cable-driven parallel robot using reaction wheels[END_REF][START_REF] Lesellier | An active stabilizer for cable-driven parallel robot vibration damping[END_REF][START_REF] De Rijk | Out-of-plane vibration control of a planar cable-driven parallel robot[END_REF]. In reference [START_REF] Lesellier | An active stabilizer for cable-driven parallel robot vibration damping[END_REF], a stabilizer consisting of rotating arms is located on-board the CDPR mobile platform to actively damp vibrations, as illustrated in Figure 1. The work reported in the present paper is part of a project aiming to embed a similar stabilizer on the platform of the 6 Degree-of-Freedom (DOF) CDPR CoGiRo [START_REF] Gouttefarde | Geometry selection of a redundantly actuated cable-suspended parallel robot[END_REF], shown in Figure 2.

The design of CoGiRo ensures that there is no cable-cable collision nor cableplatform collision within the workspace of this CDPR. However, when active mechanical devices are placed on-board the CDPR mobile platform, the moving parts of these on-board devices may collide with the cables or platform. This eventuality of collisions is an issue that must be taken into account in the design In order to prevent such collisions, a first step is to determine the volume of space occupied by each cable when the CDPR platform moves throughout a given workspace. Indeed, during the platform motions, the positions of the cables change. The set of all positions taken by one cable for all the poses of the platform in the CDPR workspace is called cable span [START_REF] Pott | Determination of the cable span and cable deflection of cable-driven parallel robots[END_REF]. The latter reference is the only previous work dealing with the issue of determining the cable span. It proposes a method to represent the cable span by a volume object but it does not deal with the issue of using this volume to check the absence of collisions.

• • • • • • • A 1 A 2 A 3 B 1 B 2 B 3 G p k 1 , l 01 k 2 , l 02 k 3 , l 03 - → z 0 - → y 0 - → z p - → y p r r r 1 O 1 λ λ λ 1 m 1 θ 1 r r r 2 O 2 λ λ λ 2 m 2 θ 2 r r r 3 O 3 λ λ λ 3 m 3 2π -θ3 - → z 0 G p - → y 0 - → z p - → y p α
While the problem of cable-cable interferences as well as cable-platform and cable-object collisions has been addressed several times in the literature, e.g. [START_REF] Merlet | Analysis of the influence of wires interference on the workspace of wire robots[END_REF][START_REF] Martin | Determination and management of cable interferences between two 6-dof foot platforms in a cable-driven locomotion interface[END_REF][START_REF] Perreault | Geometric determination of the interference-free constant-orientation workspace of parallel cable-driven mechanisms[END_REF][START_REF] Nguyen | On the improvement of cable collision detection algorithms[END_REF][START_REF] Martin | Geometric determination of the cable-cylinder interference regions in the workspace of a cable-driven parallel robot[END_REF], to the best of our knowledge, the problem of avoiding collisions between a cable and the mobile part(s) of a device located on-board the CDPR platform has never been treated yet. Hence, the contribution of this paper is a method to check the absence of such collisions within a box-shaped workspace of a CDPR. In order to accelerate computations related to collision avoidance checking, this method is based on an original bounding volume approximation of the cable span which is simpler than the one discussed in [START_REF] Pott | Determination of the cable span and cable deflection of cable-driven parallel robots[END_REF]. Moreover, this cable span approximation is calculated with respect to the mobile platform frame to enable simple testing of collisions with on-board devices.

This paper is organized as follows. The cable span of a CDPR is defined in Section 2. Based on the approximation of the cable span introduced in [START_REF] Pott | Determination of the cable span and cable deflection of cable-driven parallel robots[END_REF], two algorithms are discussed in Section 3 to test the eventuality of a collision between a cable and an object located on-board the mobile platform. A new and simpler bounding volume approximation of the cable span is proposed in Section 4. The characterization of the faces of this bounding volume and the corresponding collision avoidance testing are finally presented in Section 5.

Definition of the cable span

The frame attached to the CDPR mobile platform is denoted F p and the fixed base frame is denoted F 0 . A vector v v v expressed in frame F 0 is denoted by 0 v v v and in F p by p v v v. The pose of the platform is given by the vector x x x, composed of its position vector p p p in F 0 and of a vector θ θ θ p of three Euler angles defining the orientation of F p in F 0 . Let R R R(θ θ θ p ) be the rotation matrix describing the orientation of the platform in F 0 . Each cable is considered to be a straight line segment between its base drawing point A i and its platform fixing point B i . These notations are shown in Figure 3.

The vector along the straight line segment of cable i, denoted u u u i , is given in frame F 0 by:

0 u u u i = 0 p p p + R R R(θ θ θ p ) p b b b i -0 a a a i (1)
The interval that contains all values of a scalar variable e is denoted [e, e], with e the minimal value of e (lower bound) and e its maximal value (upper bound). The concatenation operator is written ||. In this paper, the prescribed workspace W of a 6-DOF CDPR is defined as follows:

W = { x x x = { 0 p p p, θ θ θ p } | { 0 p p p ∈ [x, x] × [y, y] × [z, z]} || {θ θ θ p ∈ [α p , α p ] × [β p , β p ] × [γ p , γ p ] } } (2)
It is a box-shaped workspace in the sense that, for a given orientation θ θ θ p , the set of positions lying inside W is a box. In the remainder of this paper, it is assumed that W is fully included in the wrench-feasible workspace [START_REF] Bosscher | Wrench-feasible workspace generation for cable-driven robots[END_REF][START_REF] Gouttefarde | Interval-analysis-based determination of the wrench-feasible workspace of parallel cable-driven robots[END_REF] and, hence, that all poses in W can be reached with feasible cable tensions. The cable span of cable i with respect to F 0 is defined as [START_REF] Montgomery | Suppression of cable suspended parallel manipulator vibration utilizing input shaping[END_REF] and according to the right-hand side of this equation and to (2), CS 0 i is the Minkowski sum of three sets:

CS 0 i = { 0 u u u i | x x x ∈ W}. Vector 0 u u u i is defined in
-The box [x, x] × [y, y] × [z, z] (position vectors 0 p p p) • • • • • • • • F 0 • • • • • • • • F p B i A i u u u i p p p Fig. 3: Schematic of the CoGiRo CDPR -The portion of a sphere {R R R(θ θ θ p ) p b b b i | θ θ θ p ∈ [α p , α p ] × [β p , β p ] × [γ p , γ p ]} -
The point A i having as position vector 0 a a a i Note that p b b b i and 0 a a a i are constant vectors. Hence, when the Euler angle set

[α p , α p ] × [β p , β p ] × [γ p , γ p ]
is not reduced to a single value, the cable span is a relatively complex geometric object (not necessarily convex) even for the simple definition of the workspace W given in [START_REF] Weber | Active vibration canceling of a cable-driven parallel robot in modal space[END_REF]. In [START_REF] Pott | Determination of the cable span and cable deflection of cable-driven parallel robots[END_REF], based on a discretization of the CDPR workspace and for a fixed orientation of the mobile platform, the cable span is approximated as a so-called generalized cone (a kind of cone whose cross section is a polygon not necessarily convex).

With the aim of checking the absence of collisions between a cable and the mobile part(s) of a device located on-board the mobile platform of a CDPR, the present paper deals with the cable span calculated with respect to the mobile platform frame F p . For cable i, this cable span is defined as

CS p i = {-p u u u i | x x x ∈ W} where: -p u u u i = R R R(θ θ θ p ) ( 0 a i a i a i -0 p p p) -p b b b i (3)
Equation ( 3) is directly obtained from (1) by multiplying both sides by R R R(θ θ θ p ) .

CS p i is thus the translation of the set {R R R(θ θ θ p ) ( 0 a i a i a i -0 p p p) | x x x ∈ W} by vector p b b b i . This set corresponds to the volume swept by the box { 0 a i a i a i -0 p p p | 0 p p p ∈ [x, x] × [y, y] × [z, z]} when this box is rotated by R R R(θ θ θ p ) for all θ θ θ p in [α p , α p ] × [β p , β p ]×[γ p , γ p ].
Similarly to the case of the cable span CS 0 i calculated in F 0 , the cable span CS p i is thus a relatively complex three-dimensional geometric object which is not necessarily convex.

Collision avoidance checking

In [START_REF] Pott | Determination of the cable span and cable deflection of cable-driven parallel robots[END_REF], based on a discretization of the CDPR workspace W, the cable span CS 0 i is approximated as a so-called generalized cone. The same method could be applied to the cable span CS p i . This generalized cone approximation is not necessarily convex (see Figure 3 in [START_REF] Pott | Determination of the cable span and cable deflection of cable-driven parallel robots[END_REF]) and may contain a large number of vertices depending on the number of points in the workspace discretization (and on the workspace definition). Therefore, it is not well suited for checking the absence of collision between a cable and mechanical parts on-board the mobile platform since this check consists in verifying that the volumes swept by the mechanical parts during their motions are fully outside of the cable span.

As an example, let us consider the convex polyhedral cone shown in Figure 4. Note that this cone is a simpler geometric object than the generalized cone considered in [START_REF] Pott | Determination of the cable span and cable deflection of cable-driven parallel robots[END_REF]. Let us also consider the simple case of testing whether or not a point Q is located inside this convex polyhedral cone. Several algorithms can be used to determine if Q is inside the cone, two of them are now briefly described.

First, a point-in-polygon approach, whose principle is illustrated in Figure 4, performs the following steps:

1. Obtain Q the projection of Q on the axis of the cone. This defines a ratio k of, on the one hand, the distance between the base of the cone and Q and, on the other hand, the length of the cone axis. 2. Apply the ratio k to the distances between the vertices of the base of the cone, which is a polygon, and the center of this polygon. The new polygon hereby obtained called P is the section of the cone containing the point Q . 3. Test whether or not Q belongs to the polygon P .

The third step can be implemented with a ray crossing algorithm [START_REF] O'rourke | Computational Geometry in C[END_REF] (which can also be used for non-convex polygons) whose complexity is O(n), n being the number of vertices of the base polygon.

Another approach consists first in determining the faces of the convex polyhedral cone. These faces may be given by the convex hull procedure or they can be determined within the polar sorting phase of the generalized cone determination as detailed in [START_REF] Pott | Determination of the cable span and cable deflection of cable-driven parallel robots[END_REF]. Then, point Q is located inside the polyhedral cone if and only if it is located on the same side of each of the planes containing the cone faces. This second approach complexity is also O(n) where n is the number of vertices (or edges) of the base polygon.

The number of vertices n depends on the number of points used to discretize the CDPR prescribed workspace. Hence, the computational time needed to test if a given set is not interfering with the cable span, i.e. to check the absence of collision, depends on n. Moreover, the check must be done N times, N being the number of cables. Hence, using one of the two algorithms described above within an iterative optimization process slows down the whole procedure when n is (relatively) large. Using a simple, yet not overly conservative, bounding volume approximation of the cable span is thus important to enhance computational efficiency.

A simple bounding volume approximation of the cable span

Based on a discretization of the CDPR workspace W, a simple bounding volume of the cable span CS p i (cable span in F p ) can be obtained as follows. Cable i is considered as a straight line segment between points A i and B i . In the mobile platform frame F p , the position of B i is constant whereas the position vector of point A i is R R R(θ θ θ p ) ( 0 a i a i a i -0 p p p) and thus it depends on the mobile platform pose x x x = { 0 p p p, θ θ θ p } ∈ W. In F p , the discretization of W generates a set of positions of point A i and taking the convex hull of all these points produces a convex polyhedron. If the discretization is fine enough, this convex polyhedron is a good approximation of all possible positions of A i in F p when x x x ∈ W. However, as discussed in Section 3, the number of vertices of the bounding volume of the cable span should be kept small. Hence, instead of the convex hull, the smallest box B (aligned with the axes of F p ) containing all positions of point A i for x x x in the discretized workspace W is calculated. To this end, it suffices to determine, along each of the three coordinate axes of F p , the minimum and maximum coordinates of this set of positions of A i .

The box B encloses all positions of points A i in F p for x x x in the discretized workspace W, as illustrated in Figure 5. Hence, the polyhedron P obtained by connecting the fixed point B i to B is a bounding volume approximation of the cable span CS p i , i.e., a bounding volume of all the positions of the cable segment A i B i for x x x in the discretized workspace W. In the remainder of this paper, it is assumed that the discretization of the workspace is such that this polyhedron P encloses the cable span CS p i . An example of such a polyhedron P forming a bounding volume approximation of the cable span is shown in Figure 6. As can be seen in this figure, P consists of the union of the box B and of a pyramid (convex polyhedral cone) having the fixed point B i as apex. The base of this pyramid is a convex polygon whose vertices are some of the vertices of the box B.

Collision avoidance checking with the new cable span bounding volume approximation

In Section 4, a polyhedron P forming a bounding volume approximation of the cable span CS p i has been introduced. A method to ensure collision avoidance between a cable and a moving device on-board the CDPR mobile platform consists in testing if the set of all possible positions of this device does not intersect P. Indeed, P being a bounding volume of the cable span CS p i , no intersection with P means no intersection with the cable span and thus no possible collision with the cable in the workspace W. In order to test if a point or a set is outside polyhedron P, the determination of the polyhedron faces is useful. Indeed, the polyhedron can be defined as the intersection of halfspaces bounded by the planes containing the faces (mathematically, a system of linear inequalities). Then, a point or a set is outside the polyhedron if and only if it is outside of at least one of these halfspaces (it violates at least one of the inequalities). The method to determine the faces of the polyhedron P forming a bounding volume approximation of the cable span is described below.

As mentioned at the end of Section 4, the polyhedron P is the the union of the box B and of a pyramid, the apex of the pyramid being the fixed point B i (Fig. 6). The number of faces of this polyhedron depends on the number of faces of the box B that are visible from point B i . Three cases must be distinguished.

-One face of B is visible from B i : As shown in Figure 7 In addition to these three cases, particular cases must be dealt with. These particular cases appear when point B i lies in one or several planes containing the faces of the box B. For simplicity, these particular cases are not detailed in this paper. They do not cause any particular difficulty.

Based on this characterization of the faces of the polyhedron P, the mathematical description of each of these faces is straightforward. Let us consider face k of P. Its mathematical description consists in a point P k lying on the face and a vector n n n k normal to the face and pointing to the outside of P. Point P k and vector n n n k define the plane containing face k. A point Q is then outside of the polyhedron if and only if, for at least one face k, it is not on the same side of this plane than P, i.e., if and only if there exists k such that --→

P k Q • n n n k > 0.
In the case of a face k of P which is also a face of the box B (a rectangle), point P k can for instance be one vertex of the rectangle or its center and vector n n n k is taken along the normal to this rectangle pointing to the outside of B. In the case of a face of the pyramid having point B i as apex, the face is a triangle whose three vertices are known so that point P k and vector n n n k are also straightforward to define. Note that the determination of the faces of P and the calculation of their mathematical descriptions (P k and n n n k ) can be done offline, i.e., before any use of P to test the absence of collision between a cable and a device onboard the CDPR mobile platform. Typically, within an iterative optimization Figure 10 show the polyhedra P which are bounding volume of the cable spans of the eight cables of the CDPR CoGiRo for a given workspace W. As can be seen, the cable span bounding volumes represent a significant part of the space around the platform and, in fact, surround the platform. This is mostly due to the cable arrangement of CoGiRo [START_REF] Gouttefarde | Geometry selection of a redundantly actuated cable-suspended parallel robot[END_REF]. This CDPR being suspended, it can also be observed that the space below the platform is free.

Conclusion

This paper dealt with the problem of verifying the absence of collisions between the cables of a CDPR and mobile devices located on-board the mobile platform, across a prescribed workspace. The cable span is defined as the set of all positions taken by one cable of the CDPR for all the poses of the mobile platform in the prescribed workspace. In this paper, the cable span as seen in the platform coordinate frame is considered. If the set of all possible motions of a device onboard the mobile platform is fully outside of the cable span, then no collision between the device and the cable can occur within the prescribed workspace. However, the cable span being a relatively complex geometric object, a bounding volume approximation of the cable span has been proposed in this paper. This bounding volume is a polyhedron and the characterization of the faces of this polyhedron has been given. Using this polyhedron as a bounding volume of the cable span allows to accelerate computations related to collision avoidance checking.

Fig. 1 :

 1 Fig. 1: Planar 3-DOF CDPR with 3 stabilization arms

Fig. 4 :

 4 Fig. 4: Convex polyhedral cone containing the cable span

Fig. 5 :Fig. 6 :

 56 Fig. 5: Convex hull of all possible positions of A i (and of the fixed point B i ) and box containing the convex hull

Fig. 7 :Fig. 8 :Fig. 9 :

 789 Fig. 7: Faces of the polyhedron P if one face of B is visible from Bi

Fig. 10 :

 10 Fig. 10: All the bounding volumes of the cable spans of the CDPR CoGiRo as seen in the platform frame F p

Acknowledgement

This work was supported by the ANR under grant ANR-15-CE10-0006, project DexterWide.