domain: chim phys

text:
Roman A Motiyenko
email: roman.motienko@univ-lille1.fr

Laurent Margulès

Maria L Senent

Jean-Claude Guillemin
email: jean-claude.guillemin@ensc-rennes.fr

Internal rotation of OH group in 4-hydroxy-2-butynenitrile studied by millimeter-wave spectroscopy

Cyanoacetylene, HCC-CN is a ubiquitous molecule in the Universe. However, its interstellar chemistry is not well understood and its understanding requires laboratory data including rotational spectroscopy of possible products coming from a reaction with another compounds. In this study we present the first spectroscopic characterization of gauche conformation of 4-hydroxy-2-butynenitrile (HOCH 2 CCCN), a formal adduct of cyanoacetylene on formaldehyde, in the frequency range up to 500 GHz. The analysis of the rotational spectrum was complicated by internal rotation of OH group that connects two equivalent gauche configurations.

The spectral assignment was aided by high level quantum chemical calculations that were particularly useful in the interpretation of torsion-rotational part of the problem.

The applied reduced-axis-system (RAS) formalism allowed fitting within experimental accuracy the lines with K a < 18. We also present the method of search for initial global solution of torsion-rotational problem within RAS formalism. Accurate spectroscopic parameters obtained in this study provide a reliable basis for the detection of 4-hydroxy-2-butynenitrile in the interstellar medium.

Introduction

Cyanoacetylene is a ubiquitous molecule in the Universe since it has been observed in interstellar clouds [START_REF] Turner | Detection of interstellar cyanoacetylene[END_REF][START_REF] Morris | Cyanoacetylene in dense interstellar clouds[END_REF][START_REF] Clark | Detection of interstellar vibrationally excited cyanoacetylene[END_REF][START_REF] Walmsley | Cyanoacetylene and cyanodiacetylene in interstellar clouds[END_REF][5] , Hale-Bopp comet [START_REF] Lis | New Molecular Species in Comet C/1995 O1 (Hale-Bopp) Observed with the Caltech Ssubmillimeter Observatory[END_REF] and in the atmosphere of Titan, the largest moon of Saturn [START_REF] Kunde | C4H2, HC3N and C2N2 in Titan's atmosphere[END_REF][START_REF] Cordiner | ALMA Measurements of the HNC and HC3N Distributions in Titan's Atmosphere[END_REF] . Cyanoacetylene is probably the precursor of many cyanopolyynes by photolysis in the presence of acetylene or polyynes. [START_REF] Cherchneff | The formation of carbon chain molecules in IRC+ 10216[END_REF][START_REF] Cherchneff | The formation of cyanopolyyne molecules in IRC+ 10216[END_REF][START_REF] Trolez | Synthesis and characterization of 2, 4-pentadiynenitrile -A key compound in space science[END_REF][START_REF] Coupeaud | Photochemical synthesis of the cyanodiacetylene HC5N: A cryogenic matrix experiment[END_REF] Besides two methyl derivatives, MeC 3 N and MeC 5 N, which could be formed by a similar approach but with propyne or 1,3-pentadiyne 13,14 instead of acetylene or unsubstituted polyynes, no other derivative containing the C 3 N moiety has been detected in the interstellar medium (ISM). For many compounds, this could be explained by the lack of rotational spectra recorded in laboratory. However, the formal addition of ammonia, hydrogen sulfide or water which respectively gives 3-amino-2-propenenitrile, 15 3-A c c e p t e d m a n u s c r i t p t mercapto-2-propenitrile 16 and 3-hydroxy-2-propenenitrile (the latter rearranges in cyanoacetaldehyde) 17 was studied and the rotational spectra of these adducts were recorded. At present, none of them has yet been detected to date in the ISM. Another approach of interstellar formation of C 3 N derivatives involves the reaction of the C 3 N radical, a species detected in the ISM, 18 with another compound, and this is much more comparable to the formation of cyanopolyynes than the Michael addition of nucleophiles on cyanoacetylene. In TMC-1, for example, the C 3 N radical and formaldehyde have been detected. 19 The addition of this radical on the carbonyl could produce 4-hydroxy-2-butynenitrile (HOCH 2 CCCN, HBN) after abstraction of one hydrogen from another compound (Scheme 1).

Scheme 1

Thus, as a first target species based on the hypothesis of interstellar compounds coming from the cyanoethynyl radical addition on an unsaturated compound, we investigated the rotational spectrum of HBN. The spectral studies were augmented by high-level quantum chemical calculations performed to aid in the interpretation of the observed spectra. Experiment 4-Hydroxy-2-butynenitrile has been prepared as previously reported 20 starting from a protected propargyl alcohol and phenyl cyanate. We recorded the rotational spectrum of HBN using fast-scan terahertz spectrometer. The details of the spectrometer except of the fastscan feature are described by Zakharenko et al. 21 In the present study, the spectrum was

Ab initio calculations

Highly correlated ab initio calculations were used to determine the geometries of the two conformers, gauche and trans, and to compute low-energy torsional levels. Electronic structure calculations were performed using both the MOLPRO 22 and GAUSSIAN packages 23 .

The equilibrium structures, gauche and trans, of HOCH 2 CCCN, as well as the most relevant spectroscopic parameters (equilibrium rotational constants and the one-dimensional potential energy surface, 1D-PES, for the hydroxyl torsion) were computed using explicitly correlated coupled cluster theory with single and double substitutions augmented by a perturbative treatment of triple excitations (CCSD(T)-F12b) [START_REF] Knizia | Simplified CCSD (T)-F12 methods: Theory and benchmarks[END_REF][START_REF] Werner | General orbital invariant MP2-F12 theory[END_REF] with an aug-cc-pVTZ basis set [START_REF] Kendall | Electron affinities of the first-row atoms revisited. Systematic basis sets and wave functions[END_REF] . For this purpose, we employed the MOLPRO default options. Second-order Möller-Plesset theory (MP2) was employed to determine vibrational corrections for the potential energy surface and the α r j vibration-rotation constants. For the explicitly correlated calculations, the MOLPRO default options were selected.

The torsional energy levels were determined by variational calculations using the procedure previously employed for other non-rigid species [START_REF] Senent | Ab initio study of the torsional spectrum of glycolaldehyde[END_REF] . The variational procedure considers the intertransformation of the minima and the tunneling effects in the torsional barriers. If the non-rigidity is taken into account, the molecule can be classified into the Molecular Symmetry Group (MSG) G 2 . Some complementary calculations, such as the vibrational corrections, were performed using the second order perturbation theory implemented in Gaussian 23, [START_REF] Barone | Anharmonic vibrational properties by a fully automated second-order perturbative approach[END_REF] . For the latter, the two point groups C 1 and C s were employed for the two conformers gauche and trans, respectively. The irreducible representations of G 2 can be correlated with those of C s . Thus, the G 2 symmetric and antisymmetric representations A 1 and A 2 can be correlated with the A and A representations of C s .

Previous references [START_REF] Császár | Ab initio torsional potential and transition frequencies of acetaldehyde[END_REF] describe how the internal rotation levels are correlated to the minima of the potential energy surface. For this purpose, the torsional wave functions obtained in the variational procedure were employed for computing the probability integrals. As was expected, the ground vibrational state can be confined in the absolute minima gauche and the A 1 component lies below the A 2 .

Below the barriers where the tunneling effects are significant, once the energy increases, the relative order of subcomponents varies and the levels cannot be localized in a single minimum. Above the barriers (i.e. levels 3 and 4), tunneling effects are not present. Those levels were classified as for a semi-rigid species.

HBN displays various very low frequency vibrational modes lying in the region or below the OH torsion fundamental. They can be defined as skeletal deformations, in plane and out of plane bending modes. To estimate their band center positions, harmonic frequencies were computed using CCSD(T)-F12 the- ory and the MOLPRO package. All this frequencies are real which assure the minimum energy character of the two conformers gauche and trans. For the gauche conformer, the OH harmonic torsion lies at 280 cm -1 , and for the trans conformer the band center is estimated at 194 cm -1 . This result is coherent with the variational calculations summarized in Figure 1. For the gauche form, three skeletal deformations, computed at 99 cm -1 , 133 cm -1 and 230 cm -1 , lye below the OH torsional fundamental. For the trans form, only two modes, at 100 cm -1

(A ) and 133 cm -1 (A ), must be considered. A third fundamental, is computed at 237 cm -1 (A ).

As was expected, the computation of anharmonic fundamentals using second order perturbation theory VPT2 implemented in Gaussian leads to unrealistic results for the very low energies. It has to be taken into consideration that the potential energy surface is very flat in the region of the skeletal deformations. However, it allows the estimation of possible Fermi interactions that are not expected for the OH torsion. This validates the one-dimensional model.

The ground vibrational state rotational constants of the two conformers were determined from the CCSD(T)-F12 equilibrium parameters using Equation 1

B 0 = B e + ∆B core e + ∆B vib , (1)
This equation has been previously tested for other species using explicitly correlated methods. 30 Here, ∆B core e , regards the core-valence-electron correlation effect on the equilibrium parameters. It was computed at the CCSD(T) level of theory [START_REF] Raghavachari | A fifth-order perturbation comparison of electron correlation theories[END_REF] as the difference between B e (CV ), (calculated correlating both core and valence electrons) and B e (V ) (calculated correlating just the valence electrons). The vibrational contribution ∆B vib was computed with MP2 and second order perturbation theory. The results for the two conformers are shown in Table 1. The low torsional energy levels were calculated using a variational solution of the Hamiltonian given in Equation 2 [START_REF] Senent | Ab InitioDetermination of the Roto-Torsional Energy Levels oftrans-1, 3-Butadiene[END_REF][START_REF] Senent | Determination of the kinetic energy parameters of non-rigid molecules[END_REF] :

Ĥ(α) = - ∂ ∂α B α ∂ ∂α + V ef f (α). (2)
Here, α is the OH torsional coordinate, B α are the kinetic energy parameters, and

V ef f (α)
is the vibrationally corrected 1D-PES [START_REF] Császár | Ab initio torsional potential and transition frequencies of acetaldehyde[END_REF] shown in Figure 1.

The ground vibrational state splits into two components E(0 -) and E(0 + ) because of tunneling in the V (gauche-gauche) barrier. Ab initio calculations predict a splitting of 173280 MHz (5.78 cm -1 ). In addition, the first excited vibrational state shows two components lying at 278.5 cm -1 (1 + ) and 322.6 cm -1 (1 -) over the ground state. The first trans level lies at 439 cm -1 (0), see Figure 1. dard Watson S-reduction Hamiltonian. However, the K a = 2 lines of 0 + state were found perturbed, as one could not fit these lines within experimental accuracy using a single state approach. To treat the tunneling splittings, we applied the method based on reduced-axissystem (RAS) method proposed by Pickett. [START_REF] Pickett | Vibration-Rotation Interactions and the Choice of Rotating Axes for Polyatomic Molecules[END_REF] It is well suited for molecules with a double minimum-potential. In matrix form, in the basis of individual wavefunctions of each tunneling substate |0 + and |0 -, the RAS Hamiltonian has the following form:

H =    H rot -H ∆ H I H I H rot + H ∆    (3)
In Eq.3, H rot is the standard Watson S-reduction Hamiltonian in the I r coordinate representation, H ∆ is the part of the Hamiltonian that allows fitting averaged rotational constants for both tunneling substates:

H ∆ = E * + E * J P 2 + E * K P 2 z + E * 2 (P 2 + + P 2 -) + ... (4)
with the energy difference between two substates ∆E = 2E * . Such definition of the Hamiltonian has two main advantages. First, a unique set of rotational and centrifugal distortion parameters permits an easier comparison with quantum chemical calculations. Second, this method is more robust and avoids correlations between different rotational and Coriolis coupling parameters. In Eq. 3, H I is a perturbation Hamiltonian containing F xy (P x P y + P y P x ),

and F yz (P y P z +P z P y ) terms, and their centrifugal distortion corrections. These non-diagonal terms determine the orientation of the reduced axis system with respect to the principal axis system.

The convergence of non-linear least-squares fit strongly depends on initial conditions. In the case of HBN, among the terms of the RAS Hamiltonian, those describing the interaction between tunneling substates, ∆E and F , initially were rather poorly determined. This may be a typical situation for the first stage of spectral analysis with limited number of At this stage, one may now let ∆E parameter to vary in order to refine the global solution.

In the case of gauche-HBN, the ∆E value refined after obtaining initial approximation at 135 GHz permitted to locate in the spectrum the origins of c Q 1,0 bands that connect two tunneling substates. The assignment and fit of rotational transitions of such bands leaded to accurate determination of ∆E, and removed its correlation with F parameters.

The following assignment was performed in a usual "bootstrap" manner starting from the results of the initial analysis and progressively adding newly assigned lines, and when needed, also adding new parameters in the model. In total, we assigned almost 3000 distinct frequency lines of gauche-HBN. These lines were fitted with overall rms of 0.035 MHz using the model of the RAS Hamiltonian that contains 34 parameters. The complete list of measured rotational transitions of gauche-HBN in the ground vibrational state is available in Supporting Information.

The values of J quantum numbers of transitions included in the fit range from 8 up to 129.

As for the values of K a , the dataset of fitted lines contains the rotational transitions with K a ≤ 17. The limitation in K a was necessary as we were not able to fit within experimental accuracy the lines with higher values of K a . In attempt to fit these lines, one had to include in the model 10th order rotational terms. The determined values of P 10 terms had the Therefore, such high-K a levels cannot be described by the same potential energy terms as low-K a levels. In this case, one has to redefine the PES, which also implies the redefinition of centrifugal distortion parameters, and consequently may lead to the Hamiltonian convergence problems.

This problem may also be considered from the point of view of the RAS approach.

The RAS method uses first order perturbation theory to treat the internal motion with double minimum potential. As the amplitude of vibrational motion may be linked to the barrier height, one may conclude that the RAS method is suitable for molecules with high barrier to internal rotation. Previously it was also shown that the RAS method is closely related to internal-axis-method (IAM) type models developed by Hougen and coworkers [START_REF] Hougen | A generalized internal axis method for high barrier tunneling problems, as applied to the water dimer[END_REF][START_REF] Ohashi | The torsional-wagging tunneling problem and the torsionalwagging-rotational problem in methylamine[END_REF][START_REF] Coudert | Tunneling splittings in the water dimer: Further development of the theory[END_REF] for molecules with several large amplitude motions. Indeed, both approaches consider the problem in terms of a phenomenological Hamiltonian, and a set of splittings which arise from tunneling of the system between equivalent non-superimposable configurations of the molecule. Both methods allow taking into account the Coriolis interaction between the tunneling motion and the overall rotation of the molecule. As the RAS method, the IAM formalism provides good convergence in high-barrier cases, because it requires the localization of individual vibrational wave functions in each minimum on PES. HBN may be considered as a molecule with medium or low barrier to internal rotation, as the first excited OH-torsional state lies very close to the top of the barrier. Therefore, the application of RAS or IAM-type models has some limitations, as it was found in the present study.

The results of the fit are presented in

Conclusions

The results of this study represent the first spectroscopic characterization of gauche conformation of 4-hydroxy-2-butynenitrile in the frequency range up to 500 GHz. We assigned and analyzed the rotational spectrum of the most stable gauche conformation of HBN. The assignment was complicated by tunneling splittings owing to large amplitude motion of the OH group. The analysis was aided by high-level quantum chemical calculations, and by the method of finding the global solution of least-squares fit. The latter proved to be very useful tool for the initial stage of spectral analysis, in the case when the information on the torsion-rotational part of the problem is limited by the results of theoretical calculations.

The final set or molecular parameters allow accurate frequency predictions throughout all the frequency range where strong lines of HBN may be found, including interpolation of spectral predictions below 50 GHz. The calculated frequency predictions at temperature of 300 K are available in Supporting Information. Thus, the results of the present study

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 33 recorded in the frequency ranges 50 -110 GHz, 150 -195 GHz, 225 -330 GHz and 400 -500 GHz. As a radiation source in the spectrometer, we use commercially available frequency multiplication chains that are driven by home-made fast sweep frequency synthesizer. In the of 23 ACS Paragon Plus Environment The Journal of Physical Chemistry A c c e p t e d m a n u s c r i t p t frequency range 50 -75 GHz we use active frequency multiplier x4 from Millitech. In the frequency range 75 -110 GHz the source is active multiplier x6 from VDI. At higher frequencies, we use passive frequency multiplication of the VDI source by factors 2, 3, 5, etc. The fast sweep system is based on the up-conversion of AD9915 direct digital synthesizer (DDS) operating between 320 and 420 MHz into Ku band by mixing the signals from AD9915 and Agilent E8257 synthesizers with subsequent sideband filtering. The DDS provides rapid frequency scan with up to 50 µs/point frequency switching rate. Because of the HBN line weakness the spectrum was scanned with slower rate of 5 ms/point or 10 ms/point depending on the frequency range. As an absorption cell in the spectrometer we used a stainless steel tube of 10 cm in diameter, and 2 m long. Owing to good stability of the synthesized sample of HBN under room temperature, the measurements were performed in a static mode with practically constant amount of the sample and consequently constant gas pressure in the absorption cell. Nevertheless, to minimize observations of decomposition products in the spectra, the absorption cell was pumped out and refilled with new sample of HBN at optimum pressure of about 20 Pa every 3-4 hours.

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Figure 1 : 8 ACS

 18 Figure 1: CCSD(T)-F12 potential energy of HBN as a function of the hydroxyl group internal rotation coordinate

Figure 2 : 9 Page

 29 Figure 2: The rotational spectrum of HBN between 85 GHz and 93 GHz. The band heads of a R 0,1 series transitions can be clearly distinguished. Since the band head frequency may be approximated as (B + C)(J + 1) one can easily provide the assignment of the quantum number J for each series, as well as the initial correction for B and C rotational constants.

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 1011 assigned lines. Due to relatively weak µ c dipole moment component and dense spectrum, s c r i t p t the assignment of 0 + ↔ 0 -transitions of HBN was not straightforward and therefore, the only information on the ∆E term were the results of quantum chemical calculations. The F terms, describing orientation of the RAS with respect to the principal inertia axes were roughly estimated from optimized molecular geometry. In addition, ∆E and F terms are highly correlated, and least-squares fit may diverge rather rapidly, when the initial values of these two parameters are far from global solution.To search for the global solution, we applied the following method. To remove the correlation between ∆E and F in the least-squares fit, one of the parameters is fixed. The method consists in performing a series of fits with different values of the fixed parameter (FP). The range of FP values in the series of fits is chosen on the basis of reasonable initial approximation, e.g. from quantum chemical calculations. Then, one can plot the root-meansquare (rms) deviation of each fit as a function of FP. The global solution should correspond to the minimum on the rms(FP) plot. It should be noted, that the method allows finding initial convergence point for global solution provided that the Hamiltonian does not contain redundant terms that may effectively take the Coriolis interaction into account. The method was implemented in a computer program. The program prepares a set of input .par files with different FP values for SPFIT code. Then, the program starts SPFIT for each .par file from the set, and performs the analysis of corresponding generated .fit file with the results of the least-squares fit. The program output contains the values of rms, FP, number of iterations, as well as the information whether the convergence was achieved.In the case of searching for global solution of the torsion-rotational problem of gauche-HBN, we preferred to fix the ∆E parameter as it has direct physical meaning of the energy difference between tunneling substates. We performed a series of fits with ∆E parameters fixed to the values in the range between 100 and 230 GHz that encompasses the value of 173.3 GHz determined from quantum chemical calculations. The dataset of fitted lines included 49 transitions with 18 ≤ J ≤ 26, and K a ≤ 2. The Hamiltonian model employed in the initial series of fits contained 13 varied parameters: three

Figure 3 : 12 Page

 312 Figure 3: Root-mean-square deviation of least-squares fits of the experimental data to the model Hamiltonian of Eq. 3 as a function of the energy difference ∆E between two tunneling substates. The ∆E was fixed in each fit. The points represent the results of the fits in which convergence was achieved after a maximum of 15 iterations. The dashed line corresponds to experimental accuracy.

13

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A c c e p t e d m a n u s c r i t p t

  s c r i t p t represent a solid basis for the searches of HBN in the interstellar medium.

A c c e p t e d m a n u s c r i t p t X

 t -ray Structure and Photochemistry; Towards an Explanation of Its Formation in the Interstellar Medium. Chemistry-A European Journal 2013, 19, 17683-17686. (14) Kerisit, N.; Rouxel, C.; Colombel-Rouen, S.; Toupet, L.; Guillemin, J.-C.; Trolez, Y. Synthesis, Chemistry, and Photochemistry of Methylcyanobutadiyne in the Context of Space Science. The Journal of Organic Chemistry 2016, 81, 3560-3567. (15) Askeland, E.; Møllendal, H.; Uggerud, E.; Guillemin, J.-C.; Aviles Moreno, J.-R.; Demaison, J.; Huet, T. R. Microwave spectrum, structure, and quantum chemical studies of a compound of potential astrochemical and astrobiological interest: Z-3-amino-2propenenitrile. The Journal of Physical Chemistry A 2006, 110, 12572-12584. (16) Møllendal, H.; Margulès, L.; Belloche, A.; Motiyenko, R.; Konovalov, A.; Menten, K.; Guillemin, J.-C. Rotational spectrum of a chiral amino acid precursor, 2-aminopropionitrile, and searches for it in Sagittarius B2 (N). Astronomy & Astrophysics 2012, 538, A51. (17) Møllendal, H.; Margulès, L.; Motiyenko, R. A.; Larsen, N. W.; Guillemin, J.-C. Rotational spectrum and conformational composition of cyanoacetaldehyde, a compound of potential prebiotic and astrochemical interest. The Journal of Physical Chemistry A 2012, 116, 4047-4056. (18) Friberg, P.; Hjalmarson, A.; Guelin, M.; Irvine, W. Interstellar C3N-Detection in Taurus dark clouds. The Astrophysical Journal 1980, 241, L99-L103.(19) Ohishi, M.; Irvine, W. M.; Kaifu, N. Molecular abundance variations among and within cold, dark molecular clouds (rp). Astrochemistry of Cosmic Phenomena. 1992; p 171. (20) Fleming, F. F.; Gudipati, V.; Steward, O. W. Alkynenitriles: stereoselective chelation controlled conjugate addition-alkylations. Tetrahedron 2003, 59, 5585-5593. s c r i t p t

Table 1 :

 1 Calculated equilibrium and ground-state rotational constants (MHz), energies and conformational barriers (cm -1 ), and dipole moments (Debye) for HOCH 2 CCCN.

	Parameter	gauche-HOCH 2 CCCN trans-HOCH 2 CCCN
	A e	26032.92	27964.26
	B e	1321.39	1320.38
	C e	1270.95	1270.90
	A 0	25989.27	27997.46
	B 0	1325.56	1326.98
	C 0	1273.50	1272.18
	∆E	447.3
	V (gauche-gauche)	325.7
	V (gauche-trans)	522.2
	µ	4.21	6.33
	µ a	3.85	5.91
	µ b	1.13	2.26
	µ c	1.25	0.0

Table 2 :

 2 Rotational parameters of gauche conformer of HBN same orders of magnitude as the values of corresponding P 8 terms which indicated that the Hamiltonian did not converge properly. This problem may be explained by relatively high energies of the levels with K a > 17. According to our estimations, these levels lie well above the barrier to OH torsion and correspond to almost free rotation of hydroxyl hydrogen.

		The Journal of Physical Chemistry	Page 14 of 23
		Rotation	Torsion
	Parameters	Experiment	Theory Parameters	Experiment
	A (MHz)	26133.1112(37) a 25989.27 ∆E (MHz) 136489.634(33)
	B (MHz)	1327.134505(64) 1325.56 E * J (MHz)	0.2041645(74)
	C (MHz)	1275.291296(60) 1273.50 E * K (MHz)	-8.97442(52)
	D J (kHz)	0.1539735(73)	0.1539 E * 2 (MHz)	0.031360(12)
	D JK (kHz)	-19.6762(10)	-19.02 E * JJ (kHz) -0.00043230(89)
	D K (kHz)	1893.157(45)	1785. E * JK (kHz)	-0.05429(32)
	d 1 (kHz)	-0.0235088(32)	-0.0231 E * KK (kHz)	2.8111(44)
	d 2 (kHz)	-0.0014701(14) -0.00133 E * 2J (Hz)	-0.09999(69)
	H J (Hz)	0.00018783(55)	F yz (MHz)	20.77149(38)
	H JK (Hz)	-0.018962(67)	F xy (MHz)	-0.41929(28)
	H KJ (Hz)	-1.4549(67)	F yzJ (kHz)	0.014185(87)
	H K (Hz)	273.68(18)	F yzK (kHz)	-5.751(61)
	h 1 (mHz)	0.04955(11)	F xyJ (kHz)	-0.001791(15)
	h 2 (mHz)	0.007578(82)	F xyK (kHz)	-4.161(95)
	h 3 (mHz)	0.001110(22)	F 2xy (kHz)	-0.001307(25)
	L J (µHz)	-0.000329(14)
	L JJK (µHz)	0.0449(17)
	L JK (mHz)	-0.01096(20)
	L KJ (mHz)	-0.305(12)
	a Numbers in parentheses are two standard deviations in the same units
	as the last digit.
			14
		ACS Paragon Plus Environment

Table 2 .

 2 The calculated energy difference ∆E = 136489.634(33) MHz is lower than predicted from quantum chemical calculations suggesting that the barrier to OH torsion should be slightly higher than the value obtained from vibrationally corrected 1D-PES. The results of the present study may be compared to the results of similar molecule 2-hydroxyacetonitrile (HOCH 2 CN, HAN)[START_REF] Margulès | Submillimeter spectra of 2-hydroxyacetonitrile (glycolonitrile; HOCH2CN) and its searches in GBT PRIMOS observations of Sgr B2 (N)[END_REF] . For HAN, the same variational approach in solving the vibrational Hamiltonian yielded theoretical value of ∆E which was lower than experimentally determined ∆E. Recently, we studied the problem of OH torsion for conformer III of methoxymethanol[START_REF] Motiyenko | Laboratory spectroscopy of methoxymethanol in the millimeter-wave range[END_REF] . Theoretical calculations suggested that the barrier to OH torsion for conformer III is 492 cm -1 , being higher than for HAN. Therefore, one had to search for the initial solution with ∆E lower than the corresponding value for HAN. Using this assumption we rapidly found the initial convergence point with ∆E around 90 GHz, and further refinement yielded the value of ∆E = 90678.0(11) MHz for conformer III of methoxymethanol. In all these cases, theoretical calculations provided a good starting point in searching for initial global solution of the torsional-rotational problem using the method described above.

	15

Acknowledgement

This work was supported by the French Programme National "Physique et Chimie du Milieu Interstellaire" (PCMI) of CNRS/INSU with INC/INP co-funded by CEA and CNES, and by the ANR-13-BS05-0008 IMOLABS of the French Agence Nationale de la Recherche. The authors also thank the projects FIS2013-40626-P and FIS2016-76418-P (Spanish ministry of economy) and CESGA and CTI-CSIC computers centers. ACS Paragon Plus Environment The Journal of Physical Chemistry

Supporting Information Available

Measured frequencies, and calculated predictions of the rotational spectrum of gauche-HBN up to 500 GHz. This material is available free of charge via the Internet at http://pubs. acs.org/.

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The Journal of Physical Chemistry


Thomas Chabot
email: thomas.t.chabot@airbus.com

Keyvan Kanani
email: keyvan.kanani@airbus.com

Alexandre Pollini
email: alexandre.pollini@csem.ch

François Chaumette
email: francois.chaumette@inria.fr

Eric Marchand
email: eric.marchand@irisa.fr

Jason Forshaw
email: j.forshaw@surrey.ac.uk

VISION-BASED NAVIGATION EXPERIMENT ONBOARD THE REMOVEDEBRIS MISSION

Airbus has been strongly involved in the design of Vision-Based Navigation (VBN) systems over the last years, with particular focus on applications such as planetary landing and orbital rendezvous. Based on this background and due to the increasing interest in Active Debris Removal (ADR), solutions for autonomous, vision-based navigation for non-cooperative rendezvous have been investigated. Dedicated image processing and navigation algorithms have been designed at Airbus and INRIA to meet this specific case, and some of them have already been tested over synthetic images and actual pictures of various spacecraft.

As the next step, a VBN experiment will be conducted onboard the upcoming RemoveDebris ADR demonstration mission. The RemoveDEBRIS mission, sponsored by the European Commission FP7 programme, started in 2013 and will launch to the International Space Station late 2017 from where it will be deployed to a 400km orbit. In addition to the VBN experiment, the mission will perform other ADR experiments such as net and harpoon capture and dragsail de-orbiting.

The VBN experiment will validate vision-based navigation equipment and algorithms, through ground-based processing of actual images acquired in flight of a debris mock-up target, in conditions fully representative of ADR. It will demonstrate state-of-the-art image processing and navigation algorithms based on actual flight data, acquired through three different but complementary sensors: two standard cameras, and a flash imaging LiDAR developed by CSEM, and validate a flash imaging LiDAR in flight.

Introduction

Orbital rendezvous in low Earth orbit has been mastered since the sixties, firstly initiated onboard US Gemini and Russian Soyuz spaceships, performed either manually or in an automated way. Orbital rendezvous subsequently became an essential technique in order to successfully assemble and service Earth-orbiting space stations and satellites, or perform lunar exploration. In the past few years, new mission concepts, and in particular Active Debris Removal (ADR), have led to the occurrence of new challenges regarding orbital rendezvous in general and relative navigation in particular.

For most rendezvous missions including ADR, navigation must be able to provide relative state estimates over a wide range of relative distances, from early detection until target capture. Depending on the specific rendezvous phase, these state estimates can be relative position and velocity only (3-DoF relative navigation), or relative position, velocity and attitude (6-DoF relative navigation). In the frame of ADR missions, the navigation function must also be robust to uncertainties regarding the target debris trajectory, its shape, rotation state, inertia characteristics, etc. The navigation function must be compatible with uncooperative targets, possibly tumbling and bearing no navigation aid whatsoever. Depending on the capture means, debris capture may require accurate relative attitude estimation. Finally, navigation must also fulfill new functions such as target identification, which consists of evaluating the target rotation state as well as reconstructing its shape if need be.

In order to address these challenges, several navigation solutions have been designed by Airbus and selected partners and will be described in this paper. Regarding 3-DoF relative navigation, a solution based on a passive, standard camera and innovative image processing algorithms (for LOS estimation at long distances and LOS plus range estimation at shorter distances) coupled with an Extended Kalman Filter (EKF) for navigation and relative states estimation has been proposed. At shorter ranges, two solutions for 6-DoF relative navigation have been proposed. The first one relies on an active flash imaging LiDAR, whose outputs are fused with Inertial Measurement Unit (IMU) and attitude sensing data in an EKF. The second solution relies on a passive standard camera and state-of-the-art image processing algorithms that provide pseudo-measurements, also fused with IMU and attitude sensing data in the navigation filter.

As a natural next step in order to prepare for future missions, these technologies are now foreseen to be demonstrated on actual space missions. The proposed navigation solutions will be implemented and demonstrated on the RemoveDebris demonstration mission. This mission is due for launch in late 2017 and will constitute the world's first demonstration of ADR to date. This demonstration will considerably raise the Technology Readiness Level (TRL) of the navigation solutions proposed by Airbus and demonstrate their performance and robustness in a flight context.

The RemoveDebris mission

RemoveDebris is a low cost mission (€15.2M) performing key active debris removal (ADR) technology demonstrations including the use of a net, a harpoon, vision-based navigation (VBN) and a dragsail in a realistic space operational environment. For the purposes of the mission CubeSats are ejected then used as targets instead of real space debris, which is an important step towards a fully operational ADR mission.

The project, led by the Surrey Space Centre, University of Surrey, consists of a consortium of 10 international partners including Airbus Germany, France and UK, and is co-funded by the European Commission in the framework of the FP7 programme. The mission proposed by the RemoveDebris project will be the world's first, and perhaps the most important demonstration of ADR to date, and the technologies that will be developed under the project have been strategically selected for their importance in future ADR activities.

The mission is targeting late 2017 for launch using the NanoRacks procurement service and via a SpaceX cargo launch to the International Space Station (ISS); from there, the satellite will be ejected and will start its main mission.

Main platform

An accommodation study of the main platform and its various payloads is shown below. The payload panel contains all the hardware for the demonstrations including: 2 x CubeSats, net, harpoon target assembly, VBN suite, dragsail. Multiple supervision cameras help record the experiments.

Experimental demonstrations

The four demonstrations undertaken are as follows: (i) in the net experiment, a CubeSat (called DebrisSat-1) is ejected and a net is fired at the CubeSat, (ii) for the VBN experiment, another CubeSat (called DebrisSat-2) is ejected and data is collected from the VBN suite, the platform and the CubeSat, (iii) in the harpoon experiment, a harpoon is fired at a target plate which is extended away from the platform on a carbon fibre boom, (iv) the final experiment is the dragsail which will rapidly de-orbit the main platform on conclusion of the mission. In this paper concentration is given to the VBN suite which includes a standard 2D camera and a flash imaging LiDAR. It is also completed by an additional, 2D camera. The data and imagery collected from the various sources are downloaded to the ground and post-processed offline.

Further information about the mission concept, payload testing and operational timelines is available in [START_REF] Removedebris | An in-orbit active debris removal demonstration mission[END_REF], [START_REF] Forshaw | Review of Final payload test results for the RemoveDebris active debris removal[END_REF] and [START_REF] Forshaw | The RemoveDebris ADR mission: preparing for an international space station launch[END_REF].

VBN demonstration

Introduction

The VBN demonstration will fulfil the following top-level objectives:

• Demonstrate state-of-the-art image processing and navigation algorithms based on actual flight data, acquired through three different but complementary sensors: two standard cameras, and a flash imaging LiDAR developed by CSEM, • Validate a flash imaging LiDAR in flight, raising its system TRL to level 7-8

In order to fulfil these objectives, all the data acquired during the VBN experiment will be processed on the ground with innovative algorithms (e.g. 2D/3D and 3D/3D matching techniques detailed in §4.3) and specifically tuned navigation algorithms based on an EKF able to fuse data from different sensors (e.g. camera images and attitude sensing data).

During the VBN experiment image acquisition will be performed by the so-called VBN payload, which is an equipment specifically designed by CSEM in the frame of the RemoveDebris project, and which includes two different sensors: a standard camera, and a flash imaging LiDAR. The VBN payload, fully detailed in §3.2, is also completed by an additional, complementary 2D camera which is provided by SSTL.

GPS measurements from both target and chaser and onboard attitude estimation software will provide "ground truth" data against which the navigation algorithms outputs will be compared for validation and performance assessment. Post-processing activities will allow demonstration of performances of innovative 2D camera based navigation and 3D camera based navigation, allowing not only estimation of relative position and velocity but also relative attitude, one of the key drivers of successful capture of an uncooperative target.

In the following, the VBN payload and the VBN demonstration scenario are described in further details.

VBN payload

The role of the VBN payload is to capture standard color 2D and 3D images of debris and to transfer the data to the satellite. The times at which images have to be taken are programmed by the satellite on-board computer and transferred to the VBN payload as an array. The array's length is defined by the number of images to be taken in a given time window of the mission. It defines the sampling time of each image and its integration time. The VBN unit will acquire images in several time windows during the overall mission duration, especially during the harpoon and net deployments, and the release of the DebrisSat-1 and 2.

The VBN payload is developed by CSEM and is made of two vision-based sensors: a color camera and a flash imaging LiDAR. Both sensors are controlled by a supervision unit. Everything is integrated into a case sized 15 by 10 by 10 centimeters. RemoveDebris is a unique chance to evaluate in-orbit ADR technologies. It is a low-cost mission with a budget only a small fraction of a larger scale, operational ADR mission. The main challenge in this context for CSEM was to develop and build a proto-flight model (PFM) based on a sensor concept for which very limited background and key components were available in Europe at the time of the project proposal in 2012. CSEM's background was based on a flash LiDAR demonstrator made in 2009 in the frame of the Pseudo-Random Noise Continuous Wave Backscatter LiDAR Prototype project with ESA. Then, the European Commission granted the Flash Optical Sensor for Terrain Relative Robotic Navigation (FOSTERNAV) project that allowed to further develop the concept of flash imaging LiDAR hybridization with multiple operation modes and for several applications such as: landing, rendezvous and rover navigation. In the US, flash imaging LiDARs demonstrated their capabilities in the frame of the Autonomous Precision Landing and Hazard Detection and Avoidance Technology (ALHAT) program started in the early 2000's. Now, second generation flash imaging LiDARs are used on several test platforms such as MORPHEUS, a NASA project to develop a vertical takeoff and vertical landing test vehicle as well as an autonomous landing and hazard detection technology [START_REF]3D flash lidar performance in flight testing on the Morpheus autonomous, rocket-propelled lander to a lunar[END_REF], and RAVEN, a technology module to be affixed outside the ISS to test technologies for autonomous rendezvous in space [START_REF] Raven | an on-orbit relative navigation demonstration using international space station visiting vehicle[END_REF].

To some extent, the RAVEN approach is reproduced in the VBN payload: several vision-based sensors are integrated into a common housing. For comparison, RAVEN is composed of cameras in the visible and infrared spectral bands and a flash imaging LiDAR, whereas in the VBN payload, there are a flash imaging LiDAR and a camera in the visible spectral band.

The VBN payload is a hardware-software co-design, the main hardware components of which are: two vision detectors (a time-of-flight (TOF) detector and a half inch 3-Megapixel CMOS digital image detector), a VCSEL laser source at 805 nm, three micro-processors (supervision unit, LiDAR and camera management), one FPGA and two local memories of 2 GB each. The software is divided in four elements implemented in the three microprocessors and in the FPGA.

For RemoveDebris, raw data provided by the vision sensors are temporary stored in a local memory, then transferred to the satellite, and finally transmitted to Earth. Raw data contains very rich information from which different key figures can be extracted for autonomous navigation, such as: line of sight (LOS), distance, 3D geometry of the target and relative velocity.

Because of the limited budget, none of the selected VBN components were space qualified before the project started. Hence, a second challenge was to define a test plan compatible with the tight budget limitation but still enabling the assessment of the VBN functionalities and resistance to environmental constraints. Consequently, the test plan was elaborated in view of achieving the respective ultimate objectives for the functional and environmental tests while sparing some steps to be conducted in the frame of a more traditional approach. The ultimate objectives of both types of tests are:

• Test the VBN payload when programmed to capture 2000 LiDAR and 2000 camera images. This is the longest sequence foreseen for the mission. • Assess if the VBN payload with its non-space qualified components will sustain the environmental conditions found in a one year LEO mission.

The final functional tests consist in executing a long sequence of image capture and transmission through the communication interface. For this purpose a ground support equipment (GSE) simulating the interface with the satellite has been prepared. The GSE is made of a hardware and a Python application. The hardware reproduces the SPI bus of the communication interface (2x 4 lines) at 6 Mbit/s with twice four LVDS signals face. The Python application implements the proprietary communication protocol elaborated on purpose for RemoveDebris. The software allows generating communication frames to test the whole set of commands and answers from the protocol. The environmental tests present radiation, vibration and thermal aspects. The radiation aspect was addressed by design and analysis. A sufficiently thick housing made out of aluminum ensures protection of the VBN components against the expected level of radiation on LEO. The resistance to vibration and mechanical shock was verified by a series of random and sinusoidal tests. Random and sinusoidal tests were executed along the three axis with a success criteria defined as: 1. the first Eigenfrequency remains above 140 Hz, 2. between the start and the end of the vibration experiment, Eigenfrequencies do not shift by a value larger than 10%, 3. the amplitude variation of Eigenfrequencies remains below +/-6 dB before and after vibration experiment, 4. the payload captures and transfers 100 LiDAR and 100 camera images before and after the test.

The VBN payload was successfully tested according to the criteria defined here above. The first Eigenfrequency is situated at 522 Hz along the y-axis direction. The thermal aspect was validated with two series of tests made in an oven at ambient pressure, and in a thermal and vacuum chamber at 10 -6 mbar. Three cycles were executed. For the first cycle, the VBN payload was tested before and after the cycle at ambient temperature, and was off during the thermal cycle. For the second cycle, the VBN payload was switched on at the minimum temperature and in operation until the end of the cycle. For the third cycle, it was switched on at the maximum temperature and operation until the end of the cycle. The environmental tests demonstrate the ability of the VBN payload to be operational in the conditions foreseen for the mission.

Random test parameters

Definition of the axes

Sinusoidal test parameters

The VBN payload main features are summarized in the table below:

VBN demonstration scenario

Demonstration needs and constraints 3D and 2D images will be captured over the three main experiments: over the net, VBN, and harpoon experiment. Following commissioning operations, images will already be acquired when the net CubeSat (DebrisSat-1) is released for preliminary checks, monitoring purposes, as well as a first collection of imagery data covering the net experiment. In a second step, the VBN demonstration itself will start, and will consist in capturing images of the VBN CubeSat (DebrisSat-2) from ejection until subpixellic distance is reached while ensuring that the widest range of visual configurations (in terms of distance to target, relative attitude, light conditions, background) is achieved. In a third step, images of the harpoon target assembly will be collected during the harpoon experiment in order to complete the set of VBN data. The following focuses on the second step, i.e. the definition of the VBN demonstration strictly speaking.

The VBN demonstration scenario was defined in order to fulfill the following high-level needs:

• The demonstration scenario should allow to demonstrate different navigation techniques which are relevant for ADR ; this includes 3-DoF relative navigation and 6-DoF relative navigation, based on 2D images and 3D point cloud, used separately or combined, • The demonstration scenario should be sufficiently representative of ADR rendezvous operations, meaning that images should be acquired from very close range (when target fills the cameras field of view) to subpixellic distance, and relative velocities should be similar to operational ADR missions typical approach scenarios, • The demonstration scenario should demonstrate image processing algorithms performances and robustness to ADR conditions, meaning that images with different illumination conditions, with different backgrounds (i.e. dark background and Earth background), with still and spinning target should be acquired

In addition, it is expected that the total volume of acquired data should represent several 1000's of images. However, several constraints coming from various levels (e.g. mission, platform, CubeSat) of this ambitious but low cost demonstration mission had also to be taken into consideration in order to design the VBN scenario. They include the following:

• No propulsion: the lack of propulsion system forbids the possibility for the main platform or the target to perform orbital maneuvers, meaning that the VBN scenario has to be such that all demonstration needs must be met with a single acquisition sequence. • Open-loop pointing: considering that no operational sensor and corresponding GNC software could be flown onboard the mission to support real-time pointing of the payload boresight towards the flying targets, only open-loop pointing based on a priori knowledge of the target trajectory relatively to the main platform can be performed. This means that the VBN demonstration scenario has to be robust to various uncertainties. These include the platform attitude pointing performances, in the range of 5 deg (3σ), and the ejection accuracy, in the range of 20% (3σ) for the deployer ejection ΔV magnitude and 5 deg (3σ) for the deployer ejection ΔV direction accuracy. • Collision concerns: the risk of collision between the main platform and DebrisSat-2 should be minimized. This means that sufficient margins should be taken when designing the relative trajectory, in particular considering the level of uncertainties discussed just above.

• No star tracker: inertial attitude measurements are required in order to retrieve relative position and velocity in the LVLH frame from vision-based measurements obtained in camera frame. However, no star tracker will be available on the main platform, due to cost reasons. Inertial attitude measurements will instead be performed by taking pictures of star background with the VBN sensors, at a specific frequency and with the adapted exposure time.

VBN demonstration scenario definition

Due to the various constraints listed above, the ejection maneuver, which fully defines the VBN demonstration scenario, must be carefully defined in order to meet the demonstration needs in the most satisfactory manner. The magnitude of the ejection velocity has been selected at 2 cm/s, which is the minimum velocity which has been considered as reasonably achievable by the CubeSat deployer mechanism. The date and direction of ejection where then selected in order to:

• Minimize the relative drift between the main platform and DebrisSat-2, while keeping collision risk low enough, • Minimize the risk of losing the target while in open-loop pointing, • Maintain favorable observation conditions for the short range VBN algorithms, which leads to a Sun phase angle less than 45 deg (3σ) following separation and until the apparent size of the target is less than 50 pixels • Ensure that the target could be acquired with both Earth and dark backgrounds Trade-off analyses led to the selection of a direction of ejection close to the Y-bar axis (perpendicular to the orbital plane), with smaller components along the R-bar and V-bar axes sized in order to meet the previously listed illumination, relative drift, collision, and background criteria in a satisfactory manner. This direction of ejection leads to the trajectory which is illustrated hereafter on Figure 7: As illustrated on Figure 7, the relative trajectory may be divided in four phases:

1. A blind zone phase following ejection, where DebrisSat-2 is too close to the main platform to be visible within the VBN sensors field of views 2. A close range phase, where DebrisSat-2 is extended within the VBN sensors field of view.

This phase starts at the end of the blind zone phase and ends when DebrisSat-2 apparent size in the 2D camera detector array is around 50 pixels. Specific image processing algorithms may be used during this phase. 3. A medium range phase, where DebrisSat-2 is still resolved in the 2D camera field of view, but insufficiently to allow the image processing algorithms mentioned in the close range phase to operate with enough confidence. However, range estimation is still possible. This phase corresponds to a size in the detector field of view between 20 and 50 pixels. 4. A far range phase, where DebrisSat-2 is insufficiently extended in the camera field of view to enable range estimation. Only line-of-sight (LOS) to the target may be measured. This phase starts when the target is smaller than 20 pixels and continues until the end of the demonstration, covering at least 9 orbits.

The background evolution along the relative trajectory is shown hereafter on Figure 8 : Based on the resulting trajectory and the VBN sensors characteristics in terms of frame rate and data storage, a complete image acquisition sequence for the three sensors (flash imaging LiDAR, two standard cameras) was generated, cumulating a total of roughly 4500 images and approximately 5 GB of data.

Impact of dispersions

As mentioned before, the VBN scenario and relative trajectory are subject to a high level of dispersions due to platform attitude pointing performances, in the range of 5 deg (3σ), and ejection accuracy, in the range of 20% (3σ) for the deployer ejection ΔV magnitude and 5 deg (3σ) for the deployer ejection ΔV direction accuracy. The impacts of these uncertainties on the range and illumination conditions are illustrated on Figure 9 : Since only open-loop attitude pointing of the platform is possible, the most critical impact of dispersions at ejection relates to the angular error between the a priori and actual directions of DebrisSat-2. This angular error is illustrated on Figure 10. Figure 10 shows that DebrisSat-2 remains in the field of view of the cameras for the whole trajectory, except for a few cases where it exits the field of view for a finite duration. Over the whole trajectory, the success rate (i.e. probability that the target is within the cameras field of view at any given time) remains higher than 98.5% which was deemed acceptable.

VBN algorithms 4.1 Functional architecture

A standard functional architecture for orbital rendezvous VBN is shown hereafter on Figure 11. The sensors to be considered are typically a camera (or a flash imaging LiDAR), an IMU, and a star tracker. The image processing building block considered in this example is a model-based tracking algorithm (such as 2D/3D matching described in §4.3). The star tracker and the IMU outputs are combined by an attitude estimator in order to provide the best spacecraft inertial attitude estimate to the hybrid navigation filter, which computes the spacecraft states w.r.t its target. Note that the image processing building block may require aiding from the navigation filter. For RemoveDebris, different image processing algorithms are to be considered. As discussed in §3.3 the relative trajectory may be divided in a close range phase, a medium range phase, and a far range phase. During the close range phase, the target is sufficiently resolved in the VBN cameras field of view so that relative attitude may be estimated and 6-DoF navigation be performed. The related image processing algorithms are described in §4.3. During the medium and far range phase, the target is too far for relative attitude to be estimated, and only 3-DoF navigation may be achieved. The related image processing algorithms are now discussed in §4.2. Navigation algorithms are described in §4.4.

Navigation Image processing Sensors

Image processing for 3-DoF relative navigation

The measurement available for relative navigation evolves throughout the rendezvous phase. When target apparent size is smaller than 1 pixel, the centre of mass can be merged with the centre of brightness. The image processing algorithms task is to detect the target and to find its subpixelic location, which, due to low brightness, may be difficult to distinguish from the stellar background.

The performances depend strongly on the target albedo, on the relative range and velocity. Relative navigation is then based on LOS measurements.

When the target extension in the field of view is larger than 1 pixel, simple image processing to find the barycenter of the target may be used. The illuminated pixel may be weighted depending on the target shape. Relative navigation is still based on LOS measurements.

Once the target is resolved, distance can be extracted, using knowledge of the target size and shape.

For instance in the Mars Sample Return (MSR) case, which shows some commonalities with ADR missions including rendezvous and capture, the target is a spherical sample canister and the goal of image processing is to position a circle over the canister with the center located over the sample canister center of mass and a radius equal to the actual size of the sample canister in the camera image. During the MREP Camera ESA study [START_REF] Chabot | Relative navigation challenges and solutions for autonomous orbital[END_REF], a trade-off including various image processing techniques has been performed by Airbus and Sodern, and led to the design of an algorithm based on Hough transform. The outputs of this algorithm are illustrated hereafter on Figure 12: Robustness and performance analyses over the last 100m have been performed with regard to Sun phase angle variations (illumination condition variations), range variations, the presence of Mars or Phobos in the field of view, the canister proper motion (up to 5 deg/s) and the occurrence of solar flare. Simulations have shown that the error in range measurement remains lower than 10% at 1σ and that LOS measurement error is lower than 0.01deg at 1σ. Since MSR, a more generic solution, based on template matching has been developed by Airbus. Originally dedicated to asteroid, it can easily be adapted to satellite-like targets, as it can manage any target shape. Template matching has recently been tested in the frame of the FP7 NeoShield-2 project [START_REF]NeoShield-2: design and end-to-end validation of an autonomous closed-loop GNC system for asteroid kinetic impactor missions[END_REF]. It will be used and tested on RemoveDebris images.

3D/3D matching

The first relative navigation solution relies on 3D pictures, provided by an active sensor, and a 3D model of the debris, either a priori known or estimated during the identification phase. 3D pictures are provided by state of the art 3D flash imaging LiDAR, developed in the frame of the FP7 projects Fosternav and RemoveDebris. The key components of flash imaging LiDAR are the laser illuminating the target and the receiver detector array. These two elements are operated in full synchronisation in order to generate three dimensional images of the target. The device determines either directly the time-of-flight (TOF) of photons with counters that started with optical pulse emission and stopped by the back-reflected signal or indirectly by measuring the phase difference between the modulated illuminating laser beam and the incoming back-reflected light per pixel.

Regarding image processing, many publications on 3D cloud matching are available [8][9]. It is typically model-based, as it aims to match the 3D model of the debris with the 3D point cloud provided by the camera. Many algorithms have been developed in the computer vision domain to solve this problem, but for different applications such as search in 3D database or object recognition. The relative navigation solution therefore consists of a 3D camera that provides 3D pictures to image processing for matching with a known model. As there is always an ambiguity between pure rotation and translation of the target within FOV, fusion of IMU data within the navigation filter is needed. As a result, reliable estimation of relative position, velocity and attitude are provided by the proposed navigation solution. Initialization Initialization aims at detecting the target in an image sequence and at providing the tracking with an initial guess of the target pose, without any prior information on the pose. It consists of matching (detection/matching stage) the image contours with a database of views built during the identification phase. This initialization is done stepwise.

Identification learning : a hierarchical model view graph leading to prototype views of the model is built. Each node of the view graph contains an image projection of the target contours at a particular point of view. The points of view are sampled on a sphere. The sampling of the views is optimized to limit the memory size of the database and to ensure the whole coverage of the space of possible views. Online target detection : silhouette of the target is extracted in the image using bilayer segmentation techniques. This method consists in minimizing an energy function combining motion and color, along with time and space priors. It allows distinguishing the foreground shape from the background and has the advantage of being real-time.

Online matching and pose initialization : the view graph is then explored to find the prototype view whose contours correspond the most to the extracted silhouette. It considers both distance and orientation of edges to match: once the closest prototype view is found, its associated pose is considered as initialization of the target pose. The matching stage can be rather time consuming. To cope with real time constraints, a Bayesian framework is set to spread the initialization over several images (time domain initialization). It enables to provide an up to date pose initialization to the GNC system.

Tracking

Once the target has been detected in the image, and its pose has been initialized, a frame to frame edge tracking is performed. Like initialization, tracking is then 3D model based. It aims at finding the target pose which makes the best match of the projection of the 3D model with the image edges.

Tracking and pose estimation are thus simultaneous. Unlike initialization, edge matching is local. As a consequence, tracking runs in real time but is less robust to high differences between edges, meaning that the predicted target pose shall be close enough (a few pixels) to the actual one. Edge-based tracking can be combined with other modalities, such as color (local histograms describing the local distribution of colors or gray levels on each side of the projected edge) and texture-based features (Kanade-Lucas-Tomasi features), thus increasing the robustness of the tracker [START_REF] Petit | Combining Complementary Edge, Point And Color Cues In Model-Based Tracking For Highly Dynamic Scenes[END_REF]. The tracking algorithm has been successfully validated on real images, as shown on Figure 17 and Figure 18.

Navigation algorithms

The vision based navigation solution presented in this paper for rendezvous is based on image processing measurements hybridization with inertial measurements. This results in a simple yet efficient design, where the core hybrid navigation Extended Kalman Filter (EKF) is able to receive visual measurements from various sensors or image processing algorithms.

The main component of the navigation consists of an Extended Kalman Filter. This filter has been developed by Airbus as a generic filter based on sensor models [START_REF] Kerambrun | Autonomous Rendezvous System: the HARVD Solution[END_REF]. The filter core is the same: only the processed measurements change. The navigation is based on LOS measurement for far range, on LOS and range measurements for medium range, and on relative position and attitude measurements for close range. The navigation filter architecture is designed to be versatile enough in order to be compatible with a whole rendezvous mission, from far range detection to capture. It is composed of the main EKF and its measurement buffers, together with a Least-Square filter designed to handle large initial dispersions which may be incompatible with the relative motion linearization assumptions used by the EKF. Although not strictly needed for ADR missions where good initial estimates of the target orbit around the Earth may be provided from ground observation means, this Least-Square filter is also part of the generic rendezvous navigation solution since it is needed for rendezvous missions where the target orbit is poorly known, such as Mars Sample Return for instance.

Simulation results

Simulation tools were used in order to support the definition of the VBN demonstration scenario as well as to perform a preliminary validation of the navigation algorithms. Synthetic images were produced with a high level of fidelity by a rendering tool developed internally at Airbus and called SurRender.

SurRender is an image simulation software developed since 2011 by Airbus and dedicated to space scene modelling:

• It handles various space objects such as planets, asteroids, and spacecraft.

• It is optimized for space scenes: it handles solar-system sized scenes without precision loss and optimizes the raytracing process to explicitly target objects. • It produces physically accurate images with quantitative radiometric values, expressed in physical units (irradiance value per pixel in W.m -², or spectral irradiance in W.m -2 .Hz -1 ). • It performs complete sensor modelling, including PSF, distortion, motion blur, electronic noises, rolling shutter, and other low-level detector effects

Based on the relative trajectory described in §3.3 and on the selected illumination conditions, images corresponding to the whole VBN demonstration scenario could be generated by SurRender.

Examples of these images for various dates along the trajectory, indicating the available measurements and the corresponding image processing algorithms are shown on Figure 20 :

Conclusion

The RemoveDebris demonstration mission, including various ADR technology experiments, is now on track for a launch late 2017. Among others, it will include the Vision-Based Navigation demonstration composed of 3 sensors (an innovative flash imaging LiDAR and two standard cameras), a flying CubeSat target as well as navigation and image processing algorithms which will be used to process on ground the images and data acquired in flight. The proposed navigation and image processing algorithms offer navigation solutions that cover the full spectrum of relative navigation needs (including both 3-DoF and 6-DoF relative navigation) for Active Debris Removal, one of the most demanding orbital rendezvous mission concepts.

Simulation campaigns in high-fidelity simulation environments have been performed, validating the proposed VBN demonstration scenario as well as the image processing and navigation algorithms on synthetic images. The proposed navigation solutions will soon be validated on flight images acquired during the actual VBN demonstration. This demonstration will considerably raise the Technology Readiness Level (TRL) of the navigation solutions proposed by Airbus and demonstrate their performance and robustness in a flight context, paving the way towards the appropriate level of maturity for flight operations on future operational missions.

Figure 1 :

 1 Figure 1: Main Platform (view on to payload panel) [1]

Figure 2 :

 2 Figure 2: During the VBN demonstration, DebrisSat-2 is ejected from the main platform (left-hand side) and imagery is acquired while it drifts away (right-hand side)

Figure 3 :

 3 Figure 3: VBN payload proto-flight model (VBN PFM)

Figure 4 :

 4 Figure 4: Example of target used for the functional test of the VBN payload with the classical 2D image generated by the camera on the left and both images generated by the LiDAR (intensity and depth map) on the right

FrequencyFigure 5 :

 5 Figure 5: Random and sinusoidal vibration tests parameters

Figure 6 :

 6 Figure 6: Thermal and vacuum test setup (left) and temperature monitoring in the VBN payload (grey line).

Figure 7 :

 7 Figure 7: VBN scenario 4 phases on relative trajectory (blind zone in black, close range in red, medium range in blue, far range in green)

Figure 8 :

 8 Figure 8: Background evolution along the relative trajectory

Figure 9 :

 9 Figure 9: Impact of dispersions on illumination conditions (left-hand side) and range evolution (right-hand side)

Figure 10 :

 10 Figure 10: Angular dispersions

Figure 11 :

 11 Figure 11: Vision-based navigation functional architecture for orbital rendezvous

Figure 12 :

 12 Figure 12: OS detection at close range for various illumination conditions [7]

Figure 13 :

 13 Figure 13: Robustness to range variations for various illumination cases [7]

Figure 14 : 4 . 3

 1443 Figure 14: Template Matching principle [12]

Figure 15 :

 15 Figure 15: Example of 3D/3D matching algorithm. Matching 3D point cloud (depth map) with a priori known 3D model using ICP algorithm.

Figure 16 :

 16 Figure 16: Principle of initialization. Several views on a sphere are selected to produce prototype views stored in a hierarchical model view graph. Target is then extracted by segmentation and matched over successive frames with closest prototype [10].

Figure 17 :

 17 Figure 17: Principle of tracking. Tracking is performed using a frame (1) and the 3D model of the target (2). The salient edges of the target are extracted (3) and projected into image (4), given an initial pose. Pose is iteratively refined to make projection edges match with image edges (5).

Figure 18 :Figure 19 :

 1819 Figure 18: Example of tracking on real images of Soyouz (from [10])

Figure 20 :

 20 Figure 20: Navigation filter architecture

Figure 21 :

 21 Figure 21: Images sequence provided by Surrender and associated measurements

Figure 22 :

 22 Figure 22: Application of 2D/3D matching for close range rendezvous

Figure 23 :

 23 Figure 23: Errors on relative position estimation (with "METIS" image processing only in green, after filtering in blue)

Table 1 : VBN payload main features

 1

	Size [cm x cm x cm]	10 x 10 x 15	Flash imaging LiDAR resolution	160 x 120
	Mass [kg]	1.8	Flash imaging LiDAR half field-of-view [° x °]	8 x 6
	Average Power Consumption [W]	3.8	Flash imaging LiDAR integration time [s]	0.0001 to 2.6
			Flash imaging LiDAR
	Peak Power Consumption [W]	5.2	image rate [Hz] (capture and storage in non-volatile	0.2
			memory)
	Command and telemetry interface	2 redundant SPI x 4 LVDS lines	Flash imaging LiDAR ADC resolution [bits]	12
	Proprietary protocol		Ranging accuracy [m]	0.02-0.08 at 20 m 0.4 at 100 m
	DC voltage [V]	20-36	Camera resolution	2048 x 1536
	Temperature range in operation [°C]	-20 to 50	Camera field-of-view [° x °]	21 x 15
			Camera integration time [s]	0.001 -10
			Camera image rate [Hz]
			(capture and storage in non-volatile	0.1 (raw image)
			memory)
			Camera ADC resolution [bits]	10


Eduardo Durán Venegas

Stéphane Le Dizès

Generalized helical vortex structures

Helical vortex structures are found in the wake of rotors in the context of helicopters and wind turbines. In the simple Joukowski model, the wake is composed for each blade of a bound vortex on the blade and two free vortices emitted from its hub and tip [START_REF] Okulov | Theory of concentrated vortices[END_REF]. For a n-bladed rotor, when the hub vortex is exactly on the axis, this model can be matched far downstream to a homogeneous solution formed of n identical helices of same circulation Γ plus a central vortex of circulation -nΓ. This solution can then be described using analytic formulae [START_REF] Hardin | The velocity field induced by a helical vortex filament[END_REF] if the vortices are sufficiently concentrated. No such analytical solution exists when the hub vortex is not exactly on the main axis (or if the rotor has a single blade). In that case, we expect the far-downstream solution not to be homogeneous anymore. In the present work, we propose new spatially-periodic solutions formed of n pairs of vortices of opposite circulation that could be used to describe the far-field.

As in Hardin [START_REF] Hardin | The velocity field induced by a helical vortex filament[END_REF], we assume that the vortices can be described as vortex filaments of small core size a such that we can use the Biot & Savart law to compute the vortex-induced velocities [START_REF] Saffman | Vortex Dynamics[END_REF]. Each vortex filament is then discretized in small segments as in the free-vortex method [START_REF] Leishman | Principles of Helicopter Aerodynamics[END_REF]. We also assume that there exists a translating and rotating frame, characterized by an axial velocity V F and angular rotation Ω F in which the vortical structure is stationary. In this frame, at each point of the filament structure, the total velocity is then aligned along with the structure. The velocity field has three contributions: the frame velocity along e θ and e z , the self-induced velocity mainly along the binormal to the structure, and the mutual induction velocity associated with the other vortices. If we consider two uniform helical vortices of opposite circulation, same axis but different radii and pitches, it is easy to find the frame velocity that cancels the self-induction velocity of both helices. However, it is not possible to cancel the radial component of the mutual induction velocity. It is this contribution that is responsible of the deformation of the helices.

Here, we show that a stationary solution with a certain spatial periodicity still exists. The periodicity is in the sense that there exists an axial distance L > 0 and an angle 0 ≤ φ < 2π such that the radial locations of each vortex are invariant by the double operation of translation by L and rotation by φ. For a given number n of vortex pairs, the solutions are found to be characterized by only four geometrical parameters

R * = R int R ext , h = h int h ext , α = h ext h int , ε = a R ext (1)
where the equivalent radii R int and R ext , and pitches h int and h ext of internal and external deformed helices are defined as follows. The radii R int and R ext correspond to the radial locations of the two vortices when they have the same azimut. After one period, the two vortices are again at the same azimut, but one of the two vortices has performed one more rotation than the other (see figure 1). If α > 1, it is the internal vortex. In that case, Illustrations of typical solutions as R * increases are shown in figure 2. We do observe that the deformations of the helices become more important as R * gets close to 1. The strength of the deformation can be measured by the ratio

∆r max = max z |r int (z) -R int | R ext .
This ratio has been plotted in figure 3 as a function of R * for several values of n. We do observe an increase of ∆r max with R * for all n but the increase becomes weaker and weaker as n increases. For n = 3, the deformation is almost invisible for R * < 0.5. The frame velocity depends on the vortex circulation Γ. Two dimensionless parameters measuring the relative strength of the two components of the frame velocity, and of the vortex strength can be defined by

λ = R ext Ω F V F , η = Γ/R 2 ext Ω F .
The first parameter is the so-called tip-speed ratio. These parameters are functions of the 4 geometrical parameters mentioned above. Their variations with respect to the pitch ratio h are shown in figures 4 and 5 for a few values of R * . It is interesting to note that λ is weakly sensible to variations of R * . It also exhibits a decreasing behavior which qualitatively follows the behavior in 2π/h that we would have been obtained for a passive scalar advection. This limit should actually correspond to η = 0. We do observe in figure 5 that η is indeed relatively small for the corresponding parameters.

In the future, we intend to use these solutions as the far-field condition for the semi-infinite solution created from a rotor.

FIG. 1 :FIG. 2 :

 12 FIG.1: Definition of the parameters from a typical illustration of a deformed configuration for n = 1.

FIG. 3 :FIG. 4 :

 34 FIG.3: Maximum deformation ratio ∆r max as a function of R * for α = 0.5, = 0.05 and different numbers of vortex pairs.

FIG. 5 :

 5 FIG. 5: Variation of η with respect to h for different values of R * . Here α = 0.5, = 0.05 and n = 1.