Xiaotong Zhan

Sabine Michaud-Chevallier

Damien Heŕault

Francoise Duprat

On-Line Analysis of the Heterogeneous Pd-Catalyzed Transfer Hydrogenation of p-Nitrophenol in Water with Formic Acid in a Flow Reactor

Keywords: fixed-bed reactor, dynamic study, reaction intermediates, transfer hydrogenation mechanism

An versatile experimental setup composed of a fixed-bed reactor and an HPLC apparatus has been developed for the study of heterogeneous catalytic reactions under transient conditions. The transfer hydrogen reaction of formic acid in water to give p-nitrophenol catalyzed by Pd@Al 2 O 3 support was chosen as the model reaction in a flow reactor. On one hand, this setup allowed the first experimental on-line measurements of p-aminophenol in an acidic medium, indicating that it is the only product of the reaction at steady state. On the other hand, the setup evidenced a quite long transient period before stationary conditions were reached, involving a transient component that is quite instable and can transform to p-aminophenol without a catalyst. Results of numerical simulations indicate that only a change in the reaction mechanism, due to a change in the catalyst activity after few minutes of reaction, can explain the transient production of this intermediate and that this occurs when the active hydrogen coverage of the catalyst is low.

■ INTRODUCTION

The use of a flow reactor as a lab tool either for optimization of reaction conditions or for determination of the rate equation implies frequent changes in operating conditions. [START_REF] Mason | Greener Approaches to Organic Synthesis Using Microreactor Technology[END_REF] Therefore, the period between experiment startup and achievement of the steady state is important to control in order to minimize the optimization period. In the case of heterogeneous catalysis, adsorption on the catalyst support can lead to an accumulation of reactant within the reactor. [START_REF] Tanimu | Heterogeneous Catalysis in Continuous Flow Microreactors: A Review of Methods and Applications[END_REF] Thus, the time to achieve the steady state may be much longer than the liquid residence time (calculated as the fluid volume divided by the flow rate). Online analysis of the reactor effluent may be useful to assess the impact of a change in operating conditions on the extent of the reaction. In addition, in the case of complex reactions, individual quantification of reactants and products flowing out of the reactor may be necessary. Here we present a polyvalent combination of a flow reactor and a UHPLC device that allows either on-line UV-vis continuous analysis or online chromatographic analysis of the reaction mixture at both the entrance and outlet of the reactor. The transfer hydrogenation of p-nitrophenol (1) with formic acid (FA) as the hydrogen source is a perfect reaction to exemplify interest in on-line analysis from both the academic and industrial points of view. [START_REF] Formenti | Reduction of Nitro Compounds Using 3d-Non-Noble Metal Catalysts[END_REF] Actually, although it is considered to be simple because aminophenol is usually the only product, the reaction may proceed via two reaction routes, the direct one and the condensation one, and involves several intermediate species, among them hydroxylamine 4, which can accumulate on the oxide catalyst support (Figure 1). [START_REF] Blaser | Basic Concepts and Recent Advances in Nitrophenol Reduction by Gold-and Other Transition Metal Nanoparticles[END_REF] In addition, transfer hydrogenation of nitroarenes with NaBH 4 as the hydrogen source has been widely utilized as a model reaction to check the catalytic activity of heterogeneous catalysts because of analysis facility. 5 Actually, under the large stochiometric excess of NaBH 4 usually employed, the extent of reaction can be easily monitored by UV-vis spectroscopy because of the strong absorption of 4-nitrophenolate ions at 400 nm and the distinct band of 4-aminophenol (2) at 300 nm. 5b-k,m However, under the acidic conditions used by Javaid and Suzuki, the maximum absorbances of 1 and 2 both shift slightly with variation of the pH. [START_REF] Javaid | Simple and Rapid Hydrogenation of p-Nitrophenol with Aqueous Formic Acid in Catalytic Flow Reactors[END_REF] Therefore, UV monitoring of the reaction mixture gives only a not very accurate evaluation of the consumption of 1.

Aniline derivatives are important building blocks in the synthesis of pharmaceuticals, agricultural chemicals, and other fine chemicals. [START_REF] Corma | Chemoselective Hydrogenation of Nitro Compounds with Supported Gold Catalysts[END_REF] The reduction of 1 to 2 is the main route for the production of paracetamol (N-acetyl-4-aminophenol) in Asia. [START_REF] Joncour | Preparation of Para -Aminophenol from Nitrobenzene through Bamberger Rearrangement Using a Mixture of Heterogeneous and Homogeneous Acid Catalysts[END_REF] The reaction is considered to be a useful transformation both in the pharmaceutical industry and in the pollutantremediation field, as 1 is a toxic byproduct of pesticide and dye production. Industrial production involves direct catalytic hydrogenation with H 2 at relatively high pressure and temperature. Recently it has been demonstrated that FA can be used as a hydrogen source for the transfer hydrogenation of nitroarenes, 9 notably for the reduction of 1 in aqueous media on palladium-coated tubes. [START_REF] Javaid | Simple and Rapid Hydrogenation of p-Nitrophenol with Aqueous Formic Acid in Catalytic Flow Reactors[END_REF] A fundamental study of hydrogen generation from formic acid decomposition on the (211) faces of Ni, Pd, and Pt showed that FA adsorption is an exothermic and thermodynamically favorable process. Formate dissociation into CO 2 and surface H, which is the rate-determining step, depends on the face concerned and is exothermic on Pd(211) and Pt(211). [START_REF] Luo | Hydrogen Generation from Formic Acid Decomposition on Ni[END_REF] FA is inexpensive, easily handled, and abundantly available. Thus, from an industrial point of view, catalytic transfer hydrogenation of nitroarenes with FA provides an efficient and environmentally benign alternative to the reduction with H 2 . Beller and co-workers indicated that FA deactivates non-noble metal catalysts through corrosion or leaching problems. [START_REF] Formenti | Reduction of Nitro Compounds Using 3d-Non-Noble Metal Catalysts[END_REF] Therefore, except for a study based on Au, 9d most of catalysts involved in transfer hydrogenation of nitroarenes with FA are Pd-based. Their activity is excellent under soft conditions (aqueous phase, 30-50 °C). [START_REF] Javaid | Simple and Rapid Hydrogenation of p-Nitrophenol with Aqueous Formic Acid in Catalytic Flow Reactors[END_REF][START_REF] Li | Photochemically Engineering the Metal-Semiconductor Interface for Room-Temperature Transfer Hydrogenation of Nitroarenes with Formic Acid[END_REF] Actually, a turnover frequency (TOF) of around 320 h -1 was obtained in a tubular reactor wall-coated with porous PdO 6 and a TOF of about 1000 h -1 on a photoinduced Pd/CN catalyst. 9e The present study deals with the transfer hydrogenation of p-nitrophenol with aqueous FA catalyzed by Pd@Al 2 O 3 in a flow reactor. A versatile experimental setup composed of a catalytic flow reactor and standard HPLC equipment was developed for this purpose. As we observed an unexpected transient component in the reaction mixture, an extensive bibliographic study of the mechanism of transfer hydrogenation of nitroarene is first summarized. Then spectroscopic and chromatographic experimental results related to the transient period until achievement of the steady state are presented and compared with patterns of the time evolution of concentrations obtained by numerical simulation. The last part is devoted to attempts to identify the transient component.

■ TRANSFER HYDROGENATION OF NITROARENES

In a large review of selective catalytic hydrogenation of nitroarenes, Zou and co-workers analyzed the mechanisms of both activation of the nitro group and production of active hydrogen species. [START_REF] Song | Review on Selective Hydrogenation of Nitroarene by Catalytic, Photocatalytic and Electrocatalytic Reactions[END_REF] The reaction mechanism for the catalytic hydrogenation of nitrobenzene, proposed by Haber et al. more than 100 years ago, is generally accepted to describe how the transfer hydrogenation proceeds. Haber's mechanism involves a direct route and a condensation route (Figure 1, adapted for 1).

Byproducts or intermediates are rarely detected in the reaction mixture, and the amine is practically the only observable product of the reaction. Several kinetic studies involving different metal nanoparticles as catalysts supposed that both reactants (the hydrogen donor and the nitroarene) must be adsorbed on the catalyst to react. 5e,f Experimental evidence was provided by Corma and co-workers, who realized the reaction in a FTIR cell and showed that the nitroso and hydroxylamine react before desorption and that the last step leading to the amine is the rate-determining step. [START_REF] Corma | A Different Reaction Pathway for the Reduction of Aromatic Nitro Compounds on Gold Catalysts[END_REF] This was also evidenced by the fact that the reaction rates of nitrobenzene and hydroxylaminobenzene with aniline are comparable. [START_REF] Figueras | Hydrogenation and Hydrogenolysis of Nitro-, Nitroso-, Azo-, Azoxy-and Other Nitrogen-Containing Compounds on Palladium[END_REF] In some cases, with Pt-based catalysts, accumulation of hydroxylamine was reported. [START_REF] Formenti | Reduction of Nitro Compounds Using 3d-Non-Noble Metal Catalysts[END_REF] Hydrogenation reactions of intermediates of the reaction give a more complex picture than Haber' mechanism. Jackson and co-workers compared the isotope effect of H 2 and D 2 and observed opposite effects on nitro-and nitrosobenzene. [START_REF] Gelder | The Hydrogenation of Nitrobenzene to Aniline: A New Mechanism[END_REF] In addition, the reaction rate of nitrosobenzene was 5 times lower than that of nitrobenzene and led to an azobenzene/aniline mixture, contrarily to nitrobenzene. The authors also proposed the formation of 4-hydroxylaminobenzene radical (8) as the key intermediate (Figure 2).

Corma and co-workers [START_REF] Corma | A Different Reaction Pathway for the Reduction of Aromatic Nitro Compounds on Gold Catalysts[END_REF] observed a similar trend: the formation of hydroxylamine is faster starting from nitrobenzene than from nitrosobenzene. They also concluded that there are two parallel routes in the direct pathway of hydrogenation: formation of phenylhydroxylamine is both a primary product (from nitrobenzene) and a secondary product (via nitrosobenzene). Theoretical considerations gave interesting insight into the reaction mechanism and could explain the previous observations. According to density functional theory calculations by Cao and co-workers, the reaction route could be influenced by the nitro group adsorption configuration: weak adsorption of NO 2 is stabilized by interaction of the aromatic ring with the catalyst, resulting in flat adsorption that makes hydrogenation easier, leading to production of the amine via the direct pathway. [START_REF] Zhang | Insights into Different Products of Nitrosobenzene and Nitrobenzene Hydrogenation on Pd(111) under Realistic Reaction Conditions[END_REF] By contrast, strong binding of the NO group leads to vertical adsorption, which is more favorable toward the formation of the azoxy compound. Two other species have been proposed as intermediates in the direct route. Ebitani and co-workers suggested that the transformation of the nitro group to the hydroxylamine could go through -N + (OH) 2 H species 10. 9c Moreover, several authors cited p-benzoquinone imine (9) as an intermediate between the hydroxylamine and amino derivatives (Figure 2). 5i,17,18 9 has been clearly identified as a product of electrochemical reduction of 1, 19 but it is also involved in the oxidation of 2 according to Conant and Pratt. [START_REF] Conant | The Irreversible Oxidation Of Organic Compounds I. The Oxidation Of Aminophenols By Reagents Of Definite Potential[END_REF] In acidic media, 9 irreversibly forms a highly colored product in the presence of 2. More recently, Lerner identified the structure of this purple dye formed by oxidation of 2 in acidic media: two different adducts reflect the UV absorption bands of the dye at 380 and 550 nm. [START_REF] Lerner | Identity of a Purple Dye Formed by Peroxidic Oxidation of p-Aminophenol at Low pH[END_REF] Moreover, the formation of the 380 nm chromogen should be accompanied by the formation of an equivalent amount of 2. The components involved in the condensation route, such as azo or azoxy, have been evidenced in several studies, and the selectivity toward one or the other route can even be modulated. 3,5h,9d,12,22 Figueras and Coq considered that coupling of the nitroso and hydroxylamine occurs as a fast homogeneous side reaction. At least, condensation means bimolecular nitroso/hydroxylamine interactions. [START_REF] Figueras | Hydrogenation and Hydrogenolysis of Nitro-, Nitroso-, Azo-, Azoxy-and Other Nitrogen-Containing Compounds on Palladium[END_REF] This contact could be favored either by high concentrations or by weak adsorption allowing mobility of the adsorbed species. Actually, Uberman and co-workers observed that the ratio amine/azoxy is reversed by a change in the amount of catalyst or hydrogen donor, the condensation route being favored by a deficit of these species. 5l According to Corma, who evidenced the formation of adsorbed intermediates by IR spectroscopy, the support may influence the reaction pathway: the direct route was clearly observed on Au@TiO 2 and the condensation route on a ceria support because of the higher concentration of adsorbed nitroso. [START_REF] Serna | Transforming Nano Metal Nonselective Particulates into Chemoselective Catalysts for Hydrogenation of Substituted Nitrobenzenes[END_REF] By contrast, changes in the reaction pathways depending on different amounts of copper in the gold nanoparticles were ascribed by Zhu 5h to weaker adsorption of the nitroarene on Au, favoring the mobility. To the best of our knowledge, only the direct route has been considered in investigations of the transfer hydrogenation with FA on Pd catalysts, which have an excellent activity at temperatures close to ambient. It should be mentioned that at higher temperatures (80-120 °C), FA acts as both a hydrogen donor and formylating agent and allows direct synthesis of Narylformamides, which are valuable intermediates in the synthesis of pharmaceuticals, agrochemicals, dyes, and fragrances. 24 In the presence of a heterogeneous noble metal catalyst, the reactions are quite slow (12-24 h), but with aqueous Pd(TFA) 2 , Lei and co-workers reported yields of 92-99% within less than 30 min. 24d ■ DYNAMIC STUDY OF CATALYTIC p-NITROPHENOL HYDROGENATION Figure 3 exhibits a typical spectrum obtained during the experimental protocol with on-line UV analysis (see Figure S1 for the experimental setup). The 3D (time-wavelengthintensity) representation is presented on the left, and on the right the UV analysis at different wavelengths is shown. It is worth noting that the peak with a strong intensity at 250 nm is unexpected and is due to the transient presence of an unknown product called X. Further experiments showed that this peak is not an artifact and that corresponds to a real component that is neither 1 nor 2. The ridge behind the figure, at 360 nm, corresponds to the profile of 1.

The left panel of Figure 4 shows the concentration profiles of 1 and 2 measured by on-line HLPC and confirms the UV profile of 1 in Figure 3. 1 flows out of the reactor very quickly, indicating quite poor adsorption of 1 on the catalyst when FA is present. The concentration of 1 exhibits a shoulder and then stabilizes; meanwhile the concentration of 2 slowly increases and reaches the stationary value after a longer time than for 1. The left panel of Figure 4 also compares the measurements of the concentration of 2, one directly at the exit of the reactor (on-line HPLC; see p S3, protocol B in the Supporting Information) and the other after a delay due to off-line HPLC (p S3, protocol A in the Supporting Information): in the first part of the reaction sequence, i.e., between 10-30 min, approximately when X flows out the reactor, the off-line concentration of 2 is significantly higher than the on-line one, while this difference is very small for 1 concentrations. This suggests a transformation of X into 2 during the off-line analysis preparation.

The deviation between the quantity of input reactant and output products is calculated as

(C 1 + C 2 -C 1 0 )/C 1 0 , where C 1 0
is the concentration in the reactor feed and C 1 and C 2 are the concentrations of 1 and 2 at the exit at the time on run under consideration. It can be seen in the right panel of Figure 4 that the deviation of the material balance is low when the steady state is reached. This average deviation over a set of 56 experiments is -4.0%, which can be considered to be in the experimental error range. Thus, within the measurement precision, the concentration of 2 produced is equal to that of 1 reacted, i.e., 2 is the only product of the hydrogenation of 1.

On the contrary, during the period corresponding to the exit of X, the difference between the input and output is up to 33%, and this difference is lower (10%) when there is a delay between output and analysis. This means that the reaction mixture contains at least one intermediate species able to be transformed in 2 without catalyst. Moreover, the observation of X flowing out of the reactor for a while, clearly indicates a change of the reaction pathway. Indeed, at the beginning of the reaction sequence, X is formed on the catalyst in sufficient amount to appear out of the reactor, and, after a certain time on stream, X is no more formed. Different experiments were performed with UV photodiode array (PDA) on-line analysis in order to relate the peak observed at 250 nm to the experimental conditions (see p 2 in the SI). Its shape and intensity depend on the history of the catalyst. In a series of tests with different washing temperatures and the same reaction conditions, it was observed that the peak intensity depends on the time elapsed between the washing sequence and the reaction sequence (see Figures S2-S4). As a first conclusion, the production of X is clearly related to the state of the surface of the catalyst, which is the only parameter that was not changed in the experiments. The X species is no longer formed as soon as enough FA has been introduced, and it is desorbed in order to promote a faster reaction route on the catalytic site.

■ NUMERICAL SIMULATION OF THE REACTOR Numerical simulation of the reactor was performed in order to understand what kind of reaction pattern can produce a transient component in a continuous flow reactor. As only partial quantitative information about the composition of the reaction mixture flowing out of the reactor is available, the simplest model is investigated: an ideal plug-flow model, which is well-suited to fixed-bed catalytic reactors and first-order kinetics. In an ideal plug-flow reactor, the composition of the fluid varies from point to point along the flow path. As the catalyst bed is washed with water between each test, the start of the reaction sequence results in step perturbation at the entrance of the reactor: at first, the catalyst is under pure water, and then at time 0 the reactant mixture is fed at a constant flow rate and composition and reacts in the reactor according to the time evolved since its entrance. As a result, at the early stage, both the composition of the fluid and composition on the catalyst surface vary all along the catalyst bed and with time.

Hence, the non-steady-state mass balance over a differential volume of catalyst dV CAT during an elementary time interval dt must be considered for every component J:

Q C V r C t q t 1 J CAT J J J ε ε -• ∂ ∂ = + - ∂ ∂ + ∂ ∂ (1)
where C J is the molar concentration of component J in the liquid phase within the reactor, q J is the molar concentration of J adsorbed on the catalyst surface, Q is the volumetric flow rate, r J is the rate of reaction of component J per unit catalyst volume, and ε is the void fraction in the catalyst bed. The boundary conditions are C J = q J = 0 within the reactor at t = 0 and C 1 = C 1 0 at the reactor entrance for t > 0. Two models of the reaction scheme were studied: one involving an intermediate species in a series of reactions and the other involving a change in the route of reaction due to a change in the surface (see section 3 in the Supporting Information). It appeared that the reaction-in-series model is not able to mimic the observations. The model with a change in the catalyst surface properties is more satisfactory because it roughly represents the pattern of experimental results. As indicated by the effect of the change in the FA/1 ratio on the peak of X, the change in surface properties could be due to decomposition of FA on the catalyst surface and active H adsorption on Pd or the Al 2 O 3 support. Changes in the early time of transfer hydrogenation of nitroarenes have already been reported in the literature. Ebitani and co-workers 9c attributed the color change of the catalyst within a few minutes of reaction to the in situ reduction of Pd(II) to Pd(0) by formic acid, while Ballauf's group 5e-g related the short initial delay in which no reaction takes place to a rearrangement of the surface atoms. These induction periods were not accompanied by a change in selectivity. However, in a study involving 2-propanol as the hydrogen donor and an iridiumbased homogeneous catalyst, Chen and co-workers observed that the direct route and condensation route coexist for a while, and then the azo derivative slowly converts into aniline over a long period of time. [START_REF] Chen | Iridium-Catalyzed Transfer Hydrogenation of Nitroarenes to Anilines[END_REF] ■ ATTEMPTS TO IDENTIFY THE INTERMEDIATE PRODUCT X Various attempts were made to identify the nature of X. At first, since the UV spectrum of X has a huge absorption band around 250 nm, intermediates involved in the mechanism of hydrogen transfer of nitroarenes that exhibit such a band were

The intermediates of the direct route are p-nitrosophenol ( 3) and p-hydroxylaminophenol (4). 3 is a commercial product and has a strong absorption band at 300 nm. The condensation route involves 4,4′-azoxydiphenol ( 5), 4,4′-azodiphenol ( 6), and 4,4′-hydrazobisphenol ( 7) (Figure 1). We succeeded in synthesizing 6 by modifying a method described in the literature, [START_REF] Li | Photochemically Engineering the Metal-Semiconductor Interface for Room-Temperature Transfer Hydrogenation of Nitroarenes with Formic Acid[END_REF] and its maximum absorption band is around 360 nm. In addition, according to Lerner, 21 pbenzoquinone imine (9) or its adducts identified as purple dyes could be formed in the reaction mixture, but 9 is not stable enough to be isolated. [START_REF] Lerner | Identity of a Purple Dye Formed by Peroxidic Oxidation of p-Aminophenol at Low pH[END_REF] We also failed to synthesize the other intermediates 4, 5, and 7. The formylated product, N-(4hydroxyphenyl)formamide ( 12), was also synthesized for comparison and has a medium absorption band at 246 nm. [START_REF] Hosseini-Sarvari | ZnO as a New Catalyst for N-Formylation of Amines under Solvent-Free Conditions[END_REF] Thus, by comparison of the UV spectra, X is none of the prepared compounds 3, 4, 6, or 12.

In further experiments, NMR spectra and mass spectrometry (MS, ES+) patterns of mixtures rich in X were analyzed (Figures S8-S14). For this purpose, samples taken at the outlet of the reactor were collected at regular time intervals over 2 min, while the composition of the reactor effluent was monitored with the on-line UV PDA. As can be seen in Figure 5, the curve of X reaches its maximum in the sample taken at 25 min after the beginning of the reaction sequence.

First of all, we look for peaks whose UV intensity is the highest in the sample taken at 25 min, in which the concentration of X should be the maximum. Then we look for peaks whose intensity varies significantly from the feed, which are shown in Figure 6. As expected, the intensity of m/z 140 fragment peaks, corresponding to 1, are lower at the exit of the reactor than in the reactor feed. One other peak, with m/z 124, exhibits the same trend. It could correspond to ionization of 3 (molar mass = 123 g/mol) and is also present in the feed analysis. Thus, it is possibly produced both during MS analysis and as an intermediate of the reaction. Only two m/z values are significantly higher after reaction than in the feed: m/z 110, corresponding to the ionization of 2, as expected, and m/z 108, which could be ionized 9 (107 g/mol). 2 increases after a delay, as observed by HPLC. According to Lerner [START_REF] Lerner | Identity of a Purple Dye Formed by Peroxidic Oxidation of p-Aminophenol at Low pH[END_REF] and Parida, [START_REF] Rana | A Simple and Efficient Protocol Using Palladium Based Lacunary Phosphotungstate Supported Mesoporous Silica towards Hydrogenation of P-Nitrophenol to p-Aminophenol at Room Temperature[END_REF] 9 could be formed from 2 or 4 in the reaction mixture and could also come from decomposition of X during the time elapsed between sampling and MS analysis. However, the sample collected at t = 25 min, which should contain the highest concentration of X, does not exhibit any intense peak.

A similar experiment was carried out with D 2 O as the solvent so that the samples could be analyzed by 1 H NMR spectroscopy. As shown in Figure 7, in the sample containing the highest X concentration, 1, 2, and FA are well-identified. There are several additional small peaks with δ between 6.89 and 7.22 that could correspond to X. The reproducibility of these peaks was verified by repeating the same experiment. They do not match with the 1 H NMR spectra of 3 or 6, but they could correspond to 12.

As we failed to undoubtedly analyze X by NMR spectroscopy or MS, we tried to observe it with on-line HPLC analysis. Figure 8 shows the series of chromatograms measured directly at the exit of the reactor during a reaction sequence. At the time corresponding to the maximum X concentration, a small HPLC peak (red, RT = 3.10 min), attributed to the intermediate X, appears between the peaks for 1 and 2 and then disappears in the following chromatograms.

This peak was not detected with off-line HPLC, which involves a step of collection of samples, i.e., a delay between reaction and analysis. With NMR spectroscopy as well as with MS, the signal that could be attributed to X is very weak and therefore difficult to analyze with accuracy. This could indicate that the intermediate X is quite unstable. Thus, the stability of X was evaluated in the following experiment: A normal flow reaction sequence was started, and the reactor effluent was continuously monitored with on-line UV spectroscopy. The pump was stopped when X reached its maximum. Thus, the spectra of the reaction mixture remaining in the UV cell were recorded until the stabilization. Figure 9 shows that intensity at 250 nm decreases rapidly, which clearly demonstrates the instability of X, with a half-life of about 3 min. This is the reason why only traces of X are detected by methods involving a delay between reaction and analysis. In addition, it was observed that the mixture composition at the end of this experiment was composed of 2 and unreacted 1 only, in quite the same amounts as in the mixture obtained at the steady state of the flow reaction. This confirms that X may react with FA out of the reactor to be transformed in 2 (see p S19 in the Supporting Information). Control experiments with the reaction of 2 alone or in the presence of FA (3 equiv) in the presence of the catalyst demonstrated its stability.

Additional UV-spectra calculations of possible intermediates 4-9, 10′, and 11 were realized (Figure 10 and pp S20-S22 in the Supporting Information). Among them, the simulation of 8′ and 9 exhibits a strong absorption band around 250 nm.

Moreover, components of the same molecular weight were detected by mass spectrometry. Therefore, as mentioned in previous studies, 5i,15,17,18 they could correspond to unstable X.

To sum up, it was observed that the reaction may proceed according to at least two competitive reaction paths (Figure 11), one of them involving a transient unstable component that is observable by on-line UV, which we have called X. The route via X formation is favored at the beginning of the reaction sequence and promoted by the deficit of FA. As soon as the catalyst equilibrates with the reaction mixture, the X route becomes less favored, to the release of X out of the reactor. Comparison of different reaction schemes by numerical simulation indicated that the change in the prevalence of the routes must be related to a change in catalyst reactivity. This change is most probably due to the production of active hydrogen on the catalyst. The structure of X was not strictly elucidated. It was only shown that it is not the nitroso, azo, or formamide derivative. The strong UV absorbance suggests several π-conjugated electrons, which could correspond to 8′ or 9. It was also observed that X transforms to 2 without catalyst. 9 closely fits the observations. According to the literature, 2 oxidizes easily to 9, and this reaction is reversible in a redox medium. 5a,17,18,26 Thus, at the beginning of the reaction sequence, the first molecules of 2 formed could transform to 9, giving two hydrogen atoms, until the active hydrogen concentration on the catalyst is in equilibrium with the FA concentration. After that, the reduction of 9 to 2 becomes dominant, and 9 is no longer formed. It can be noted that in this reaction scheme, X results in a successive reversible reaction and is not involved in the classical mechanism of hydrogenation of nitroarene. 8′ could also correspond to X. It has been postulated [START_REF] Zhang | Insights into Different Products of Nitrosobenzene and Nitrobenzene Hydrogenation on Pd(111) under Realistic Reaction Conditions[END_REF] that it can react with itself to produce 5 with elimination of water without the assistance of any catalyst. However, 5 has not been observed outside of the reactor.

■ CONCLUSION

The experimental setup combining a catalytic fixed-bed microreactor, a photodiode array detector, and an HPLC device has been shown to be particularly useful in the study of complex reactions such as transfer hydrogenation of 1 with FA. With on-line HPLC analysis, the quantitative analysis of both 1 and 2 can be realized, and therefore, the time-concentration profile of these components can be obtained in aqueous acidic media, which has not been done previously. The simultaneous quantification of 1 and 2 indicates that within the experimental error range, 2 is the only product of the reaction at steady state. On-line UV analysis highlights the observable transient production of a quite unstable intermediate species, X, characterized by a strong absorbance at 250 nm. These experimental observations, associated with comparison of two reaction schemes by numerical simulation, allowed the X transient formation to be related to a change in the active hydrogen coverage of the catalyst. Additional UV-spectra calculations support the proposition of a new mechanism in the transfer hydrogenation of 1 to 2 involving 8′ or 9 not as a reaction intermediate but as a successive byproduct.

The usefulness of the experimental setup should be emphasized because only the dynamic study of the reaction under transient conditions, coupled with 3D on-line UV analysis, allowed the clear observation of the formation of the transient component X and its possible identification as 8′ or 9. Knowing the complexity of this reaction, further kinetic studies will be realized on various oxide supports in order to compare their effects on the reaction pathways.

Figure 1 .

 1 Figure 1. Proposed mechanism for the hydrogenation of p-nitrophenol with formic acid on a Pd catalyst (adapted from Blaser 4 for p-nitrophenol).

Figure 2 .

 2 Figure 2. Plausible intermediates described in the literature.

Figure 3 .

 3 Figure 3. Example UV analysis during a reaction test. (left) 3D (time-wavelength-intensity) representation: (A) reactor feed; (B) reactor effluent. (right) 2D (time-intensity) plot. Conditions: C 1 0 = 0.4 mmol/L; C FA 0 = 1.2 mmol/L; T = 40 °C; Q = 0.5 mL/min.

Figure 4 .

 4 Figure 4. (left) Concentration profiles measured by HPLC analysis: □ , 1 on-line; ×, 1 off-line; •, 2 on-line; ○, 2 off-line. (right) Corresponding deviations of the mass balance: •, on-line analysis; ○, off-line analysis. Conditions: C 1 0 = 0.6 mmol/L; C FA 0 = 1.8 mmol/L; T = 40 °C; Q = 1 mL/ min; steady-state 1 conversion rate = 0.69.

Figure 5 .

 5 Figure 5. UV profiles of samples collected at different reaction times and then analyzed by MS and 1 H NMR spectroscopy. Conditions: C 1 0

Figure 6 .

 6 Figure 6. Intensity of the MS peaks of samples taken in the feed mixture (points at t = 0) and at the outlet of the reactor at different times (ES+ mode): ■ , m/z 140 (1); •, m/z 110 (2); ×, m/z 124; △, m/z 108.

Figure 7 .

 7 Figure 7. 1 H NMR spectrum of the sample containing X. Conditions: C 1 0 = 0.5 mmol/L; C FA 0 = 3 mmol/L; Q = 0.5 mL/min; T = 25 °C.

Figure 8 .

 8 Figure 8. Investigation with on-line HPLC analysis of the reactor effluent. Conditions: C 1 0 = 0.6 mmol/L; C FA 0 = 1.8 mmol/L; Q = 1 mL/min; T = 40 °C.

Figure 9 .

 9 Figure 9. Evaluation of the stability of X in the UV cell. The intensity at 250 nm is shown as a function of time. Conditions: C 1 0 = 0.6 mmol/ L; C FA 0 = 1.8 mmol/L; T = 40 °C; Q = 1 mL/min.

Figure 10 .

 10 Figure 10. Possible intermediates for the reduction of 1.

Figure 11 .

 11 Figure 11. Overview of the possible paths allowing the formation of 2 with the presence of the transient observed molecules 8′ and 9.

■ ASSOCIATED CONTENT * S Supporting Information

The Supporting Information is available free of charge at https://pubs.acs.org/doi/10.1021/acs.oprd.9b00291.

Mass spectrometry patterns, 1 H NMR spectra of the reaction run in D 2 O, UV spectra at different times, comparison of UV and 1 H NMR spectra for a usual reaction and the reaction when the flow is stopped at the maximum X concentration, and UV spectra calculations of possible intermediates in the 200-600 nm window (PDF)

Corresponding Authors *E-mail: damien.herault@centrale-marseille.fr. *E-mail: francoise.duprat@centrale-marseille.fr.

ORCID

Damien Heŕault: 0000-0001-7753-3276

Notes

The authors declare no competing financial interest.

■ ACKNOWLEDGMENTS

The


Alexander Antonio Oliva
email: alexander.oliva@inria.fr

Paolo Robuffo Giordano
email: paolo.robuffo_giordano@irisa.fr

François Chaumette
email: francois.chaumette@inria.fr

Franc ¸ois Chaumette

A General Visual-Impedance Framework for Effectively Combining Vision and Force Sensing in Feature Space

Keywords: Visual Servoing, Force Control, Compliance and Impedance Control, Sensor-based Control

Robotic systems are increasingly used to work in dynamic and/or unstructured environments and to operate with a high degree of safety and autonomy. Consequently, they are often equipped with external sensors capable of perceiving the environment (e.g. cameras) and the contacts that may arise (e.g. force/torque sensors). This paper proposes a general framework for combining force and visual information in the visual feature space. By leveraging recent results on the derivation of visual servo dynamics, we generalize the treatment regardless of the visual features chosen. Vision and force sensing are coupled in the feature space, avoiding both the convergence to a local minimum and the arising of inconsistencies at the actuation level. Any task space direction is simultaneously controlled by both vision and force. Compliance against interaction forces is achieved in feature space along the features defining the visual task. Experiments on a real platform are carried out to evaluate the effectiveness of the proposed framework.

I. INTRODUCTION

For many real-world robotic applications, interaction with the environment is a fundamental requirement and the ability of robots in managing this interaction often determines the successful execution of a task. For example, assembly or polishing requires to control the exchanged forces at contact by regulating them to a specific value. The contact wrench between the end-effector and the environment is the most complete and effective quantity describing the state of the interaction, which is naturally described in the operational space (often the end-effector frame) [START_REF] Khatib | A unified approach for motion and force control of robot manipulators: The operational space formulation[END_REF].

For implementing an interaction control, either an exact knowledge of the location and geometry of the environment is required for accurately planning the task trajectory, or the robot needs to be equipped with force sensing capabilities in order to better adapt to uncertainties and avoid high contact forces along the constrained directions. An effective way to deal with constrained motions is via active compliance, which can be achieved through impedance control [START_REF] Hogan | Impedance control: An approach to manipulation: Part I-Theory[END_REF] by imposing a mass-spring-damper behavior of the robot in contact with the environment. This scheme, as well as compliance or stiffness control, belongs to the category of indirect force control methods [START_REF] Siciliano | Robotics: Modeling, Planning and Control[END_REF], since they achieve open-loop force control via closed-loop position control. Many other approaches have been explored in the past decades for including force sensing capabilities inside a motion control scheme, such as the widely studied Hybrid Position/Force [START_REF] Raibert | Hybrid position/force control of manipulators[END_REF] that is based on the task description [START_REF] Mason | Compliance and force control for computer controlled manipulators[END_REF], the inner/outer [START_REF] Schutter | Compliant robot motion ii. a control approach based on external control loops[END_REF], or the parallel scheme [START_REF] Chiaverini | The parallel approach to force/position control of robotic manipulators[END_REF]. The ability of these methods to perform closed-loop force control via explicit closure of a force feedback loop places them among the direct force control methods [START_REF] Siciliano | Robotics: Modeling, Planning and Control[END_REF].

Motivated by the desire of reducing or avoiding the need for accurate environmental modeling, many robotic systems have been equipped with external exteroceptive sensors, like cameras, to perceive the surroundings. This allows such systems to perform the required tasks without having an accurate preliminary knowledge of the environment.

Given the complementarity of vision and force sensing, these two sensing modalities are often used together, especially in the context of physical human-robot interaction [START_REF] Cherubini | Sensor-based control for collaborative robots: Fundamentals, challenges, and opportunities[END_REF]. Cameras are capable of providing a rich description of the scene, while force sensing can provide local information about the contact itself. However, due to the very different nature of these two sensing modalities (e.g., difference in the measured physical quantities, data rates, delays, etc.), obtaining an effective combined use of vision and force is not straightforward. To this end, several of the above-mentioned motion/force control schemes have been revisited and expanded mostly by replacing the motion control loop with vision. Those schemes share therefore the same capabilities and drawbacks of their position-based counterparts. For instance, the hybrid vision/force scheme presented in [START_REF] Baeten | Integrated Visual Servoing and Force Control -The Task Frame Approach[END_REF] aims at controlling force along constrained directions while vision controls the motion of the remaining ones. The task geometry needs to be known a priori in order to properly design the controller via a selection matrix for ensuring orthogonality between vision and force controlled directions. This sensory separation does not fully exploit the complementarity of vision and force sensing.

In [START_REF] Morel | Impedance based combination of visual and force control[END_REF] a position-based impedance controller is used to achieve compliance in Cartesian space while an external vision control loop is closed around the former. The main disadvantage of this control scheme is that it can get stuck in a local minimum where the simultaneous convergence towards the force and visual reference will not be reached [START_REF] Mezouar | External hybrid vision/force control[END_REF]. Recently, three image-based visual impedance control laws have been proposed [START_REF] Lippiello | Image-based visualimpedance control of a dual-arm aerial manipulator[END_REF]. Although the presented first-and second-order controllers rely on the regulation of the visual error, compliance of the end-effector carrying the object is achieved along/about its Cartesian directions.

Constraint-based methods are an alternative way to integrate vision and force sensing. Those frameworks allow overspecifying constraints along a given direction. The conflicts are resolved by adding weights to such constraints imposing a compliant behavior [START_REF] Schutter | Constraint-based task specification and estimation for sensor-based robot systems in the presence of geometric uncertainty[END_REF], [START_REF] Cai | Visual servoing in a prioritized constraint-based torque control framework[END_REF]. This weighted addition of contribution may however lead to convergence to a local minimum, as in [START_REF] Morel | Impedance based combination of visual and force control[END_REF].

To the best of our knowledge, the literature lacks a general framework capable of blending visual servoing (VS) and force regulation simultaneously, regardless of the choice of the visual features and defined directly in the feature space (i.e., the task space for vision systems). Moreover, being the robot motion guided by vision and the tasks defined in the image plane, we aim at achieving compliance along the directions defining the visual task, i.e. along the visual features, rather than in the Cartesian or joint space as done in the literature.

II. RELATED WORKS

Mezouar et al. [START_REF] Mezouar | External hybrid vision/force control[END_REF] developed the External/Hybrid visualforce control scheme to overcome the drawbacks of the Hybrid and Impedance-based vision-force schemes, for which they have provided an exhaustive comparative analysis. In their approach, the external wrench is transformed into a displacement of the image feature reference. This transformation is equivalent to an undamped spring which, as we show in Section V, can start oscillating without ever reaching the convergence of the task or, in more serious cases, damaging the tool. We then seek for a higher order relation linking forces and features motion. One of the first works aiming at figuring out this relationship for vision driven robotic systems is [START_REF] Zhang | Visual servoing with dynamics: control of an unmanned blimp[END_REF], in which the VS dynamics for a ball target is derived and, by exploiting a general definition and pose invariance of the Lagrangian function in the feature space, authors yields to an ad hoc simplified model dynamics for the features and the system considered. Vice versa, we are interested in the full Lagrangian model of the manipulator and in a generalized treatment that is independent of the type of visual feature.

Carelli et al. [START_REF] Carelli | Combined force and visual control of an industrial robot[END_REF] proposed a Hybrid force-and vision-based impedance controller to perform a peg-in-hole task. Posebased VS (PBVS) is used to guide the end-effector towards the hole. Interaction forces are fed back to correct small errors of visual guidance by modifying the visual reference along the horizontal plane. Pure force control is used along the vertical axis. The use of selection matrices does not allow to use vision along the vertical axis. The interaction forces are fed back simply by changing the point of application through a coordinate transformation limiting its applicability only to point features.

In this work, we instead leverage results on the derivation of the VS dynamics [START_REF] Fusco | A comparison of visual servoing from features velocity and acceleration interaction models[END_REF], [START_REF] Vandernotte | Dynamic sensor-based control[END_REF] that do not depend on the particular choice of the visual features: this allows us to derive a general framework that can effectively combine vision and force sensing directly in feature space. This differs from previous works on this topic since the derivation of secondorder models has often been formulated ad hoc from the definition of the considered features. Furthermore, thanks to this formulation, the projection of the wrench applied on the camera into the feature space can also be generalized. This projection allows us to design a controller that makes the closed-loop system to behave as an equivalent mass-springdamper system fully defined in the feature space and with an isotropic response to external forces (i.e., the interaction does not depend on the manipulator configuration). Moreover, a feature admittance law is coupled with a force control law (FCL) to ensure precise force regulation. Finally, experiments are carried out on a real platform to validate the effectiveness of the proposed approach. A comparison with the external hybrid method in a critical situation is also discussed for further illustrating the benefits of our approach.

The advantages of the proposed framework are several. First of all, it allows to treat the combination of vision and force sensing in a unified way regardless of both the camera configuration (i.e., eye-in-hand or eye-to-hand) and of the chosen visual features. Indeed, any visual feature suitable for either Image-Based Visual-Servoing (IBVS) (e.g. image points, slopes and offsets of lines, image moments, etc) or (PBVS) (i.e. Position and orientation (pose) of objects observed by the camera) can be used. Furthermore, since the vision-force coupling is obtained in the feature space, both convergence towards a local minimum and inconsistencies at actuation level are avoided. Besides that, compliance is achieved in feature space along/about the features defining the visual task resulting in an intuitive choice of the admittance parameters. Unlike in the Hybrid approach, any task direction is fully controlled using both vision and force sensing, and both physical and fictitious forces (i.e. generated in the image plane) can be handled in this framework to account for e.g., the physical interaction with the environment or a visually generated repulsive force field in a collision avoidance tasks. Finally, force regulation can also be achieved.

The rest of this paper is organized as follows. In Sec. III a description of the system kinematics and dynamics is given. The wrench projection in feature space as well as the derivation of the framework is explained in Sec. IV. In Sec. V experimental results are discussed while in Sec. VI, we present some conclusions and an overview of possible future works.

III. PRELIMINARIES

Without loss of generality we consider the fixed world frame of reference, named Σ w and with the z-axis pointing upwards, to be coincident with the robot base frame Σ b . The manipulator is a succession of links and actuated joints whose configuration is described by the joint vector q ∈ R n . The endeffector frame is denoted with Σ e . The robot is equipped with a wrist-mounted force/torque sensor whose reference frame is denoted with Σ f t . Moreover, although we assume here to be using a camera in a eye-in-hand configuration (frame Σ c ), the development for the eye-to-hand case is formally analogous. Σ d represents the desired camera frame. Finally, an object is visually tracked and the pose of its reference Σ o in the camera frame is estimated, or descriptive image features are extracted from the image through computer vision algorithms. Any required geometrical transformation between the abovedefined reference frames is supposed to be known, except for those concerning the object frame. An overview of the system setup and main reference frames defining the system is shown in Fig. 1.

A. Manipulator Dynamics

The dynamic model of a robotic arm can be written using the Lagrange formulation in the joint space as described in [START_REF] Siciliano | Robotics: Modeling, Planning and Control[END_REF]:

B(q)q + C(q, q) q + g(q) + τ e = τ (1)
where q, q ∈ R n are respectively the generalized joint velocities and accelerations. B(q) ∈ R n×n is the symmetric and positive definite inertia matrix, C(q, q) ∈ R n×n is the matrix of centrifugal and Coriolis effects, g(q) ∈ R n is the configuration dependent vector of gravitational forces, τ e = e J e e h e ∈ R n is the joint vector corresponding to the external wrench e h e ∈ R 6 acting on the end-effector frame and e J e ∈ R 6×n is the robot Jacobian, being both expressed in end-effector frame. Finally, τ ∈ R n is the vector of joint actuation torques.

B. Visual Servoing Kinematics and Dynamics

In the following we recall the derivation of the visual-servo dynamics which relates the motion of visual features with the joint motion at acceleration level. This relationship will then be used, together with the visual-servo kinematics, to express the dynamic model of the manipulator in feature space.

Let us consider a vector s ∈ R k of k image features, e.g., the positions of points in the image plane or parameters of lines. The kinematic relationship between the motion of the visual features and the relative twist c v ∈ R 6 , which is the difference between camera ( c v c ) and object ( c v o ) twists in the camera frame, is given by the following differential relation:

ṡ = L s c v = L s ( c v c -c v o ) (2)
being L s ∈ R k×6 the well-known interaction matrix [START_REF] Espiau | A new approach to visual servoing in robotics[END_REF] (in this derivation we will assume that it has full rank, thus constraining the 6 degrees of freedom (DoF) of the camera motion). The explicit expression of the interaction matrix for many types of visual features can be found in [START_REF] Espiau | A new approach to visual servoing in robotics[END_REF]. When the relative motion between the camera and the object is only due to the robot motion (i.e. c v o = 0), the previous equation can be rewritten to link the features velocities with the joint velocities through the robot Jacobian as:

ṡ = L s c T e e J e q (3)
being c T e ∈ R 6×6 the Twist-transformation matrix that transforms the twist from the end-effector to the camera frame. By time differentiation of (2) one obtains the expression of the feature accelerations:

s = L s c v + Ls c v
or when differentiating (3):

s = Ls c T e e J e q + L s c Ṫe e J e q + L s c T e e
Je q + L s c T e e J e q (4) We can rewrite (4) in a more compact form as:

s = J s q + h q (5)
where J s = L s c T e e J e denotes the so called Feature Jacobian [START_REF] Chaumette | Visual servoing[END_REF], [START_REF] Fusco | A comparison of visual servoing from features velocity and acceleration interaction models[END_REF] and:

h q = ( Ls c T e e J e + L s c Ṫe e J e + L s c T e e Je ) q
IV. VISUAL IMPEDANCE CONTROL FRAMEWORK In this section we start by deriving the model of the manipulator in interaction with the environment in the feature space up to the definition of a general framework for combining vision and force sensing in feature space.

A. Impedance Control in Feature Space

Impedance control aims to achieve a dynamic behaviour for the robot end-effector equivalent to a mass-spring-damper system subjected to an external force. Our purpose here is to replicate this behaviour between the current and desired visual features lying on the image plane. Let Σ c be the current and Σ d the desired camera frames and e s = s ds ∈ R k be the error vector between the desired and current visual features. We formally want to obtain the following behaviour in feature space:

M s ës + D s ės + K s e s = f s (6)
where M s , D s and K s are positive definite k × k matrices representing the relative per unit mass/inertia (p.u.m.i.) virtual mass, dampers and stiffness of the impedance equation while f s ∈ R k is the vector of p.u.m.i. virtual forces (accelerations) acting on the features. Equation ( 1) is a set of n nonlinear and coupled secondorder differential equations for which the inverse dynamics control is a well-known control strategy for trajectory tracking aiming at linearizing and decoupling the manipulator dynamics via feedback linearization under the assumption of perfect model knowledge. We can rearrange (1) as:

q = B(q) -1 (τ -b -e J e e h e ) (7)
having compacted in b = (C(q, q) q + g(q)). After replacing (7) into (5), we find the dynamic equation that governs the features motion:

J s B(q) -1 τ = s -h q + J s B(q) -1 b + J s B(q) -1e J e e h e . (8
) Taking into account the expression of the feature Jacobian J s , the wrench-transformation matrix that projects the external wrench acting on the camera into the end-effector ( e h e = e F c c h c ) and recalling that c T e = e F c [START_REF] Siciliano | Robotics: Modeling, Planning and Control[END_REF], we can rearrange the last member of (8) as:

L s c T e e J e B(q) -1e J e c T e c h c = L s B c (q) -1c h c (9)
where B c -1 = c T e e J e B(q)

-1 e J e c T e is the inverse of the manipulator inertia matrix projected in the camera frame. Equation ( 9) highlights how the wrench acting on the camera frame (expressed in its own coordinates c h c ) projects in feature space as virtual p.u.m.i. forces (accelerations) acting on the image features. By renaming some terms in (8) as:

f s = J s B(q) -1 τ b s = J s B(q) -1 b f sext = L s B c (q) -1c h c ( 10
)
one obtains the manipulator model in feature space:

s -h q + b s + f sext = f s . (11)
As we can see from the previous equation, the system is not endowed of inertia (behaves as a mechanical system with unitary mass/inertia). The new control input for the manipulator model in feature space is the vector of p.u.m.i. virtual forces u = f s . At this stage we suppose not to have any force measurement. By then choosing our feature space control input u as to compensate for any dynamic term in [START_REF] Mezouar | External hybrid vision/force control[END_REF], we have:

u = w -h q + b s (12)
and by injecting it back into (11) yields to:

w = s + f sext ( 13
)
in which w ∈ R k represents a resolved acceleration in feature space and constitutes the new control input that has to be opportunely designed. A natural choice for w is a PD controller with acceleration feed-forward:

w = s * + D s ės + K s e s
that replaced in (13) leads to the closed-loop dynamics of the system:

ës + D s ės + K s e s = f sext (14)
The behavior of the closed-loop system is as we were looking for i.e., as ( 6) but with M s as the identity matrix. The resulting joint space controller is:

u τ = (J s B(q) -1 ) † (s * + D s ės + K s e s + J s B(q) -1 b -h q ) (15
) where (.) † is the pseudo-inverse of the matrix in the argument. Even though we have considered the manipulator interacting with the environment in our derivation, if we do not have the force measurement, we arrive at an indirect control of the force through a position controller such as the one derived in [START_REF] Fusco | A comparison of visual servoing from features velocity and acceleration interaction models[END_REF], [START_REF] Vandernotte | Dynamic sensor-based control[END_REF].

The drawback of this controller is that the closed-loop system exhibits a configuration-dependent compliant behavior due to the presence of the inertia matrix of the manipulator in the external wrench projected in the feature space (see [START_REF] Morel | Impedance based combination of visual and force control[END_REF]). An easy way to overcome this issue and render the manipulator behaviour isotropic, is to measure the external forces being applied on the robot and fully compensate for them. This will make the manipulator infinitely rigid with respect to the measured forces but, thanks both to the fact that we have this measure and that we know how to project the wrenches into the feature space, we can impose the desired system behavior during the interaction. Redefining the feature space controller [START_REF] Lippiello | Image-based visualimpedance control of a dual-arm aerial manipulator[END_REF] as:

u = w -h q + b s + L s B c (q) -1 c h c
and plugging it again into (11) we obtain

s = w
For control purposes it is convenient to impose a constant apparent inertia matrix of the camera in order to have an homogeneous behavior along the Cartesian directions of the camera frame and manage the compliance along the visual feature by opportunely tuning the impedance parameters. This Fig. 2: By assigning a constant apparent inertia to the end-effector or camera frame, we impose the desired interaction behavior along/about the Cartesian directions. We choose an homogeneous inertial behavior so that the end-effector is equivalent to a sphere of mass. Applied forces on the end-effector will be homogeneously distributed among the features. can be done by choosing as resolved accelerations in feature space the controller:

w = s * + D s ės + K s e s -L s Bc -1 c F e e h e (16)
being

Bc = diag(m c d , m c d , m c d , J c d , J c d , J c d ) in which m c d [kg] and J c d [kg.m 2 ]
are respectively the desired apparent mass and inertia that the camera should exhibit. Having to deal with contacts with the tool, it can be useful to exhibit isotropy on the end-effector frame by choosing a constant inertia matrix Be , as done before for Bc , and then project it in the camera frame as Bc -1 = c T e Bc -1 c T e . The resulting joint space controller is therefore:

u τ = (J s B(q) -1 ) † (s * + D s ės + K s e s + J s B(q) -1 b -h q + f sext -L s Bc -1 c F e e h e ) (17)
The closed loop dynamics has the same expression as in [START_REF] Cai | Visual servoing in a prioritized constraint-based torque control framework[END_REF], but now the projected external forces in feature space do not depend on the manipulator configuration anymore. This translates in a more intuitive tuning of the admittance parameters since this controller would make the manipulator under interaction to behave in the same manner, no matter its configuration while preserving the same stability properties of the previous controller [START_REF] Zhang | Visual servoing with dynamics: control of an unmanned blimp[END_REF].

B. Feature Space Admittance

Despite its theoretical appeal, the feature impedance control cannot be implemented as is with classical cameras due to their intrinsic technological limitations, (e.g., slow frame rate compared to the faster force/torque sensing), which makes it impossible to control a manipulator at torque level. The low control bandwidth resulting from the use of low-rate cameras is in contrast with the need of high gains in the impedance controller for ensuring good tracking performances and disturbance rejection. It follows that there exists a trade-off between the trajectory tracking accuracy and the compliance given to the robot. This limitation motivates the definition of the admittance control in feature space.

In Section IV-A it was shown how the external wrench projects into the feature space as virtual p.u.m.i. forces that act on the visual features. Exploiting this relationship and the concept of compliant frame (Σ * ), we can link the desired reference (Σ d ) and the compliant frame defined before with a secondorder relation that will be used to feed the vision control loop. For the case of PBVS, the admittance is equivalent to the one defined in the task frame, as reported in [START_REF] Siciliano | Robotics: Modeling, Planning and Control[END_REF], and depends on the chosen representation of the orientation (e.g., Euler angles, axis/angle, etc.). In our case the task frame is the camera frame rather than the end-effector frame. For IBVS, we extend to the feature space the admittance law linking the desired s d (t) and compliant feature s * (t) vectors. We will denote this error with ēs = (s ds * ) and from now on e s = (s * -s) (see Fig. 3):

M s (s d -s * ) + D s ( ṡd -ṡ * ) + K s (s d -s * ) = fsext (18)
with fsext the external wrench projected in feature space with the constant inertia as in [START_REF] Carelli | Combined force and visual control of an industrial robot[END_REF]. When no external forces act on the end-effector, the compliant and the desired reference frames are coincident (Σ * ≡ Σ d ). From ( 18) we then isolate s * and integrate it twice in order to obtain ṡ * and s * . It is evident that modifying the visual reference accordingly to the sensed force, we are not facing anymore a regulation problem but a trajectory tracking one, for which an appropriate visual control law is necessary in order to better track the moving visual reference [START_REF] Chaumette | Visual servoing[END_REF]. Since we dispose of both the desired features and camera velocities, we can use this information to implement the following visual control law (VCL):

c v c = λL s † e s + L s † ( ės + J s q) ( 19
)
where λ is a scalar positive gain.

It is interesting to notice that depending on both the type of visual feature chosen and the values assigned to the admittance parameters for each feature, we can have a different compliant behavior and this can be exploited to our advantage.

C. Force regulation

For many robotic applications the regulation of the exchanged forces with the environment is of particular importance for the correct execution of the task itself. It should be stressed that since the impedance/admittance control is an indirect force control scheme, the amount of exerted force is a consequence of the positional error and the chosen control stiffness. In particular, for the visual-feature impedance/admittance control, from [START_REF] Vandernotte | Dynamic sensor-based control[END_REF] at the equilibrium (i.e., ës = ės = 0) and referring directly to the external wrench in the end-effector frame, we have:

ēs = K s -1 L s Bc -1 c F e e h e
Our intention is to regulate the amount of exchanged force along/about a certain direction to a specific value. To this purpose we use, together with the visual-feature admittance, a PI controller based on the force error in Cartesian space (where the wrench is naturally defined) projected into the feature space. We can replace then the second member of ( 18) with the following (FCL):

f * sext = L s Bc -1 c F e e h
being e h e d the desired wrench in the end-effector frame, K fP and K fI two 6 × 6 positive gain matrices for the proportional and integral force error terms respectively. The presence of the integral term in the controller creates a dominance of the force loop over the internal positional loop.

It is of course clear that such a desired force/torque to be regulated has to be specified accordingly to the task geometry (along/about a constrained direction) otherwise velocities will arise along/about unconstrained direction.

D. The Extended External Hybrid Vision-Force Scheme

Once all the parts of the framework have been explained, it is possible to put them all together. Figure 3 shows the block diagram of the proposed controller: it presents a hierarchical structure in which a FCL, together with a feature space admittance law, is closed around an inner vision control loop implementing the VCL in [START_REF] Espiau | A new approach to visual servoing in robotics[END_REF]. The reference trajectory Fig. 3: Extended external hybrid vision/force control scheme. A feature space admittance is used as reference modifier to achieve compliance along visual features directions. Force control law ensures force regulation when the integral term is activated.

s d (t) feeds the admittance [START_REF] Vandernotte | Dynamic sensor-based control[END_REF], which opportunely modifies it proportionally to the output of the FCL implementing [START_REF] Chaumette | Visual servoing[END_REF]. We named the resulting controller as Extended External Hybrid vision-force scheme since it presents the same structure of the External Hybrid. The main advantage over the latter is that our framework offers more flexibility in the choice of the compliant behavior we want to implement, thanks to a greater number of parameters in the admittance that can be tuned, besides to give the possibility to achieve force regulation.

V. EXPERIMENTAL RESULTS

In this section, we show the results of our proposed Extended External Hybrid controller executing a Peg-in-Hole task. We then compare it to the External Hybrid controller [START_REF] Mezouar | External hybrid vision/force control[END_REF] in a critical situation and conclude with a series of peg insertions against pure VS to highlight the greater potential and the range of applicability that comes from a small increase of the controller's complexity. For a better understanding of the work done we suggest to refer to the accompanying video in which, in addition to the experiments in the paper, we show a trial using lines as visual features and another trial that simultaneously copes with physical and fictitious forces to maintain the visual references in the field of view.

A. Experimental Setup

The setup consists of a lightweight Franka Emika Panda arm with 7 revolute joints and its control software running on a Desktop PC with an Arch-Linux distribution patched with a Preemptive RT-Kernel 5.4.52-rt31. A wrist mounted six axis force/torque sensor Alberobotics FT45 with force and torque ranges of F z ± 1000N, F x , F y ± 500N and M x,y,y ± 20N m respectively is present as well as a RealSense RGB-D SR300 camera, mounted in a eye-in-hand configuration (see Fig. 1).

Force/torque sensors are capable of measuring any kind of force, being them gravitational, inertial or contact forces. We are interested only in the contact forces. Since force measurements modify the visual reference, an accurate gravitational and inertial effects compensation should be performed. If the payload is not well estimated, spurious force/torque readings remain that cannot be compensated for without resorting to online estimation strategies of the payload parameters. These spurious readings will be interpreted as forces/torques acting on the features reference and will move them according to the admittance stiffness.

To make the system more robust against misestimation of the payload parameters (i.e. mass, inertia, and center of mass) or inertial effects, we can choose higher values of the virtual p.u.m.i. stiffness of the admittance at the expense of a more rigid system. In our setup, in addition to the standard gripper, we have the camera, the force/torque sensor and some 3D printed parts whose weight has to be estimated. An efficient way to estimate these parameters is reported in [START_REF] Gaz | Payload estimation based on identified coefficients of robot dynamics -with an application to collision detection[END_REF] that rely on the identified coefficients of the robot dynamics that can be found in [START_REF] Gaz | Dynamic identification of the Franka Emika Panda robot with retrieval of feasible parameters using penalty-based optimization[END_REF] for our robot. As we use a wristmounted force/torque sensor, we need to compensate only for the payload downstream the sensors flange. In all the reported experiments, 3 rd -order Butterworth low-pass filters with a cutoff frequency of 2 Hz are used.

B. Peg-in-Hole Experiment

The task consists in inserting a peg into a hole present in a wood workpiece, both with a diameter of 1cm. The depth of the hole is of 2cm while the length of the peg is 4cm. An AprilTag of the 36h11 family of size 6.45cm is applied to the surface of the workpiece. The latter is supported by a wooden structure fixed to the work table, which holds an inclined groove of about 45 • with respect to the horizontal plane on one side and about 10 • on the other (see Fig. 4(a)). The experiment consists of two phases. In the former the robot has to insert the peg in the hole without computing any trajectory while in the latter it pushes the peg towards the bottom of the hole and simultaneously applies lateral forces such that the workpiece slides into the groove until a desired force is reached along both directions. The task is executed using our proposed Extended Exteral Hybrid controller (see Fig. 3) for which the VCL gain is set to λ = 1.5 s -1 . The vision system guides the camera towards a desired final position of the features in the image plane. This final position corresponds to the position in which the peg, held by the robot gripper, is inserted in the hole at a depth of about 1.5 cm. Using Visp [START_REF] Marchand | Visp for visual servoing: a generic software platform with a wide class of robot control skills[END_REF], the AprilTag on the workpiece is tracked and the coordinates of its corners are used as visual features s ∈ R k , with k = 8. The expression of the interaction matrix L s ∈ R 8×6 associated to these features can be found in [START_REF] Chaumette | Visual servoing[END_REF].

During the first phase of the task, the FCL only projects the external wrench into the feature space allowing the system to accommodate for unmodeled interaction forces. So, accordingly with (20), we have:

f * sext = -L s Bc -1 c h c , meaning
that K fP = I 8 , the identity matrix of dimension 8 × 8, K fI = 0 s -1 and e h e d = 0. The admittance parameters have been chosen in order to have small interaction forces and sufficient damping to attenuate the oscillations that can be triggered while maintaining the overall reactiveness of the system (M s = I 8 kg kg , K s = diag(300) N/m kg , D s = diag(200) N/m.s -1

kg

). During the second phase, that is the force regulation phase, the FCL fully implements eq. ( 20) with K fP = diag(0.2), K fI = diag(5) s -1 so as to guarantee fast force convergence and limited overshoot while keeping the system stable. The experimental setup and the framework's behaviour during the task execution are shown in Figs. 4 and5 respectively. As we can appreciate from the plots in Fig. 5c and the image points trajectory (almost straight) in Fig. 5b, the visual task begins to converge exponentially until it hits the structure, not being aware of it since there is neither a previous knowledge of the environment nor a pre-calculated trajectory. The impact force in the approach direction is approximately 35 N and it projects into the feature space as virtual p.u.m.i. forces that pull the four point features reference towards the target centroid causing the robot to slow down along this direction while it continues converging along the others. The robot then approaches the hole and the peg is successfully inserted. These two collisions are perfectly visible both in Fig 5b (small sawteeth close to the desired features) and Fig 5d (two peaks along z-axis). Once the peg is within the hole, we observe that the visual error converges allowing the system to autonomously switch to the second phase in which the integral term in the FCL is activated. The lateral force pushes the workpiece into the groove and against the wall of the structure. The integral term makes the output of the FCL to increase until the force error is nullified. This creates a dominance of the force loop over the internal vision loop.

C. Extended External Hybrid vs External Hybrid

The external hybrid approach [START_REF] Mezouar | External hybrid vision/force control[END_REF] has been shown to be successful where impedance-and hybrid-based vision/force schemes have failed. Then follows our interest in comparing this control scheme with the proposed one, as we inherit its structure and extend it, eliminating its drawbacks.

In [START_REF] Mezouar | External hybrid vision/force control[END_REF], a Cartesian displacement dX ∈ R 6 is firstly computed as dX = K -1 ( e h e de h e ) being K ∈ R 6×6 the contact stiffness. This displacement is then projected in feature space as ds = L s L X -1 dX, with L X the interaction matrix of the pose parameters. Finally, the compliant reference is obtained by adding the computed feature space displacement to the desired reference s * = s d + ds.

To evaluate their relative performance over the task, we have executed different trials with both methods, each starting and ending from a different position. This time the workpiece is clamped on the work surface, preventing it from moving. The results of one of these experiments are in Fig. 6. To make the comparison as fair as possible, we choose the same gain λ = 1.5 s -1 for both controllers and the proportional gain of the external hybrid, i.e., the contact stiffness, in such a way that both methods achieve the same displacement of the visual reference when the same force is applied leading to

choose K = (L X L s † K s -1 L s Bc -1 c F e ) -1
. On the other hand, Bc , K fP , K fI and M s are as in the previous experiment, for both phases, while for this experiment we impose a less stiff behaviour by choosing K s = diag(200) N/m kg and D s = diag(150) N/m.s -1 kg for the first phase. At the beginning, both methods starts converging towards the target with exactly the same behaviour. In fact, as long as there are no interaction forces, the reference is not modified and the task is a pure VS. When the peg approaches the hole, it hits the border before entering. As shown in Fig. 6, for both the external hybrid and our method, the impact force along the approach direction stays quite limited even though for our method it is slightly higher. This is due to the presence of the damping term. Both methods succeed in the insertion of the peg tip but the increase of lateral forces once the peg is inside the workpiece, triggers the oscillation of the non-damped spring of the stiffness control for the external hybrid method. If these oscillations remain limited, they do not allow to reach the convergence of the visual reference while, in the event they explode as it is the case, it can lead to damage the manipulated object or even the robot tool. This experimental result has shown that endowing the feature's motion with a dynamic capable of damping their velocity, improves the performance of the system, managing to dampen the oscillations that can be triggered.

D. Further Experiments

We have conducted a series of insertion tasks to evaluate the success rate of our proposed extended external hybrid method. Starting from 10 different initial conditions covering almost all the dexterous work-space of the robot, we tested the efficiency of our method in inserting the peg in the hole against the task being executed by pure VS.

As expected, being able to account for interaction forces, our method succeeded 9/10 times, while the pure VS only 5/10. It should be noticed that the last experiment was purposely started from a configuration for which the approach direction will converge before the other ones. This is to highlight that no trajectory planning or insertion strategy was used. The controller simply nullifies the visual error. The method succeeds in every case the pure VS has failed.

VI. CONCLUSIONS

We presented a general framework for both IBVS and PBVS regardless of the visual feature chosen or camera mount. It allows for potentially 6 DoF force regulation. External wrenches are projected in feature space in a general fashion and compliance is achieved along the directions defined by the visual task. This can open a new research line that uses machine learning to learn how to dynamically tune the admittance parameters based on the provided images.

We are interested in performing high-speed interaction tasks and this means taking robot dynamics into account by implementing eq. ( 17), that controls the robot at torque level. To this end we will focus on increasing the camera rate by predicting the state of the features e.g., with a Kalman filter designed in feature space. We are also interested into studying the resulting system energy in feature space to design passivitybased controllers capable of passivize the destabilizing effects of low camera rates and time delays.

Fig. 1 :

 1 Fig. 1: System setup and reference frames.

Fig. 4 :

 4 Fig. 4: Peg-in-hole experiment setup: (a) The robot at the initial configuration. (b) Forces exerted by the end-effector on the environment during phase 2, the task requires to apply [5, -5, -15]N along the end-effector's x-(blue), y-(green) and z-axis (red arrow) respectively.

[ 5 N

 5 The desired wrench is set to e h e d = -5 N -15 N 0 0 0] and is transformed to the camera frame as c h c d = c F e e h e d . For both phases, the desired apparent constant inertia we want the camera to exhibit is Bc = c T e Be -1 c T e with Be = diag(1 I 3 kg, 0.1 I 3 kg.m 2 ).

Fig. 5 :

 5 Fig. 5: Peg-in-hole experiment: (a): Initial camera view of the experiment. The green crosses are the current features while the red crosses are the references. (b): Final camera view. It is possible to appreciate (in green) the trajectory of the features in the image plane. (c): Feature errors (s * -s), (d) End-effector forces and (e) moments.

Fig. 6 :

 6 Fig.6: Peg-in-hole comparison: (a) the results obtained with our method and, (b) those obtained with the external hybrid[START_REF] Mezouar | External hybrid vision/force control[END_REF]. The images show the initial and final camera views with the current and reference feature trajectories in green and red respectively. The plots report, from top to bottom: the visual feature errors (s * -s), measured end-effector forces and moments. e he d = [5N , 0 , -20N , 0 , 0 , 0]