Nicolas Ranger
email: nicolas.ranger@etu.unilim.fr

Catalin Constantinescu
email: catalin.constantinescu@cnrs.fr

Romain Lucas-Roper
email: romain.lucas@unilim.fr

Alexandre Boulle
email: alexandre.boulle@cnrs.fr

Nicolas Glandut
email: nicolas.glandut@unilim.fr.

Keywords: titanium carbide, laser ablation, thin films, electrochemistry, heteroepitaxy, stoichiometry

Structural and electrochemical properties of high quality epitaxial titanium carbide thin films grown by pulsed laser deposition on MgO (111) and Al2O3 (001) substrates

Nicolas Ranger, Catalin-Daniel Constantinescu, Romain Lucas-Roper,

Alexandre Boulle, Nicolas Glandut

To cite this version:

Nicolas Ranger, Catalin-Daniel Constantinescu, Romain Lucas-Roper, Alexandre Boulle, Nicolas Glandut. Structural and electrochemical properties of high quality epitaxial titanium carbide thin films grown by pulsed laser deposition on MgO (111) and Al2O3 (001) substrates. Thin Solid Films, 2023, 782, pp.140007. 10.1016/j.tsf.2023.140007. hal-04286785

Introduction

Titanium carbide (TiCx) exists as a homogeneous phase over a wide range of stoichiometry, i.e., a solid solution, with 0.5 < x < 1. TiC is generally prepared in bulk from highpurity titanium dioxide blended with carbon black, between 1973 and 2373 K, with controlled carbon vacancy. TiC is a very hard, refractory material used in bulk, as thin films, or as nanoparticles [START_REF] Martin | Handbook of Deposition Technologies for Films and Coatings: Science, Applications and Technology[END_REF][START_REF] Kaiser | Review of the fundamentals of thin-film growth[END_REF][START_REF] Chang | Low-Temperature Elastic Properties of ZrC and TiC[END_REF][START_REF] Kieffer | Hartstoffe und Hartmetalle[END_REF][START_REF] Becker | Die Kristallstrukturen einiger binaerer Carbide und Nitride[END_REF], for manufacturing metal-working tools, high wear resistance, and lightweight parts and components. This non-oxide ceramic also finds usage as a catalysts support in hydrogenation-dehydrogenation processes, as well as for SO2 decomposition and hydrotreating (hydrofining, hydrodesulfurization, hydrodearomatization) and reforming applications in the modern refinery to produce cleaner fuels, with excellent results especially when used in TiC (111) crystalline orientation [START_REF] Zhang | Transition Metal Carbides (TMCs) Catalysts for Gas Phase CO2 Upgrading Reactions: A Comprehensive Overview[END_REF][START_REF] Back | TiC-and TiN-Supported Single-Atom Catalysts for Dramatic Improvements in CO2 Electrochemical Reduction to CH4[END_REF][START_REF] Rodriguez | CO2 hydrogenation on Au/TiC, Cu/TiC, and Ni/TiC catalysts: Production of CO, methanol, and methane[END_REF][START_REF] Rodriguez | Highly active Pt/MoC and Pt/TiC catalysts for the low-temperature water-gas shift reaction: Effects of the carbide metal/carbon ratio on the catalyst performance[END_REF].

The interest in developing TiC as thin films has recently further increased due to energy conversion applications breakthroughs, such as hydrogen storage and lithium intercalation, as electrodes in sensors, supercapacitors, and charge-storage devices, or in microwave absorption and electromagnetic protection [START_REF] Gringoz | Electrochemical hydrogen storage in TiC0.6, not in TiC0.9[END_REF][START_REF] Nguyen | Electrochemical Hydrogen Insertion in Substoichiometric Titanium Carbide TiC0.6: Influence of Carbon Vacancy Ordering[END_REF][START_REF] Nguyen | Hydrogen insertion in substoichiometric titanium carbide[END_REF][START_REF] Nguyen | Stockage électrochimique d'hydrogène dans le carbure de titane[END_REF][START_REF] Bautista-Ruiz | Characterization of tungsten/titanium carbide coatings deposited by cathodic arc deposition for hydrogen evolution[END_REF][START_REF] Dev | Lithium intercalation studies in cubic titanium carbide thin films[END_REF]. However, the use of conventional methods to promote the growth of high purity carbide materials usually requires a substrate temperature in the range of 773 -1273 K, while the technological requirements are to grow films at temperatures that do not surpass ~573 K.

Crystalline TiC thin films can be synthesized at any substrate temperature, including at room temperature, by using pulsed laser deposition (PLD) [START_REF] Martin | Handbook of Deposition Technologies for Films and Coatings: Science, Applications and Technology[END_REF][START_REF] Kaiser | Review of the fundamentals of thin-film growth[END_REF]. This technique has already been widely used for its capability to evaporate and deposit refractory materials, i.e. iridium or INCONEL alloys.

Herein, we present and discuss on the electrochemical properties and the growth of TiCx (x = 0.55 -1.0) thin films with (111) crystallographic orientation, grown on (111)-cut MgO single-crystal substrates and on (001)-cut Al2O3 single-crystal. Their morphology and structure are investigated by atomic force microscopy (AFM), scanning electron microscopy (SEM), and high-resolution X-ray diffraction (HR-XRD). A comparison of the crystalline properties, the thickness and the morphology of the films is presented. Films are of high quality on all substrates tested and no delamination is observed. Subnanometric roughness and heteroepitaxial growth are observed in films grown both on MgO and Al2O3 substrates. The electrochemical properties of the films are rationalized with respect their crystallographic properties. Subsequently, the sintering temperature was reached at a rate of 0.25 K/s, and held for 3.5 h (i.e. 12 600 s). The 40 MPa pressure was applied at 1373 K, and released after the 3.5 h hold.

Experimental methods

Titanium carbide synthesis (bulk)

To finish, the cooling from 1973 K to ambient was done at a rate of 0.16 K/s. The complete temperature program is shown in Figure 1. The stoichiometric compound (TiC0.98≈1) was also purchased from Cerac (purity 99.5%), used as provided, without any further purification, and sintered in the same manner as the TiC0.55 bulk sample.

Thin film growth (PLD)

As demonstrated below, the choice for these specific substrate types, i.e., MgO(111) and Al2O3(001), allowed us to grow TiCx films with the same (111) orientation, which facilitates the comparison between the two film/substrate systems. The substrates, thoroughly cleaned with isopropanol, ethanol and water, and finally dried in constant airflow, have been continuously monitored during the deposition by using a thermocouple. The deposition of TiCx films was carried out in high vacuum (10 -7 Pa), and at a temperature of 523 K, by using a KrF excimer laser (TuiLaser AG, model "Thin Film Star" / TFS 100-248nm-CT-T V2.0) operating at a wavelength of 248 nm, 25 ns pulse duration, 20 Hz repetition rate (maximum), and at a fluence of 4,5 J/cm 2 . The deposition time lasted for 30 minutes at a target-substrate distance of 4 cm.

Chemical, electrochemical, morphological, and structural investigations

Optical microscopy images have been taken to rapidly assess the quality of the films, with clear details as small as 1 µm, on a Kayence Optical Microscope. Scanning electron microscopy (SEM) has been used to assess information about the samples surface topography, composition, as well as about their thickness in a freshly broken/exposed cross-section.

Results and discussion

Optical, scanning and atomic force microscopy

Rapid optical microscopy observations revealed that no delamination effects are observed in our films. Top-view and cross-section SEM measurements reveal that the TiC films exhibit a smooth surface and a thickness of up to 200 nm on both substrates, and regardless of the targets stoichiometry, as presented in Figure 2a and Figure 2b, respectively.

a.) b.)

Electrochemical investigations

Figure 4a shows the cyclic voltammogram obtained in 0.1 M H2SO4 aqueous solution for TiC film grown on MgO(111). A broad wave in oxidation can be observed, centred at 1.06

V vs. NHE, and with a peak current density of 750 A cm -2 . This corresponds to the electrochemical passivation of TiC by the formation of a hydrated titanium dioxide film, well-described now in the literature [START_REF] Saha | Titanium carbide: An emerging electrocatalyst for fuel cell and electrolyser[END_REF][START_REF] Ignaszak | Titanium carbide and its core-shelled derivative TiC@TiO2 as catalyst supports for proton exchange membrane fuel cells[END_REF][START_REF] Beverskog | Corrosion properties of TiC films prepared by activated reactive evaporation[END_REF][START_REF] Hintermann | The anodic behaviour of titanium carbide in sulphuric acid solutions[END_REF]. Carbon dioxide, which is the other thermodynamically stable compound [START_REF] Pourbaix | Atlas of Electrochemical Equilibria in Aqueous Solutions[END_REF], also evolves during this passivation and where n1 = 8 electrons per TiC are involved. The charge integrated under the curve is ca.

Q1 = 2.4 mC cm -2 .
Figure 4b shows the same experiment as the previous one, in the case of the TiC / Al2O3 (001) system. It is worth emphasizing that the target used during growth is the same as the one used in the previous experiment, i.e. stoichiometric TiC. A broad wave in oxidation can still be observed, with the same simple shape, also centred at 1.06 V vs. NHE, but with a peak current density two times smaller. The charge under the curve is consequently smaller, ca.

Q2 = 1.75 mC cm -2 .
There are two possible causes for this result. The first is a composition change in the deposited carbide. This can be reasonably suggested because titanium carbide in its bulk form is well-known to possess a wide range of substoichiometry, i.e., 0.5 < x < 1 in TiCx [START_REF] Storms | The Refractory Carbides[END_REF][START_REF] Gusev | Phase equilibria, phases and compounds in the Ti-C system[END_REF]. Let us assume that the deposited carbide on sapphire is TiC0.5; the passivation reaction can then be rewritten: TiC0.5 + 4H2O  TiO2.H2O + 0.5 CO2 + 6H + + 6e -

where n2 = 6 electrons are transferred. The charge being proportional to the number of electrons involved, we can therefore write Q1/Q2 = n1/n2. The ratio Q1/Q2 = 1.37, obtained from experiment, is very close to the ratio n1/n2 = 1.33, obtained from the theoretical electrochemical reactions. This is a clear indication that a drastic composition change for PLDdeposited TiC on Al2O3 (001) is highly probable, with a chemical formula close to TiC0.5.

The second possible reason for Q2 < Q1 and a smaller current in the cyclic voltammograms could be the thickness of the TiO2 passive layer formed. Indeed, the charge is also proportional to this thickness, and one could argue that oxidation does not occur to the same depth. To assess whether or not this mechanism takes place, other thin layers have been deposited by PLD, but with a bulk target made of TiC0.55, and treated electrochemically. The result is displayed in Figure 4c. The shape and the orders of magnitude of the current and charge, are very similar to Figure 4b, and above all independent from the either substrate type, i.e. MgO (111) or Al2O3(001).

High-resolution energy-dispersive X-ray spectroscopy

In order to swiftly assess the carbon content of the materials (bulk and thin films), we used EDS. However, due to the high background counts in SEM-EDS, an artificial carbon peak is always visible and thus a value of more than 2% carbon is normally measured even in the raw substrates [START_REF] Berlin | Recent Advances in EDS and EBSD Technology: Revolutionizing the Chemical Analysis of Chondritic Meteorites at the Micro and Nanometre 5 scale[END_REF]. Although the SEM/EDS technique has historically been limited to relatively thick films when dealing with carbon-containing structures, and with more emphasis on film/surface morphology rather than compositional analysis, a reasonable difference in carbon content was found in the thin film samples as, corresponding to the TiC and TiC0.5

structures (semi-quantitative analysis). Carbon signals are present on the EDS spectra of all samples, revealing carbon depletion for PLD-deposited TiC on Al2O3 (001). However, due to the high energies of incident electrons that are required to compensate for the low X-ray yield of carbon, appreciable penetration depths and low signal-to-noise ratio effects occur [START_REF] Puttichaem | Characterization of Ultra-Thin Diamond-Like Carbon Films by SEM/EDX[END_REF].

Thus, even with the use of modern surface-sensitive SEM and high-resolution EDS with lownoise electronics, the results must be corroborated by another high-resolution technique.

High-resolution X-ray diffraction analysis

To further support the scenario described above, we characterized the crystallographic There are therefore two equiprobable ways to grow TiC on Al2O3, which gives rise to two in-plane epitaxial variants. From the position of 018 peaks (red dotted lines), or the 119 peaks (blue dotted lines) of Al2O3, it can be concluded that one variant is such as [110]TiC ||

[210]Al2O3 whereas the other is rotated by 60°, i.e.

[110]TiC || [120]Al2O3. This is also consistent with previously published results [START_REF] Eklund | Epitaxial TiC/SiC multilayers[END_REF]. The fact that all peaks of the φ-scan have a similar intensity indicates that both variants are present in equal proportions.

Figure 6a shows a close-up of the θ-2θ scans in the vicinity of the 111 reflections of TiC. From this figure it can be observed that the 111-peak position of TiC differs depending on the underlying substrate, and that, in both cases, the peak position is smaller than the standard value of TiC (2θ = 35.907°, dotted line) [PDF card #00-32-1383] which indicates an elongation of the unit-cell in the direction normal to the surface. This elongation can be due either to a difference in the level of residual strains in the films and/or a different Ti/C molar ratio as compared to the reference material. In the case of epitaxial films, the respective effects of residual strains and composition can be disentangled by using XRD reciprocal space maps (RSMs) following a method previously used to analyse oxide and metallic films [START_REF] Théry | Combined strain and compositioninduced effects in the metal-insulator transition of epitaxial VO2 films[END_REF][START_REF] Trupina | Texture and interface characterization of iridium thin films grown on MgO substrates with different orientations[END_REF][START_REF] Heinke | Relaxation and mosaicity profiles in epitaxial layers studied by high resolution X-ray diffraction[END_REF]. The strain-free lattice parameter and the level of residual strain can be precisely derived by measuring the peak position (Qx, Qz) in hhl RSMs (i.e. reflections emanating from planes inclined with respect to the surface), for instance the 113 reflections. In this case, the

x and z axes are parallel to the [110] and [111] directions, respectively, and the strain-free lattice parameter is obtained through:

where dx and dz are obtained from the RSM via dx = 2π / Qx and dz = 2π / Qz, k is the theoretical d111/d110 ratio in the TiC phase, and ν2 the biaxial Poisson ratio, respectively. The former is equal to 0.565 and the latter is given by (2C11 + 4C12 -4C44) / (C11 + 2C12 + 4C44), which equals 0.59368 using the Cij values reported elsewhere [START_REF] Dang | Thermodynamic and mechanical properties of TiC from ab initio calculation[END_REF].

Finally, the lattice strain is computed by using e = (dx -dx (bulk )/dx (bulk) . 113 of RSMs of TiC are shown in Figure 6(b,c). It should be emphasized that, in the case of C-deficient TiC materials, C vacancy might be non-randomly distributed, eventually leading to symmetry 1 changes [PDF card #04-017-1603], like for instance the Ti2C phase. In the present work we verified that no such ordering occurs by carefully checking the lack of superstructure peaks characteristic of C-deficient phases in the θ-2θ scans (in particular around 2θ = 17.8° which correspond to the ½½½ superstructure peak of TiC1-x). By using the above-mentioned approach, the in-plane strain of TiC/MgO is e = -2.1%. This value is consistent with the value corresponding to the epitaxial (misfit) strain which, with the above mentioned in-plane epitaxial orientations, is -2.6%. The fact that both values are not equal indicates that part of the strain is relaxed during growth. This in-plane compressive strain is also consistent with out-of-plane elongation observed in Figure 6a. Surprisingly, the strain-free lattice parameter is found to be larger (4.3463 Å) than the value usually reported for TiC (4.3247 Å). The origin of this discrepancy is not yet understood, yet a couple of possible models might be envisaged in this context, to explain it:

1. Deviations from the 1:1 (Ti:C) stoichiometry cannot explain an increase in the lattice parameter [START_REF] Pourbaix | Atlas of Electrochemical Equilibria in Aqueous Solutions[END_REF]. Oxygen interdiffusion at the TiC/MgO cannot be straightforwardly excluded, even with the high vacuum during thin film depositions (at 10 -7 Pa and even at 10 -8 Pa), and may imaginably explain the dilatation of the unit cell [START_REF] Storms | The Refractory Carbides[END_REF]. Further work is due to validate or invalidate this hypothesis.

2. The derivation of the residual strain and the lattice parameter rely on the value of the elastic constants, Cij, which are assumed to be known and equal to those of TiC. However, in the case of large deviations in the Ti/C molar ratio (i.e. the carbon deficiency / depletion), the Cij values might also very likely deviate from their nominal value, hence casting some doubt regarding the exactness of the values derived previously. In such a situation, it is safer to consider those calculated values on a relative (rather than an absolute) scale.

Let us now consider the TiC/Al2O3 case. The epitaxial strain at the TiC/Al2O3 interface, using the orientations found above, is -9.7%. The value derived from the RSMs is -2%, which indicates a significant amount of strain relaxation, which is not unexpected. The strain-free lattice parameter is 4.3058 Å, which is also a very large deviation from the standard value, but in the opposite direction, i.e. we now observe a 0.5% contraction of the unit-cell. Bearing in mind the limitations evidenced in the TiC/MgO case, this value should not be considered as a perfectly precise measurement. However, since both films exhibit a similar level of residual strain (-2.1% and -2%), the difference in peak position in Figure 6a can only be accounted for by different bulk (strain-free) lattice parameter, i.e. aMgO/Al2O3 < aMgO/TiC, which clearly points to a loss of carbon in the material. For instance, the lattice parameter of TiC0.62 (corrected for the unit-cell size doubling due to vacancy ordering) is 4.312 Å [PDF card #04-017-1603], which is only 0.14% different from our measurement. Additionally, according to [START_REF] Storms | The Refractory Carbides[END_REF] (Fig. 6 therein), a lattice parameter of 4.306 Å roughly corresponds to the TiC0.55 composition, which corresponds to the value inferred from electrochemical measurements.

To conclude, a possible driving force for the loss of carbon is strain relaxation: during growth, the composition of the film varies to minimize the interfacial strain, a phenomenon sometime observed in oxide films exhibiting non-stoichiometry [START_REF] Théry | Combined strain and compositioninduced effects in the metal-insulator transition of epitaxial VO2 films[END_REF][START_REF] Conchon | Effect of tensile and compressive strains on the transport properties of SmNiO3 layers epitaxially grown on (001) SrTiO3 and LaAlO3 substrates[END_REF].

Conclusion

Summarizing, in the present manuscript we report original research on the use of cyclic voltammetry corroborated with high-resolution X-ray diffraction in order to assess the carbon content of TiC thin films. For that, we have grown epitaxial TiC on MgO(111) and Al2O3(001)

substrates by using pulsed laser deposition from TiC targets with various compositions. The films grown on sapphire substrates exhibit an electrochemical behaviour significantly different from those grown on MgO. Moreover, their cyclic voltammograms are strikingly similar to those of TiC0.55 films although the deposition target is stoichiometric TiC. High-resolution Xray diffraction measurements confirmed that films grown on sapphire are actually carbon deficient, with a composition of TiC0.55, the driving force for the carbon deficiency being the relaxation of the compressive interfacial strain. On the contrary, the interfacial strain at the MgO/TiC interface is tensile which cannot be compensated by variations in the Ti/C ratio.

Figure 1 :

 1 Figure 1: Temperature program used for the synthesis of the PLD targets, i.e. TiC and TiC0.55.

  A field emission gun (FEG-SEM) setup from FEI (model Quanta FEG 450) equipped with a secondary electron detector (model SE R580) was used in order to avoid any bias that may be induced by the surface topography. Energy-dispersive X-ray spectroscopy (EDS) has been employed for the elemental analysis and chemical characterization of the samples. An EDS device from Oxford Instruments (model X-Max 150) equipped with a very large area (150 mm²) silicon drift detector (SDD) was used, installed in situ on the FEG-SEM setup. The AZtec analysis software from Oxford Instruments plc, UK was employed for analysis and data processing. Next, topographical observations were performed by using an atomic force microscope (AFM) on an Agilent AFM 5100 setup, with two-dimensional (2D) images and roughness parameters evaluated. High-resolution X-ray diffraction (HR-XRD) measurements were conducted on a Bruker D8 Discover diffractometer, equipped with Cu target (λ = 1.5406 Å), and a parabolic mirror associated with a two-reflection Ge monochromator. Diffracted X-rays are collected using a 1D (LynxEye) detector covering a 2° 2θ range with an angular resolution of 0.01°. Conventional θ-2θ scans and Φ-scans where performed to assess the film/substrate epitaxial relationships, whereas the level of strain was assessed by recording XRD reciprocal space maps (RSMs) from reflections with hkl indices containing both in-plane and out-of-plane components, by using the DxTools software[START_REF] Boulle | DxTools: processing large data files recorded with the Bruker D8 diffractometer[END_REF]. Finally, electrochemical measurements have been carried out at room temperature, i.e., 298 K, in a standard three electrode cell. An Autolab PGSTAT30 potentiostat was used, controlled by GPES software (EcoChemie, The Netherlands). The solution was a 0.1 M H2SO4 aqueous solution (Aldrich) and deionized ultrapure water (Millipore, Milli-Q, 18.2 M.cm resistivity). It was deaerated by bubbling pure argon gas (Alphagaz 1, Air Liquide, France), prior to measurements, in order to remove dissolved oxygen, and argon gas was continuously blown onto the solution surface during the experiments. The contacts have been made directly with electrical clips and the samples were dipped in the electrolyte. After each experiment, the submerged areas have been accurately measured by optical microscopy and subsequent image analysis (ImageJ software). The reference electrode was a K2SO4-saturated Hg/Hg2SO4 electrode. Potentials were recalculated vs. normal hydrogen electrode (NHE), i.e. 0.64 V was added. The counter electrode was a platinum disk (10 mm in diameter), and the working electrodes, consisted of the PLDdeposited films of titanium carbide on either MgO (111) or Al2O3(001).

Figure 2 :Figure 3 ,Figure 3 :

 233 Figure 2: Scanning electron microscope (SEM): top view (a) and cross-section (b) images of TiC on an MgO (111) substrates grown by PLD from a TiC target; film thickness: ~200 nm.

Figure 4 :

 4 Figure 4: Cyclic voltammograms of TiC deposited by PLD, from a TiC target, for (a) MgO (111) substrate, and (b) sapphire Al2O3 (001) substrate. (c) From a TiC0.55 target for both types of substrates. Aqueous solution: 0.1 M H2SO4. Scan rate: 100 mV s -1 . T = 298 K.

  the overall reaction for the entire potential range 0.8 ~ 1.3 V vs. NHE can be summarized as follows:TiC + 5H2O  TiO2.H2O + CO2 + 8H + + 8e -[START_REF] Martin | Handbook of Deposition Technologies for Films and Coatings: Science, Applications and Technology[END_REF]

  structure of the TiCx films, as grown on the MgO(111) and Al2O3(001) substrates. Conventional θ-2θ scans recorded from TiC/MgO and TiC/Al2O3 (not shown) reveal that only the hhh reflections of TiC and MgO and the 00l reflections of sapphire are present in the whole accessible angular range. This evidences that the (111) planes of TiC are parallel to (111) planes of MgO (in the case of TiC/MgO), and the (111) planes of TiC are parallel to the (001) planes of Al2O3 (in the case of TiC/Al2O3). This result is rather expected, with respect to previously published results, in similar systems[START_REF] Jansson | Low temperature epitaxial growth of metal carbides using fullerenes[END_REF][START_REF] Palmquist | Magnetron sputtered epitaxial single-phase Ti3SiC2 thin films[END_REF] Φ-scans of the 113 reflection of TiC (in-plane orientations) are given in Figure5. In the case of TiC/MgO, it can be straightforwardly noticed that the 113 peak position of TiC exactly correspond to the corresponding peak position of the substrate (black dotted line). The inplane film/substrate orientation is therefore [110]TiC ||[110]MgO. This observation was also verified by HR-TEM on TiC films grown on MgO substrates (data not shown here). In the case of TiC/Al2O3 the situation is slightly complicated by the fact that the (111) plane of TiC exhibits a three-fold symmetry, whereas the (001) plane have a six-fold symmetry.

Figure 5 :

 5 Figure 5: Φ-scans of the 113 reflection of TiC from the TiC/MgO system (upper, black line) and the TiC/Al2O3 system (lower, red line). The stars indicate the reflections originating from one epitaxial variant. The other reflections belong to the other variant.

Figure 6 :

 6 Figure 6: (a) θ-2θ scans in the vicinity of the 111 reflection of TiC. Black line: TiC/MgO; red line: TiC/Al2O3; gray dotted line: standard TiC 111 peak position. (b) and (c) RSMs recorded around the 113TiC reflection in TiC/MgO and TiC/Al2O3, respectively.


Pamela S Soltis
email: psoltis@flmnh.ufl.edu

Luiza Teixeira-Costa

Pierre Bonnet

R Gil

Luiza Teixeira

I N T R O D U C T I O N

Advances in plant imaging across scales New imaging technologies are dramatically transforming all of biology. From remote sensing of continents to computed tomography (CT) scanning of individual organisms or parts of organisms, novel views are emerging that span planetary to suborganismal scales. In plant biology, observations from satellites (e.g., [START_REF] Deneu | Convolutional neural networks improve species distribution modelling by capturing the spatial structure of the environment[END_REF][START_REF] Cavender-Bares | Integrating remote sensing with ecology and evolution to advance biodiversity conservation[END_REF] and airborne instruments (e.g., [START_REF] Sun | UAVs as remote sensing platforms in plant ecology: Review of applications and challenges[END_REF] are providing new insight into the distribution of botanical diversity, species abundance, and ecosystem productivity and how these features are changing in response to human activity. At the same time, advances in X-ray technologies are revealing exquisite anatomical detail of both living and fossil plant structures [START_REF] Brodersen | New frontiers in the threedimensional visualization of plant structure and function[END_REF]. Innovations in imaging, largely enabled by the development of new sensors and analysis capabilities, are also capturing specific attributes of individual plants as well as their community context in the field.

In this special issue of Applications in Plant Sciences (APPS), we explore innovations in imaging and their contributions to plant biology. The 10 papers included in this collection span imaging of live plants in the field to chemical mapping of specific compounds. The authors emphasize sample preparation techniques, practical aspects of image capture, standardization of imaging techniques and resulting images, multiple forms of image analysis, and alternatives for image archival in public repositories. Moreover, the diversity of the imaging approaches and protocols presented in this collection can be applied to a broad range of research, teaching, and public outreach.

Two papers in this special issue note the lack of consistency in photographs of plants taken in the field. These photographs might serve as a virtual voucher of a rare species (when destructive sampling would be detrimental to the population) or as a source of plant traits for ecological or evolutionary research, but field photographs of plants are rarely standardized. Unlike other groups of organisms for which "standard views" have been developed, the vast diversity of plants in terms of both size and structure precludes many traditional approaches to standardization. These issues, as well as others, render currently available collections, such as those downloadable from iNaturalist (https://www.inaturalist.org/), less useful than they could be if images were captured, processed, and archived following specified standards. To standardize and improve the usefulness of field-captured images of plants, Weaver and Smith (2023a) report the development and implementation of FieldPrism, a system of photogrammetric markers, QR codes, and software to automate the curation of snapshot vouchers. They also developed FieldStation, a mobile imaging system that records images, GPS location, and other metadata on multiple storage devices. The combined use of FieldPrism and FieldStation will facilitate the rapid and standardized capture of fieldbased plant traits.

The application of a standard protocol for capturing field images can also facilitate downstream image analysis and modeling, allowing the creation of three-dimensional (3D) models of plants. These models allow the digital preservation of the shape, size, and architecture of an organism, as these features would otherwise be lost when captured only via pressed specimens or two-dimensional photographs. Thus, [START_REF] James | Rapid imaging in the field followed by photogrammetry digitally captures the otherwise lost dimensions of plant specimens[END_REF] provide detailed protocols for capturing images of plant specimens in the field and producing 3D models from the images using photogrammetry, a modeling approach that has become increasingly popular in different areas of biodiversity research. To showcase the applicability of their customizable protocol, the authors consider specimens of six different species exhibiting a range of surface:volume proportions. Moreover, the authors provide a thorough list of all equipment used in the field for photographing the specimens.

Beyond individual specimens, the uses of digital imaging and photogrammetry methods are also explored by [START_REF] Tirrell | Using photogrammetry to create virtual permanent plots in rare and threatened plant communities[END_REF] for their increasing value in integrating systematics, conservation, plant ecology, and the broader study of plant diversity. The authors propose and demonstrate the use of photogrammetry as a nondestructive protocol for critical long-term monitoring of research plots while reducing the possibility for inadvertent damage to sensitive, difficult-to-access, unpermitted, or otherwise inaccessible plant communities. The photogrammetry and structure-from-motion methods they describe are low-cost, efficient, less technical to implement than some other photogrammetric solutions, and allow for continued surveying efforts in areas where permanent structures or other surveying methods are not feasible. These methods will also allow users to accurately survey and record sensitive plant communities through time. Although the techniques described have been developed and tested largely in alpine landscapes, they are broadly applicable to a wide range of monitoring activities.

A fourth paper using field-captured photographs focuses on the analysis of color using images available on iNaturalist. To allow the rapid generation of color data, [START_REF] Luong | A pipeline for the rapid collection of color data from photographs[END_REF] present a computational pipeline developed using R scripts and showcasing the utility of R shiny apps for enhancing iNaturalist collections and aiding users, including students, in natural history research. As an example, the authors analyze variation in Erysimum capitatum, a native North American species that exhibits a wide range of flower colors. The pipeline they developed allowed the testing of interesting hypotheses related to color spatial autocorrelation, climate correlation, and elevational gradients. This work highlights the enormous potential of citizen/participatory science data sets to increase the breadth of sampling for scientific research. This new method of extracting color from non-standardized photographs makes it possible to take advantage of the large quantities of multimedia data generated on flora. The work also reinforces the value of collaborations between ecologists, computer scientists, and citizen/participatory science networks in conducting research in ecology and plant evolution.

In a complement to these innovations regarding fieldcaptured photographs, two papers in this special issue deal with images of samples in herbarium or other research collections. Although seeds often carry valuable information about local environmental conditions and evolutionary history, scoring seed characters has remained tedious and time-consuming. Moreover, non-standardized imaging techniques have yielded inconsistent results that make it difficult to quantify and interpret variation in seed traits. In response to these impediments, [START_REF] Steinecke | A standardized and efficient technique to estimate seed traits in plants with numerous small propagules[END_REF] report a standardized high-throughput technique to record seed number, seed area, and seed color from a collection of images using a model that relates seed area to pixel count. Application of this approach to seeds of Arabidopsis thaliana, Brassica rapa, and Mimulus guttatus demonstrated high reliability in the measurement of seed traits, opening the door to future studies of seed traits and the ecological and evolutionary drivers that have shaped them.

The second paper addressing images from herbarium specimens, which is also the second contribution by [START_REF] Weaver | From leaves to labels: Building modular machine learning networks for rapid herbarium specimen[END_REF], updates and expands on a machine learning tool designed to autonomously measure leaves from images of digitized herbarium specimens. The original iteration of this approach, LeafMachine, was published by Weaver et al. (2020) and was trained on 2685 specimens spanning 20 plant families. The expanded LeafMachine2 approach published in this issue included training on an impressive 494,766 manually prepared annotations from 5648 herbarium images representing 2663 species. This updated version used a set of plant component detection and segmentation algorithms to isolate not just individual leaves, but also petioles, fruits, flowers, wood samples, buds, and roots. With this ability to rapidly generate large amounts of trait data, LeafMachine2 will become a critical tool for scientists seeking to understand taxonomic and phylogenetic relationships, species distributions, phenological responses to climate change, collection bias, and species interactions.

Segmentation algorithms are also at the core of the paper by Wolcott et al. (2023), who provide a new application of X-ray micro-CT scanning to help solve a persistent puzzle in pollination biology. The authors focus on the minute flowers of one of the world's most economically important agricultural species, Theobroma cacao (cacao, Malvaceae), whose yields are pollinator-limited. The reduced size of the flowers and their elaborate morphology appear to limit pollinator access and movement within the flowers. While several small insects have been suggested as cacao pollinators, there is still uncertainty about the species involved. To advance the identification of specific pollinator species, Wolcott and colleagues combine the scanning of both flowers and potential pollinators with digital segmentation and tridimensional morphometric analysis. Their results reveal the main bottleneck for pollinator access and identify different levels of likelihood for putative pollinators and floral reward microstructures. The methods described by the authors, including sample preparation protocols and detailed codes for geomorphometric analysis, can inspire the further incorporation of geometry and floral reward studies to strengthen plant-pollinator trait-matching models for cacao and other species.

The study by [START_REF] Long | Spatially resolved detection of small molecules from press-dried plant tissue using MALDI imaging[END_REF] also describes advances in sample preparation, addressing the case of using matrixassisted laser desorption/ionization (MALDI) mass spectrometry imaging (MSI) for a variety of plant species. In this technique, which allows the spatial analysis of chemical distribution in a tissue, a laser beam is fired at a matrixcoated sample, transferring energy to the molecules extracted from the tissue. These molecules are then resealed from the surface, ionized, and detected using mass spectrometry. As noted by the authors, each of these steps can present difficulties when analyzing plant samples. Thus, Long and collaborators provide a general procedure for the easy preparation of press-dried samples for analysis by MALDI-MSI without the need for freezing or cryosectioning. Their simple protocol covers all steps of sample preparation, from the drying, delipidation, and application of the MALDI matrix to the parameters used for data acquisition. By analyzing flowers and leaves of plants with a variety of polyphenolic compounds, the authors confirm the wide applicability of the proposed protocol.

A third paper dedicated to improving protocols and sample preparation is provided by [START_REF] Klahs | A maceration technique for soft plant tissue without hazardous chemicals[END_REF] for maceration of soft plant tissues. While a wealth of maceration techniques have been described, most protocols employ hazardous chemicals, thus rendering such methods unsuitable for classrooms. To help solve this issue in a costeffective way, the authors propose a protocol using pectinase as the agent for disrupting the adhesion among the cells of plant tissues. The protocol is shown to be effective in macerating both fresh and herbarium-sampled leaves of different species, including plants with thick cuticle, abundant trichomes, and latex. This method can potentially be applied to a wider variety of species than current methods allow and can be used in both research laboratories and classrooms.

Finally, also focusing on images obtained from leaf samples, [START_REF] Green | How dense can you be? New automatic measures of vein density in angiosperm leaves[END_REF] developed an opensource code suitable for high-throughput automation for measuring the length of leaf veins per area. This measurement has become the standard for comparing leaves with different vein densities and exploring the diversity of patterns expressed by different species. Since its first use, many approaches have attempted to standardize, automate, and facilitate its recording. However, major disagreements remain and to date have not been resolved. In their contribution, the authors propose three alternative new methods for measuring vein density using image analysis, making it possible to improve on current approaches. Each of the solutions presented in this work, and explored on more than 230 angiosperm leaves, has distinct practical, statistical, and biological limitations and advantages. Furthermore, the authors highlight that progress toward a more complete understanding of leaf vein biology requires not only the adoption of improved techniques and the use of advances in microscopy and computational speed, but also a commitment to sharing the original imagery and open-source analytical code generated by researchers.

Together, collection of papers demonstrates some of the innovations in imaging and image analysis in the plant sciences, and we hope that it will stimulate further developments in both image capture and analysis. Connecting novel imaging approaches with machine learning and other AI methods, such as those reported in a previous special issue of APPS ("Machine Learning in Plant Biology"; June and July, 2020), is likely to yield even further advances of the spectacular imaging techniques and pipelines reported here. AUTHOR CONTRIBUTIONS P.S.S. and R.G.N. initiated this special issue, and L.T.-C. and P.B. contributed to its development. In addition to handling editorial duties for the manuscripts in this issue, all authors wrote portions of this article, made comments and suggestions to improve it, and approved the final version of the manuscript.

ACKNOWLEDGMENTS

The authors thank iDigBio (National Science Foundation grant DBI-2027654) for support.


Paolo Ferrari

Marco Cognetti

Giuseppe Oriolo

Sensor-based Whole-Body Planning/Replanning for Humanoid Robots

We propose a sensor-based motion planning/replanning method for a humanoid that must execute a task implicitly requiring locomotion. It is assumed that the environment is unknown and the robot is equipped with a depth sensor. The proposed approach hinges upon three modules that run concurrently: mapping, planning and execution. The mapping module is in charge of incrementally building a 3D environment map during the robot motion, based on the information provided by the depth sensor. The planning module computes future motions of the humanoid, taking into account the geometry of both the environment and the robot. To this end, it uses a 2-stages local motion planner consisting in a randomized CoM movement primitives-based algorithm that allows on-line replanning. Previously planned motions are performed through the execution module. The proposed approach is validated through simulations in V-REP for the humanoid robot NAO.

I. INTRODUCTION

Researchers envision a future where humanoid robots are able to effectively assist or even replace humans in repetitive, tiring and dangerous activities. To achieve such objectives, these robots must be able to plan and execute whole-body motions that avoid collisions, maintain balance, and satisfy all existing kinematic/dynamic constraints. These requirements, together with the typical high-dimensionality of the planning space, make the motion planning problem for humanoid robots very challenging.

Over the last decade, many methods have been proposed to address the above problem in the case of known environment. They range from simple footstep planners (see [START_REF] Perrin | Biped footstep planning[END_REF] for a survey on existing techniques), that only generate isolated contacts with the ground, to full-fledged whole-body planners, that produce task-oriented motions, either relying on some reshaping of the final motion (e.g., [START_REF] Dalibard | Dynamic walking and whole-body motion planning for humanoid robots: an integrated approach[END_REF]), or not easily generalizable to dynamic walking (e.g., [START_REF] Bouyarmane | Humanoid robot locomotion and manipulation step planning[END_REF]).

Differently from these works, in [START_REF] Cognetti | Whole-body motion planning for humanoids based on com movement primitives[END_REF], we introduced a randomized motion planner that, hinging on the concept of CoM movement primitives (representative of typical humanoid actions, such as static walking, dynamic walking, and more), simultaneously generates foot placements and wholebody motions, without the need of any form of reshaping.

Most approaches work off-line, firstly producing a complete plan, whose computation may require high planning times, depending on the scenario complexity, forcing the robot to wait before being able to start moving. To address this problem, in [START_REF] Ferrari | Anytime whole-body planning/replanning for humanoid robots[END_REF], we have proposed an anytime algorithm that interleaves planning and execution intervals: a previously planned partial solution is executed, while a 2-stages local planner simultaneously plans a new solution for the subsequent execution interval. To ensure on-line performance, such local planner firstly builds a tree of CoM movement primitives sequences, performing lazy collision checks (in the spirit of [START_REF] Bohlin | Path planning using lazy prm[END_REF] and [START_REF] Sánchez | A single-query bi-directional probabilistic roadmap planner with lazy collision checking[END_REF]), and then searches the tree to validate a feasible, collision-free whole-body motion.

In this paper we propose a sensor-based whole-body planning framework for the case of unknown environments. This work extends [START_REF] Ferrari | Anytime whole-body planning/replanning for humanoid robots[END_REF], removing the assumption of a priori knowledge of the obstacles geometry. This is a non-trivial extension, since the planning and mapping capabilities are highly interconnected. In fact, in unknown environments, the ability of on-line building a map and accordingly planning collision-free motions is of fundamental importance to allow a robot to fulfill an assigned task. The contribution of this paper consists in a framework that allows a humanoid robot, equipped with a depth sensor, e.g., a Kinect, to incrementally build a map of its surroundings while executing previously planned motions, and simultaneously plan future motions, without any assumption about the environment.

In literature, some methods rely on the idea of monitoring the workspace with off-board, fixed sensors to provide a planner with the positions of the humanoid and obstacles (e.g., [START_REF] Michel | Vision-guided humanoid footstep planning for dynamic environments[END_REF], [START_REF] Baudouin | Real-time replanning using 3d environment for humanoid robot[END_REF]). Off-board sensing requires an appropriate setting that is difficult, or even impossible, in unstructured environments. Thus, on-board sensing is clearly preferable.

To reduce the computational complexity, allowing the robot to plan its motions on-line according to environmental information collected through on-board sensors while moving, the planning problem is often reduced to searching footstep sequences by detecting planar surfaces that define safe regions where the robot can step onto (as in [START_REF] Okada | Autonomous 3d walking system for a humanoid robot based on visual step recognition and 3d foot step planner[END_REF], where binocular stereo-vision is used), or by representing the environment through a heightmap (using data provided by, for example, a monocular on-board camera as in [START_REF] Michel | Gpu-accelerated real-time 3d tracking for humanoid locomotion and stair climbing[END_REF], or a pivoting laser scanner mounted on the humanoid torso as in [START_REF] Chestnutt | Biped navigation in rough environments using on-board sensing[END_REF], [START_REF] Nishiwaki | Autonomous navigation of a humanoid robot over unknown rough terrain using a laser range sensor[END_REF]). Planning only at footsteps level implicitly assumes that collisions occurs only at robot soles, which is not the case for most real-world scenarios.

Only few methods have been proposed that take into account the 3D structure of an unknown environment. Most of them, in order to make the planning problem tractable on-line, rely on simplifying assumptions on either the environment or the robot geometry. For example, in [START_REF] Gutmann | 3d perception and environment map generation for humanoid robot navigation[END_REF] the environment is classified into areas of predefined different types, according to which the robot motions are chosen.

In [START_REF] Nakhaei | Motion planning for humanoid robots in environments modeled by vision[END_REF], instead, a robot bounding box is used to check collisions within a 3D occupancy grid. A more recent work, [START_REF] Maier | Real-time navigation in 3d environments based on depth camera data[END_REF], proposes an approach integrating mapping, planning and localization. It maintains a 3D representation of the environment through an Octomap constructed from depth data, similarly to our work. Nevertheless, collision checks are performed using a floor projection of the 3D map and a circular robot model, impeding the humanoid of passing in narrow passages. The authors extended this work in [START_REF] Maier | Integrated perception, mapping, and footstep planning for humanoid navigation among 3d obstacles[END_REF], where they introduced the concept of inverse heightmaps precomputed for each possible robot action, for checking collisions within a 2.5D maps. This does not allow the robot to perform motions aimed at passing below obstacles.

Differently from these approaches, the sensor-based framework proposed in this paper does not rely on any form of simplification of either the environment or the robot geometry. Instead, to achieve the on-line performances, we leverage on the efficiency of an adaptation of the local motion planner proposed in [START_REF] Ferrari | Anytime whole-body planning/replanning for humanoid robots[END_REF] that checks collisions directly using an incrementally built 3D environment map, and considering the humanoid whole-body structure. Furthermore, our framework does not require any previous knowledge about obstacle positions and shapes.

The rest of the paper is organized as follows. We introduce the planning problem in Sect. II. The proposed approach is presented in Sect. III, hinged on a local motion planner discussed in Sect. IV. V-REP planning experiments for the NAO humanoid robot are illustrated in Sect. V. Conclusions and some future work are discussed in Sect. VI.

II. PROBLEM FORMULATION

In the situation of interest, the humanoid is assigned a loco-manipulation task, i.e., a manipulation task that implicitly requires locomotion. In particular, the robot must bring a specified hand (hence, the end-effector) to a desired setpoint, e.g., for grasping an object that is in general outside the workspace of the humanoid at its initial configuration. Furthermore, the robot acts in an unknown environment and it is equipped with a head-mounted depth camera, e.g., a Kinect, through which it can continuously acquire information about its surroundings while moving. In our framework, an environmental map is firstly created and, then, continuously updated when the sensor acquires new information. The proposed motion planner uses this map in order to generate task-oriented whole-body robot motions that are feasible (in the sense formally described below) in the so far explored area.

Throughout this paper, we assume that the environment is populated only by static obstacles and that the robot can perfectly localize itself with respect to a fixed inertial frame using an external module. Removing these two assumptions is part of our future work (see Sect. VI).

Let q = (q CoM , q jnt ) T be the generic configuration of the humanoid. Here q CoM ∈ SE(3) is the world pose (position and orientation) of a reference frame attached to the Center of Mass (CoM) and q jnt ∈ C jnt is the n-vector of joint angles. The assigned task must be fulfilled through a sequence of whole-body motions q(t), t ∈ [t ini , t fin ], constituted by a succession of on-line planned partial solutions, that satisfies four requirements: R1 The assigned set-point is reached at a finite time t fin . R2 Collisions with workspace obstacles are avoided. R3 Position and velocity limits on the joints are respected. R4 The robot is in static or in dynamic equilibrium at all times.

In the following, we will call feasible the motions that satisfy requirements R2-R4.

III. SENSOR-BASED PLANNING/REPLANNING FRAMEWORK

To address the described problem, we propose a framework constituted by three cooperating modules, namely the mapping, planning, and execution modules, that are in charge of, respectively, incrementally build an environment map, computing on-line feasible whole-body motions, and sending commands to the humanoid actuators.

At the beginning, the mapping module generates a 3D map M(t ini ) according to information that the robot can acquire at its initial configuration q ini . Then, an initial plan constituted by whole-body motions that are feasible within M(t ini ) is computed by the planning module. Once such initial plan is computed, the robot starts performing it, according to the commands sent by the execution module. Then, an interleaved procedure (described below), in which the three modules run in parallel, starts. Hereafter, we refer to the time instant in which the robot starts moving as t 0 .

During the interleaved procedure, the planning module works iteratively with the aim of computing future motions; meanwhile, previously planned motions are performed through the execution module, and the map M is continuously updated by the mapping module according to the newly acquired information. In particular, at any time instant t c , the robot will be in the configuration q(t c ) as specified in the available, previously planned, sequence of feasible wholebody motions q(t), henceforth referred to as the current plan, with t ∈ [t 0 , t]. Thus, such plan will be composed by two portions: the committed part that the robot has already executed in the time interval [t 0 , t c ], and the remaining part that defines the future motions of the robot in the time interval (t c , t].

The objective of each iteration of the planning module is to compute an extension of the current plan that starts at its final configuration q = q( t), at which the robot will be at the associated time instant t, and is feasible according to newly acquired information. To extend the current plan before the robot reaches q, each iteration of the planning module must complete within (at maximum) the remaining time on the current plan. The idea is to repeatedly extend the current plan, each time considering an enlarged environment map, until it allows the robot to complete the assigned task.

In the following we describe separately the three modules.

A. Mapping Module

The mapping module is in charge of continuously integrating information gathered by the depth camera into the environment map M. To take full advantage of the humanoid capabilities in scenarios containing complex shaped obstacles, we maintain the map M in the form of a 3D occupancy grid, which models both free and occupied space, and, at the same time, implicitly models unknown space, just by missing information. This feature is particularly relevant within our planning process, since it allows to produce task-oriented motions (for details, see Sect. IV).

In our framework, the map M is kept as a volumetric octree-based map, called OctoMap, whose characteristics perfectly match the needs described above. This representation compactly models free and occupied areas by voxels, each one containing an occupancy probability that can be dynamically updated. More details about this powerful mapping framework can be found in [START_REF] Hornung | Octomap: An efficient probabilistic 3d mapping framework based on octrees[END_REF], while the software is available as an open-source C++ library at http://octomap.github.io.

At the initial time instant t ini , the map M(t ini ) is

M(t ini ) = R(q ini ) ∪ M 0 (t ini ) (1)
where R(q ini ) represents the free volume that the robot body occupies (computed on the basis of proprioceptive sensors), and M 0 (t ini ) is the initial knowledge at the configuration q ini , that may consist of a limited exogenous knowledge of the starting location, further enlarged by collecting information through, e.g., a pan-tilt motion performed on the spot. The map is then updated while the robot moves in the unknown environment. At each reading, the camera provides a depth image in which each pixel contains the distance between the 3D point in the Cartesian space to which the pixel refers to, and the camera image plane. Such depth image indicates a beam of rays originating in the camera origin and ending at the observed Cartesian points. Given the coordinate z f of the camera far clipping plane on the principal axis, if the depth of a certain pixel is less than z f , the endpoint of the corresponding ray is on the surface of an obstacle. In this case, the voxel corresponding to the endpoint is updated in M as occupied, and all the other voxels along the ray are updated as free; otherwise, all the voxels along the whole ray are updated as free.

B. Planning Module

The planning module generates the whole-body motions that the robot performs through the execution module. As already mentioned, this module firstly generates an initial plan within the initial environment map, and then enters an iterative phase, where extensions of the current plan are computed thanks to the continuously updated map provided by the mapping module described in Sec. III-A.

At the i-th generic iteration, the planning module invokes a specifically designed local motion planner (LMP), described in Sect. IV, that is in charge of producing a whole-body motion (henceforth referred to as a local plan) that starts at the final configuration qi of the current plan q(t), where t ∈ [t 0 , t i ], provides an extension of it for further exploration aimed at completing the task, and is feasible within the currently available map. Such local plan must be computed before the time instant t i . Thus, the LMP is allowed to run for a limited time budget. While such time budget determines the duration of the i-th iteration of the planning module, the duration of the local plan to be computed is not specified, as it is autonomously determined by the LMP. In the following, we denote the duration of the i-th iteration of the planning module, i.e., the time budget given to the LMP at the i-th invocation, by ∆T P,i , and the duration of the local plan that it produces by ∆T E,i .

Let t c be the time instant at the beginning of the ith iteration of the planning module; at the corresponding invocation, the LMP is provided with:

• The planning map M P,i , that coincides with the currently available map M(t c ). The planning map M P,i is then fixed during the i-th replanning, while the map M is continuously updated by the mapping module. • The time budget, that is computed as a portion of the remaining time on the current plan

∆T P,i = α P (t i -t c ) (2)
where α P ∈ (0, 1) is a predefined value. Note that, the larger (smaller) α P , the less (more) frequent the replanning, the more (less) enlarged the planning map M P,i w.r.t. the previous one M P,i-1 . Choosing a large α P potentially allows to find longer local plans. On the other hand, a small α P reflects in a more reactive behavior. The planning module is shown in Algorithm 1. It starts by invoking the LMP that is in charge of producing, within a predefined time budget ∆T P , the first local plan q(t), with t ∈ [t 0 = t ini + ∆T P , t 1 = t 0 + ∆T E,0 ], with ∆T E,0 its duration, starting at the initial robot configuration q ini . This plan is guaranteed to be feasible in the initial map M(t ini ). Once such plan is computed, the robot starts executing it and the planning module waits for a portion α P ∆T E,0 of its duration before entering the iterative phase. The rationale beyond this choice is to avoid an immediate replanning on the same map used to compute the initial plan. In fact, since at this point the robot is not moved yet, the mapping module has not gathered new information about the environment, and replanning would not provide any plan extension.

At the i-th iteration, the planning module computes the time budget ∆T P,i devoted to the current invocation of the LMP according to (2) and retrieves the planning map M P,i as the one currently provided by the mapping module. This invocation of the LMP produces a local plan q i (t), t ∈ [t i , t i+1 = t i + ∆T E,i ], that starts at the final configuration qi of the current plan q(t) and is feasible within the map M P,i . The current plan is then extended by concatenating the computed local plan to it.

This iterative procedure terminates when the LMP computes a local plan such that the desired set-point is definitely reached, i.e., f (q i ) = y * M with f (q i ) the end-effector Algorithm 1: Planning Module 1 ∆TP,0 ← ∆T P ; 2 MP,0 ← M(tc); 3 q(t), t ∈ [t0, t1] ← LMP(q ini , ∆TP,0, MP,0); 4 wait for αP ∆TE,0; 5 extract q1 from q(t); 6 i ← 1; 7 while f (q i ) = y * M do 8 compute time budget ∆TP,i according to (2); 9 MP,i ← M(tc);

10 q i (t), t ∈ [ti, ti+1] ← LMP(q i , ∆TP,i, MP,i); 11 q(t), t ∈ [t0, ti+1] ← concatenate q(t), t ∈ [t0, ti],
and q i (t), t ∈ [ti, ti+1]);

12 i ← i + 1;
13 extract qi from q(t); 14 end position at the last configuration qi of the extended plan. In this case, the planning module stops and the execution module continues until the humanoid completes the task.

C. Execution Module

This module is in charge of sending the joint commands to the robot low level controllers. At each time instant, such commands are all taken from the current plan, except for the robot yaw neck joint that is used to directly control the pan angle of the depth camera, rigidly attached to the head. With the aim of favoring the mapping module in enlarging the environment map in the area where the extension of the current plan has to be computed through the planning module, the yaw neck joint velocity qp is computed on-line in such a way to make the robot looking in the direction of the location that it will reach at the end of the current plan.

At each time instant, the robot yaw neck joint velocity qp is computed using a simple proportional control

qp = K p (q d p -q p ) (3)
where q d p and q p are, respectively, the desired and current yaw joint positions. Given the final configuration q on the current plan and the configuration q specified for the current time instant, q d p is defined as the angle between the robot sagittal axis at q (that can be easily identified through the subvector q CoM ), and the line joining the origins of the CoM frames at q and q. K p is a positive scalar gain.

Note that, when the current plan is extended, its final configuration q changes, and consequently also q d p .

IV. LOCAL MOTION PLANNER (LMP)

In this section, we describe the local motion planner (LMP) that is invoked at each iteration of the planning module. It consists in an adaptation, for the case of unknown environments, of the LMP presented in [START_REF] Ferrari | Anytime whole-body planning/replanning for humanoid robots[END_REF]. Within this planner, humanoid whole-body motions are produced as concatenations of precomputed CoM movements primitives, as firstly introduced in [START_REF] Cognetti | Whole-body motion planning for humanoids based on com movement primitives[END_REF]. The LMP is provided with a catalogue U of N primitives, each one representing an elementary humanoid motion. In general, U will include Procedure 1: LMP(q, ∆T P , M P ) 1 split the time budget ∆TP in two intervals ∆T L P and ∆T V P ; 2 T ← LazyStage(q, ∆T L P , MP ); 3 q(t) ← ValidationStage(T , ∆T V P , MP ); 4 return q(t); basic walking movements, e.g., static and dynamic steps, and possibly more complex ones, e.g., crauching or crawling. A pure manipulation primitive, namely the free CoM, is also included in U . Each primitive, henceforth indicated as u CoM , has an associated duration, and specifies reference CoM and swing foot trajectories for the whole duration 1 .

The LMP, whose pseudocode is provided in Procedure 1, is composed of two consecutive stages, namely lazy and validation stages, amoung which the time budget ∆T P assigned by the planning module to the LMP is split as

∆T L P = α LM P ∆T P , (4)
∆T V P = (1 -α LM P )∆T P , (5)
where α LM P ∈ (0, 1), and serves as a design parameter.

The lazy stage (see Procedure 2) is a RRT-based algorithm that builds a tree T in configuration-time space. To speed up such tree construction, the algorithm performs collision checks lazily, i.e., only at vertexes level by means of a simplified occupancy volume of the robot. In the tree T :

• A vertex v = (q, t) consists of a configuration q, and its associated time instant t. • An edge represents a feasible whole-body motion connecting two adjacent vertexes, produced through a certain CoM primitive u CoM . • A branch of the tree provides a candidate local plan if its ending vertex (i.e., the leaf) is such that one of the these conditions holds: (i) the simplified occupancy volume of the robot at the corresponding configuration q does not completely lie within the map M P ; (ii) it has been generated through the free CoM primitive, i.e., it potentially allows to finalize the assigned task. The tree T is rooted at v 0 = (q, t) , where q is the final configuration on the current plan, and t its associated time instant. At the generic iteration, the algorithm picks a random sample point y rand in the task space, and retrieves its nearest vertex v near = (q near , t k )2 in T using a metric d(•, y rand ) 3 . From the catalogue U a primitive u k CoM is randomly selected. Let T k be its duration. The reference CoM and swing foot trajectories specified by u k CoM determine the reference poses of, respectively, the CoM frame q new CoM and the (new) support foot q new sup (that we do not explicitly include in the vertex Procedure 2: LazyStage(q, ∆T L P , M P )

1 root the tree T at v0 = (q, t); 2 V ← {v0}; for sake of illustration) at the time instant t k+1 = t k + T k , i.e., after applying u k CoM to q near . At this point a collision check is performed within the map M p using a simplified occupancy volume of the robot S(q new ), with q new = (q new CoM , ∅) T (the subvector q jnt is left undefined). In our implementation, we check collisions at footsteps level using the pose q new sup . Other choises, like conservative bounding boxes with pose q new CoM , are also possible. If S(q new ) results collision-free, a new vertex v new = (q new , t k+1 ) is added to T as a child of v near . This iterative procedure stops when the time budget ∆T L P assigned to the lazy stage runs out. At this point, the validation stage (see Procedure 3) is run. With the aim of further approaching the desired set-point, and possibly completing the task, the candidate local plan, among the ones resulting from T , whose ending vertex is the closest to y * M in terms of the metric d(•, y * M ) described above, is chosen for a validation attempt.

Let p * = {v 0 , . . . , v K-1 } be the chosen candidate local plan, with K the number of vertexes along the corresponding branch. The validation attempt consists in generating the whole-body motion between each pair of consecutive vertexes, and checking its feasibility w.r.t. requirements R2-R4.

This procedure proceeds iteratively. At the k-th iteration, the configuration q k = (q k CoM , q k jnt ) T , and the associated time instant t k , are extracted from the vertex v k . If the sub-vector q k jnt is undefined, a motion generator is called to produce the whole-body motion that connects q k-1 to q k through the primitive u k-1

CoM (such information may be stored with the edge at the time of its creation during the lazy stage), i.e., the joint trajectory that realizes the specified CoM and swing foot trajectories in the time interval

[t k-1 , t k = t k-1 + T k-1 ], with T k-1 the duration of u k-1
CoM , and possibly reaches the desired set-point y * M . To this end, the motion generator works by integrating the joint velocities produced by a priorities-based kinematic control law in which the locomotion and manipulation tasks are, respectively, the primary and secondary tasks. The generated joint trajectories are continuously checked for collisions within the map M P using the actual occupancy volume R(q) of the robot Procedure 3: ValidationStage(T , ∆T V P , M P )

1 select the best local plan p * in T ; 2 te ← 0; 3 while p * = ∅ and te ≤ ∆T V P do 4 q(t) ← ∅;

5 k ← 1; 6 while k < K and q k-1 = (∅, ∅) T do 7 extract q k jnt from v k ; 8 if q k jnt = ∅ then 9 [q k , q k-1 q k ] ← MotionGeneration(v k-1 , v k ); 10 if q k = (∅, ∅) T then 11 if q k-1 q k ⊂ MP then 12
update vertex v k with q k and add edge q k-1 q k to T ; 13 q(t) ← append q k-1 q k to q(t); (requirement R2), and for violation of position/velocity joint limits (requirement R3). Static equilibrium is also checked in case u k-1

CoM is free CoM, while for the other primitives, static or dynamic equilibrium is guaranteed by construction (requirement R4). More details about the motion generator can be found in [START_REF] Cognetti | Whole-body motion planning for humanoids based on com movement primitives[END_REF], [START_REF] Ferrari | Anytime whole-body planning/replanning for humanoid robots[END_REF].

In case of no violations in the motion generator, the validation stage proceeds or stops depending on whether the produced whole-body motion q k-1 q k is entirely contained in the map M P , i.e., the actual occupancy volume of the robot R(q) at each configuration q of the latter completely lies in M P (in this case, q k-1 q k is concatened to the portion of the candidate local plan that has been validated so far), or not (in this case, the validated local plan is returned).

In case of violations in the motion generator, the tree T is pruned of the subtree T k rooted at v k , and a new candidate local plan is selected for another validation attempt.

V. PLANNING EXPERIMENTS

The proposed sensor-based framework has been implemented in V-REP on an Intel Core i7 running at 2.70 GHz. The chosen robotic platform is the NAO humanoid robot, and the right hand is employed as end-effector. The robot is equipped with a Kinect camera that provides 320×240 depth images. To maintain the 3D environment map, we use an Octomap with a resolution of 5 cm.

The set of CoM primitives is defined as

U = {free CoM∪ U D CoM }.
Here, free CoM is a non-stepping primitive that allows the CoM to move freely, as long as both feet remain fixed; U D CoM is a subset of dynamic steps extracted from various types of ZMP-based gaits precomputed by the intrinsically stable MPC framework presented in [START_REF] Scianca | Intrinsically stable MPC for humanoid gait generation[END_REF]. In particular, U D CoM includes forward, backward, curved and diagonal steps. In our simulations, we activate the manipulation task only when the robot hand is inside a spherical region centered at the desired set-point y * M , where we allow the choice of the free CoM primitive 4 .

We consider two planning scenarios. In both of them, the robot is assigned the task of grasping a ball placed on a table that is outside its initial workspace. The map M 0 (t ini ) consists of an initial knowledge provided in advance within a cylindrical area of radius 0.5 m and height 1.2 m centered at q CoM (t ini ), and further knowledge acquired through an initial pan-tilt motion, whose duration is 18 s. After this phase, the planning module starts to compute an initial plan within this map through the first invocation of the LMP, with a predefined time budget of ∆T P = 15 s. The parameters α P and α LM P are respectively set to 0.5 and 0.6.

In the first scenario (see Fig. 1), obstacles of different kinds (chairs, tables and sofas) obstruct the path between the robot at the initial configuration, at which only portions of few obstacles can be seen, and the destination. Once the initial partial plan is available, the robot starts to perform it through 4 Planning smoother reaching motions is out of the scope of this paper, although this can be easily accounted in the proposed framework by involving the strategy proposed in [START_REF] Ferrari | Humanoid whole-body planning for loco-manipulation tasks[END_REF]. the execution module, while the planning module computes future motions. At each replanning, previously unknown obstacles are taken into account, and collisions are correctly avoided. The mapping-planning-execution cycle is repeated until the robot grasps the red ball (last snapshot). The overall robot motion (constituted by a sequence of dynamic steps and concluded by the free CoM primitive to finally grasp the ball) results fluid, without the need for the robot to stop in any case. This proves the on-line performances of the proposed framework. Furthermore, we emphasize the capability of our LMP in managing narrow passages. In fact, taking into account the 3D structure of both the environment and the robot, the LMP is able to produce motions allowing the robot to pass, e.g., in the strict free space between the sofa and the chair (third snapshot). Note that, due to the complex shape of the chair, approaches using bounding boxes (e.g., [START_REF] Nakhaei | Motion planning for humanoid robots in environments modeled by vision[END_REF]) or 2D projections of swept volumes (e.g., [START_REF] Maier | Integrated perception, mapping, and footstep planning for humanoid navigation among 3d obstacles[END_REF]) to check collisions would fail to find a feasible plan in this case.

In the second scenario (see Fig. 2), we show the capability of the proposed framework of recovering from dead-ends. At its initial configuration (first snapshot), the robot cannot see the wall obstructing the straight path to the destination, as it is outside the initial camera field of view. Among all the candidate local plans bringing towards unexplored areas, the LMP chooses, and validates, the one that allows the robot to approach as much as possible the destination. This local plan leads the robot to proceed ahead the wall, entering a dead-end (second snapshot), that is incrementally discovered through the mapping module while walking. Once the deadend is included in the new map, the LMP generates an extension of the current plan that allows the robot to exit the closed space and to proceed towards the free boundary of the map (third and fourth snapshots). We emphasize that such effective behaviour is the result of the intrinsic bias towards unexplored areas of the proposed planner. Once the robot is outside the dead-end, it proceeds towards the destination, appropriately planning its motions according to continuously acquired information. Also in this case, the task is completed by pure manipulation.

Table I collects, for the three scenarios, some performance data of the planning module. The experiments have required, respectively, four, and ten invocations of the LMP. For each invocation, the table reports: the assigned time budget, the number of candidate plans produced by the lazy stage, and the duration of the generated extension of the current plan. Note that, in the second scenario, in two cases the LMP returned no extension of the current plan. This means that, among the candidate local plans produced by the lazy stage, the best one consists in a branch of the tree such that only the configuration in the root vertex is inside the current map. This automatically postpones the extension of the current plan to the subsequent LMP invocation, which will work with a new time budget computed as in eq. ( 2) within a new map that has been updated during the robot motion. We encourage the reader to see the accompanying video to better appreciate the effectiveness of the generated motions.

VI. CONCLUSIONS

In this paper, we proposed a sensor-based framework for humanoids aiming at fulfilling tasks that implicitly require locomotion. The planner is hinged on three cooperating, highly interconnected modules: mapping, planning and execution modules. The mapping module is in charge of building and updating a 3D environment map during the robot motion. While the execution module sends the commands to the humanoid actuators based on previously planned whole-body motions, the planning module on-line computes future plans using a local motion planner that takes into account newly acquired information. Its 2-stages design allows for rapid replanning and proved to be particularly suitable for online application. V-REP simulations with the NAO humanoid have shown the ability of the proposed framework to generate fluid robot motions, without the need for the robot to stop and plan. Furthermore, thanks to the fact that our framework considers the 3D structure of both the environment and the robot, narrow passages are correctly negotiated.

Our current research focuses on removing the static environment and perfect robot localization assumptions mentioned in Sect. II by, respectively, equipping the robot with the possibility of replanning also when a moving obstacle invalidates the current plan, and substituting the mapping module with a full-fledged SLAM module, providing the robot with full autonomy. Other possible extensions of this work will include the design of strategies for on-line generating movement primitives according to the planning needs, e.g., for managing uneven grounds and tasks that require mobile manipulation of heavy objects.

  T k rooted at v k from T ; local plan p * in T ; 24 te ← get the elapsed time; 25 end 26 return ∅;

Fig. 1 .

 1 Fig. 1. Planning scenario 1: snapshots from a solution.

Fig. 2 .

 2 Fig. 2. Planning scenario 2: snapshots from a solution.

TABLE I PLANNER

 I PERFORMANCE DATA.

Dipartimento di Ingegneria Informatica, Automatica e Gestionale, Sapienza Universita di Roma, via Ariosto

25, 00185 Roma, Italy. E-mail: {ferrari, oriolo}@diag.uniroma1.it.2 CNRS, Univ Rennes, Inria, IRISA, Rennes, France, E-mail: marco.cognetti@irisa.fr.This work is supported by the EU H2020 COMANOID project.

This is true for all primitives, except for free CoM, as it does not provide any reference CoM trajectory, leaving it to freely move while maintaning both feet fixed on the ground.

Selection of ending vertexes of already existing candidate local plans is carefully avoided as their expansion does not produce any new local plan.

In our implementation, the metric d(q, y), that measures the distance between a configuration q and a point y in the task space, is defined as the Euclidean distance between the ground projections of the robot CoM positions at q and y.