Francesca Ferri

Özgür Karatekin

Stephen R Lewis

Francois Forget

Alessio Aboudan

Giacomo Colombatti

Carlo Bettanini

Stefano Debei

Bart Van Hove

Veronique Dehant

François Forget

Ari-Matti Harri

Mark Leese

Teemu Mäkinen

Ehouarn Millour

Ingo Muller-Wodarg

Gian Gabriele Ori

Andrea Pacifici

Sebastien Paris

Manish Patel

Mark Schoenenberger

Jeffrey Herath

Tero Siili

Aymeric Spiga

Tetsuya Tokano

Martin Towner

Paul Withers

Sami Asmar

Dirk Plettemeier

Håkan Svedhem

Christopher T Russell

ExoMars Atmospheric Mars Entry and Landing Investigations and Analysis (AMELIA)

Keywords: Mars, Entry Descent and Landing (EDL), dynamical models, trajectory, attitude, atmospheric investigations

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INTRODUCTION

The Entry, Descent and Landing System (EDLS) of an atmospheric probe or lander requires engineering measurements to trigger and to control autonomously the events of the descent sequence. These measurements are primarily intended to support a successful and safe landing, but can also provide information for the engineering assessment of the EDLS and essential data for an accurate trajectory and attitude reconstruction of the vehicle. They also have great value as rare in situ measurements for atmospheric scientific investigations.

Only eight robotic probes to date have successfully entered the atmosphere and landed on Mars (USSR Mars 3, NASA Viking 1 and 2 Landers, Mars Pathfinder, the two Mars Exploration Rovers: Spirit and Opportunity, Mars Phoenix, and MSL Curiosity), on Venus (8 USSR Venera 7-14's probes, 2 USSR Vega 1 and 2 landers, and four NASA Pioneer Venus probe), or on Titan, the largest moon of Saturn (ESA Huygens probe).

The ExoMars program, with the Schiaparelli Entry, descent and landing Demonstrator Module (EDM) in 2016 and the entry module containing the Surface Platform and Rover scheduled for 2020, provides the opportunity for new, direct in situ measurements over a wide altitude range and with resolution not achievable over the full altitude range by remote sensing observations. On the basis of successful experience with the Huygens probe at Titan, a similar opportunity for an experiment concerning the ExoMars entry, descent and landing (EDL) science was proposed. At a later time (November 2010), a dedicated Announcement of Opportunity (AO) for "ExoMars Entry, Descent and Landing Demonstrator Module (EDM) science" was issued by ESA in the framework of the NASA-ESA Joint Mars Exploration Programme; besides the provision of a Surface Payload for the ExoMars EDM, the AO also called for Entry and Descent Science with spacecraft EDL engineering sensors. Two proposals were submitted for the EDL Science (March 2011) and selected (June 2011) to be combined into one EDL experiment: AMELIA.

The main objective of the AMELIA experiment was to assess the local atmospheric science and the surface landing site by using the existing EDLS engineering sensors for more than their primary role in monitoring and evaluating the performance of the EDL technology demonstrator. The data recorded during different EDL phases would be used for an accurate trajectory and attitude reconstruction and for the retrieval of atmospheric profile to study the atmospheric structure, dynamics and static stability and to assess the landing site context.

AMELIA's objectives included studying some of the major properties of the martian atmosphere, such as density, pressure, temperature and wind, from an altitude of about 120 km all the way down to the surface, and characterizing the nature of the landing site by means of touch-down measurements.

Despite the ultimate failure of Schiaparelli in its landing phase, sufficient EDL data were returned in order to reconstruct the trajectory and attitude of the EDM and to retrieve atmospheric profiles over the altitude range from 121 km to 4 km above the surface [START_REF] Aboudan | ExoMars 2016 Schiaparelli Module Trajectory and Atmospheric Profiles Reconstruction: Analysis of the On-board Inertial and Radar Measurements[END_REF], even if at lower resolution, with a significant gap in the middle atmosphere and with higher uncertainty ranges than those that would have been achievable had the full Schiaparelli data-set been recovered after landing, as was originally planned. The EDL sequence (Fig. 1) was designed to last about 6 minutes starting with a hypersonic atmospheric entry, followed by a passive descent under parachute and an active proximity phase during which retrorockets should have been activated in order to decelerate Schiaparelli and improve the horizontal accuracy of the landing site location. Schiaparelli should have finally landed on a crushable structure, designed to dampen the impact [Ball et al. this issue].

ExoMars 2016 EDL SCENARIO AND

MEASUREMENTS

Schiaparelli was equipped with a set of engineering sensors (Fig. 2, Table 1) in order to monitor the performance of the EDL subsystems and the environment during EDL for verification of the design and technological assessment [Ball et al. this issue].

The EDL instrumentation included Guidance, Navigation and Control (GNC) equipment: one Miniaturized Inertial Measurement Unit (MIMU) containing three gyroscopes and three accelerometers, a sun sensor (SDS) located on the back shield for attitude determination prior to atmospheric entry, a Radar Doppler Altimeter (RDA), for altitude determination in the lowest 6-3 km of the atmosphere, and three pairs of landing accelerometers (for axial and tangential accelerations) to monitor Mars landing. A set of aerothermal sensors, embedded within the Thermal Protection System (TPS) of the Front Shield (FS) and Back Cover (BC) of the entry probe, complemented the EDL instrumentation: these included pressure transducers (4 on the FS and 1 on the BC as part of COMARS+), thermal plugs and thermistors (7 on the FS and 3 on the BC), and COMARS+ calorimeter and radiometer [START_REF] Gülhan | Combined Instrumentation Package COMARS+ for the ExoMars Schiaparelli Lander[END_REF]. After a successful landing, Schiaparelli telemetry data would have been downloaded by the Mars relay orbiters.

The engineering sensors, their measurements and the expected flight data are reported in Table 1. The telemetry data included also GNC processed data derived from these measurements; EDL measurements and GNC estimates were downsampled or decimated as required to fit the maximum data volume to be transmitted during EDL (e.g. essential telemetry data) and to be stored on-board for post-landing download.

AMELIA SCIENCE OBJECTIVES

The experiment AMELIA was aiming at the assessment of the atmospheric science and landing site by using sensors of the Entry, Descent and Landing system (EDLS), over and above the expected engineering information.

The primary science objective was to retrieve an in situ atmospheric profile along the entry and descent trajectory. This profile permits the investigation of Mars' atmospheric structure and dynamics at high spatial resolution, so as to detect meteorological perturbations and waves, for example, thermal tides and gravity waves.

The scientific analysis of the landing measurements was aimed at the determination of the landing site context (e.g. surface mechanical characteristics, geomorphology, etc.), its characterization and assessment. This analysis would be conducted in combination with remote sensing imaging and mapping.

Of 2).

The USSR Mars 6 probe in 1973 failed upon impact, but it provided the first in situ measurements of the planetary atmospheric structure by transmitting data during its entry (for 224 s, the link was lost before retrorockets ignition).

Although the data were unusable as a result of a design flaw, an assessment of the atmospheric parameters from 12-90 km was retrieved from the Doppler measurements of the radio signal received by the Mars 6 descent module [START_REF] Kerzhanovich | Mars 6: Improved analysis of the descent module measurements Icarus[END_REF].

To date only seven profiles of density, pressure and temperature have been published from in situ measurements: both Viking 1 and 2 in daytime [START_REF] Seiff | Structure of the Atmosphere of Mars in Summer at Mid-Latitudes[END_REF]; Mars Pathfinder in nighttime [START_REF] Schofield | The Mars Pathfinder Atmospheric Structure Investigation/Meteorology (ASI/MET) Experiment[END_REF][START_REF] Magalhães | Results of the Mars Pathfinder atmospheric structure investigation[END_REF]; two more profiles from the MER Spirit and Opportunity [START_REF] Withers | Atmospheric entry profiles from the Mars Exploration Rovers Spirit and Opportunity Icarus[END_REF]] with much lower accuracy; Mars Phoenix providing the first profile from the martian polar region [START_REF] Withers | Observations of atmopheric tides on Mars at the season and latitude of the Phoenix atmospheric entry[END_REF]; and, most recently, by MSL-Curiosity [START_REF] Chen | Reconstruction of Atmospheric Properties from Mars Science Laboratory Entry, Descent, and Landing[END_REF][START_REF] Holstein-Rathlou | Atmospheric studies from the Mars Science Laboratory Entry, Descent and Landing atmospheric structure reconstruction[END_REF]] (Fig. 3). Reference [START_REF] Kerzhanovich | Mars 6: Improved analysis of the descent module measurements Icarus[END_REF] [ Seiff & Kirk. 1997[START_REF] Schofield | The Mars Pathfinder Atmospheric Structure Investigation/Meteorology (ASI/MET) Experiment[END_REF]], [START_REF] Magalhães | Results of the Mars Pathfinder atmospheric structure investigation[END_REF] In addition to atmospheric science, AMELIA was also intended to characterise and assess the surface at the landing site by means of the in situ measurements taken during the terminal descent and at touch-down. The engineering data and the descent images recorded by DECA were intended to be used for supporting characterization of the landing area along the ground track and at the impact site, in the context of the high resolution mapping of the landing ellipse performed with remote sensing observations [Ori G.G. et al. 2014, Pacifici et al. 2014].

SIMULATION AND RECONSTRUCTION METHODS

An atmospheric profile of density, pressure and temperature can be retrieved along the entry and descent trajectory using similar methods to those employed in previous entry probe missions, e.g. ESA Huygens at Titan [START_REF] Fulchignoni | In situ measurements of the physical characteristics of Titan's atmosphere and surface[END_REF], Aboudan et al. 2008, Colombatti et al. 2008], NASA Mars Pathfinder [START_REF] Magalhães | Results of the Mars Pathfinder atmospheric structure investigation[END_REF], Mars Exploration Rovers [START_REF] Withers | Atmospheric entry profiles from the Mars Exploration Rovers Spirit and Opportunity Icarus[END_REF],

Phoenix [START_REF] Desai | Entry, descent, and landing performance of the mars phoenix lander[END_REF] • and landing (proximity), from retrorocket activation to touch-down.

The Schiaparelli EDM, protected by its frontal heat shield, was modelled as a single rigid body with 6 degrees of freedom (dof) subject to Mars' gravity and aerodynamic forces. A priori expected atmospheric conditions were retrieved from the Mars Climate Database (MCD 5.2) [START_REF] Millour | The Mars Climate Database (MCD version 5.2)[END_REF]] derived from numerical simulations performed with the Laboratoire de Meteorologie Dynamique (LMD) Global Climate Model [START_REF] Forget | Improved general circulation models of the Martian atmosphere from the surface to above 80 km[END_REF]]. Different "dust loading" atmospheric scenarios were used to compute the aerodynamic forces and torques starting from the aerodynamical database. After parachute deployment, the Schiaparelli module and the parachute system were modelled as two bodies connected by a spherical joint, resulting in a 9 to 12 dof system depending on whether the parachute was modelled as a 3 or 6 dof body. For the separation phase, a model at 18 dof was used for three rigid bodies (i.e. surface platform, front shield and aft cover). The aerodynamical interactions between the different elements of the EDM were taken into account and modelled using inputs from the aerodynamic database.

Simulations were performed and the models were validated against the expected

RADIO LINK DOPPLER SHIFT RECONSTRUCTION

A near-real-time reconstruction of the trajectory can be performed using the radio communication link between the EDM, the radio receivers on board the relay orbiters, and the carrier signal detection by ground telescope [START_REF] Withers | Trajectory and atmospheric structure from entry probes: Demonstration of a real-time reconstruction technique using a simple direct-to-Earth radio link[END_REF]].

From the Doppler shift and rate of the signal, it is possible to detect the different events, retrieve the position and velocity of the probe, and to estimate the wind velocity [Withers 2015[START_REF] Karatekin | Entry Trajectory Reconstruction Using Phoenix Radio Link: 8 th International Planetary Probe Workshop[END_REF][START_REF] Asmar | Curiosity's Landing Dynamics as Observed at the CSIRO Parkes Radio Telescope[END_REF].

ATMOSPHERIC RECONSTRUCTION

Atmospheric profiles of density, pressure and temperature, can be derived by several methods including: direct inversion from deceleration measurements, from hypersonic dynamic pressure data recorded during entry, or using more sophisticated estimation methods in which a priori knowledge of atmospheric parameters and vehicle dynamics are blended with all the available measurements.

In order to reconstruct the atmospheric parameters (e.g. density, static pressure and temperature) from the measured accelerations and dynamic pressures, the physical properties of Schiaparelli in its different configurations (ref. Fig. 4), its aerodynamical and its aerothermal characteristics must be known.

RECONSTRUCTION FROM INERTIAL DATA

Of the possible methods, historically the primary approach [e.g Seiff, andReese,1965, Seiff and[START_REF] Seiff | Structure of Mars' atmosphere up to 100 km from the entry measurements of Viking 2[END_REF], has been the direct numerical integration of the IMU measurements to derive velocity, position and altitude. Measured accelerations can be converted into atmospheric parameters by using the vehicle's aerodynamical database (AeDB): starting from the velocity and position of the probe, its angle of attack (AoA) and the side slip angle (SSA) can be obtained as the ratio of the normal and side to axial accelerations. Atmospheric density is directly related to the deceleration by the atmospheric drag, a pressure profile can be computed using the hydrostatic equilibrium law and then temperature by means of the ideal gas law. Furthermore, having a dynamic model of the EDM (mass, inertia and AeDB), having a sensor model of the on-board accelerometers, and assuming an atmospheric standard model, makes it possible to predict the atmospheric drag and hence update the density profile to match the measured accelerations using an Extended Kalman Filter [START_REF] Aboudan | Huygens probe entry trajectory and attitude estimated simultaneously with Titan atmospheric structure by Kalman filtering[END_REF]]. This method can be further extended to blend any other available measurements from both on-board sensors (e.g. the radar Doppler altimeter, FADS) and remote sensing data (e.g. imaging and radio science).

During the last part of the descent (terminal descent) a direct measurement of the elevation and velocity of the EDM above Mars' surface was provided by the radar Doppler altimeter. These data, together with the descent images of DECA, were intended to contribute to the assessment of the EDM trajectory and attitude in its terminal part of the parachuted descent

RECONSTRUCTION FROM PRESSURE DATA

Schiaparelli was equipped with aerothermal sensors embedded into the thermal protection system (TPS) of the frontshield and aft cover [Ballet al. this issue].

These sensors together with CoMARS+ [Gülhan et al. this issue] were aimed at monitoring the entry vehicle's surface pressures and heat shield temperature in order to investigate Mars' entry environment and the vehicle's response to it. The readings of the four heatshield pressure sensors, one placed at the stagnation point and the others at three radial locations, provide the pressure distribution across the shield and could be used for an independent reconstruction of the atmospheric parameters. Atmospheric free stream conditions and density may be determined with the help of aerothermal dynamical database (ATDB) using all pressure sensors at once, or at a single location [Karlgaard et al. 2013, Van Hove andKaratekin 2017]. . These profiles do not depend on assumed EDM aerodynamics, and provide independent observations of the atmospheric conditions.

The pressure-based reconstruction using all pressures consists of making a leastsquares fit of the surface pressure measurements to the modelled pressure distributions to obtain a minimum-variance estimate of the atmospheric pressure.

Multiple pressure measurements give the stagnation location and pressure and the true flow angles. All pressure measurement locations can be processed simultaneously to determine the atmospheric state variable estimates.

Combining the information from environmental sensors with velocity and attitude derived from the inertial measurements by IMU can enable the estimation of atmospheric winds [START_REF] Karlgaard | Mars Entry Atmospheric Data System Trajectory Reconstruction Algorithms and Flight Results[END_REF].

SYNTHESIS OF DIFFERENT TECHNIQUES

The final step in the overall analysis is the consolidation of the reconstructions by different techniques and using different data and measurements (Fig. 5); the resulting combined reconstruction can be assessed by checking the agreement of the different techniques and data assimilation, and by performing the optimal blending of all the measurements by Bayesian estimation (e.g. using Extended

Kalman filters or smoothers as baseline).

MARS ATMOSPHERE AND ENVIRONMENT MODELLING

In order to safely design the entry, descent and landing operation of a probe the status of the atmosphere and the variability of the environmental and dynamical conditions that it will face need to be predicted sufficiently accurately.

Various tools have been developed and implemented in order to model Mars' environment at different scales, taking into account the different processes and phenomena that govern atmosphere dynamics: Global Circulation Models (GCMs) with resolution on the order of 100 km; Mesoscale models simulating regional environments (resolution ~10 km); and Large-Eddy Simulations able to resolve the convective boundary layer in the altitude range below 20 km (resolution ~10-50 m) (Fig. 6). The outputs of the LMD GCM [START_REF] Forget | Improved general circulation models of the Martian atmosphere from the surface to above 80 km[END_REF] have been implemented into a Mars Climate Database (MCD wwwmars.lmd.jussieu.fr) that can provide the expected mean environmental parameters at a specific place, season, time of the day, and altitude (from the surface to the thermosphere). The amount of dust in Mars' atmosphere is one of the main sources of variability for the weather conditions, with different processes acting at different scales, e.g. from global dust fronts, to regional dust storms, to local gusts and dust devils, dust laden convective vortices that cross the surface of Mars.

Within the AMELIA team, considerable effort has been put into atmospheric modelling [e.g. Forget et al. 1999, Spiga andForget 2009] and data assimilation [e.g. [START_REF] Lewis | A climate database for Mars[END_REF], 2007[START_REF] Montabone | Read Interannual variability of Martian dust storms in assimilation of several years of Mars global surveyor observations[END_REF]] in order to improve

ATMOSPHERIC SCIENCE

The main objective of the AMELIA experiment was to retrieve the atmospheric profile, in terms of density, pressure and temperature, along the entry and descent trajectory by means of an accurate trajectory and attitude reconstruction.

In situ measurements made by an entry probe permit retrieval of atmospheric profiles with higher vertical resolution than remote sensed data and provide 'ground truth' for remotely-sensed observations and important constraints for updates and validation of the Mars atmospheric models.

The density profile can be retrieved directly from measurements of the deceleration of the probe due to the atmospheric drag; pressure and temperature can be derived assuming the hydrostatic equilibrium law and by means of the ideal gas law.

AMELIA characterises the atmospheric structure along the entry probe trajectory, thereby contributing to study of the general atmospheric structure. Attempts to measure winds in the free atmosphere were also planned by retrieving the wind profile along the entry probe path from the EDM radio tracking both by TGO and from Earth, e.g. as was done by the Huygens Doppler Wind Experiment (DWE) [START_REF] Bird | The vertical profile of winds on Titan[END_REF], and from trajectory and attitude variations and the horizontal motion of the pendulum system of parachute chain and EDM during the descent phase [e.g. [START_REF] Seiff | Mars Atmospheric Winds Indicated by Motion of the Viking Landers During Parachute Descent[END_REF]].

Based on the sampling rate of the Schiaparelli engineering sensors, the expected spatial resolution of the retrieved atmospheric profiles should range from 13 to 2 m. This resolution, achievable only by means of in situ measurements, would allow the detection and resolution of small, localised and wave-like structures propagating within the atmosphere.

By resolving and detecting horizontal structures, AMELIA could observe inertiogravity waves and therefore help to constrain their properties and parameterization. AMELIA was also intended to characterize the thermal tides and their sensitivity to dust loading in the atmosphere, and to determine the vertical propagation of both gravity waves and tides to characterize the range of the vertical variations of temperature and density in the Martian troposphere and mesosphere.

SURFACE SCIENCE

Scientific analysis of the landing measurements were aimed at the determination of the landing site context (e.g. surface mechanical characteristics, geomorphology, etc.), its characterization and assessment also in combination with remote sensing imaging and geological mapping (Fig. 7). From the impact trace (that should have been recorded by the IMU and the landing accelerometers had the landing been successful) it would have been possible to derive the dynamic response of the EDM structure to the impact, to retrieve the post-impact movements and attitude, and possibly to determine the mechanical properties/characteristics of the soil at the touch-down.

From radio tracking and the radar Doppler altimeter data the orographic profile (i.e. elevation) over the ground track of the descent module should have been retrieved and returned after landing.

The a priori characterization of the landing site of the ExoMars2016 (Fig. 8) was performed by a careful analysis of the engineering constraints used in order to assess the safety of the landing in Meridiani planum [START_REF] Ori | The Analysis of the ExoMars 2016 Landing Site[END_REF][START_REF] Ori | The ExoMars 2016 Landing Site[END_REF]. Low to very high-resolution data acquired by previous and current Mars missions have been used in order to distinguish and characterize geomorphological units and in order to realize a geological-geomorphological map within the landing ellipse [START_REF] Pacifici | Geological and Geomorphological Map of ExoMars 2016 Landing Site[END_REF]]. The radio signal and the flight data, although more limited than would be ideal, are essential to investigate the anomaly that caused the crash landing and in order to achieve the AMELIA scientific objectives. At the time of writing, the data were under analysis to establish the reasons for the Schiaparelli's landing failure and under embargo. Then at a later time, the outcome of the Schiaparelli flight anomaly investigation was officially presented (T. Tolker-Nielsen, 2017) and the results of the analysis published (e.g. [START_REF] Portigliotti | ExoMars 2016, the Schiaparelli mission. EDL demonstration results from real time telemetry before unfortunate impact[END_REF][START_REF] Bonetti | ExoMars 2016: Schiaparelli coasting, entry and descent post flight mission analysis[END_REF] as were the results of the AMELIA reconstructions [START_REF] Aboudan | ExoMars 2016 Schiaparelli Module Trajectory and Atmospheric Profiles Reconstruction: Analysis of the On-board Inertial and Radar Measurements[END_REF].

CONCLUSIONS

The ESA -Roscomos ExoMars Project provided a rare opportunity (once per mission) for in situ measurements within the atmosphere of Mars and at the landing site. These measurements allow for sounding the atmospheric structure along the trajectory of the descent module and the assessment of the landing site. We have been able to make reconstructions of the profile down to 4 km, but at reduced resolution compared to what would have been achievable had the spacecraft landed successfully and returned all its data. The vertical resolution achieved was still significantly higher than is possible by remotely-sensed measurements, even those made with a limb-sounding instrument such as MCS, and cover a much larger altitude range than is possible with radio occultation retrievals. Unfortunately, data taken during the plasma blackout (e.g. in the altitude range from 70-30 km) and the terminal descent phase (the last 4 kilometres above the surface) are impossible to recover. Data that would enable a refined reconstruction by assimilation and measurements blending have been lost, as have images from DECA and landing investigations. The techniques described above have been adapted and further developed to make use of the limited returned data and to cope with the transmission loss in order to retrieve the atmospheric profiles along the entry and descent trajectory of Schiaparelli into the atmosphere of Mars.

ExoMars 2016

 2016 Schiaparelli was designed in order to demonstrate and validate a European capability for Entry, Descent and Landing on Mars. Launched on 14 th March 2016, carried by the Trace Gas Orbiter (TGO), Schiaparelli reached Mars in October 2016. Following separation from TGO (on Oct. 16 th ), Schiaparelli continued its ballistic trajectory to Mars in a state of hibernation (in order to save battery power) for 72 h and was activated one hour before the nominal atmospheric entry point on Oct. 19 th .

Fig. 1 :Fig. 2 :

 12 Fig. 1: ExoMars2016 Schiaparelli EDL scenario (credit: ESA)The sequence of entry, descent and landing of the Schiaparelli EDM and relevant events are reported together with the expected timing, altitude and velocity, as simulated for the reference mission using forecast atmospheric scenarios.

  the multiple Mars landings attempted by robotic unmanned spacecraft, only eight were successful: USSR Mars 3 in 1971, NASA Viking 1 and 2 Landers in 1976, Mars Pathfinder in 1997, the two Mars Exploration Rovers (MER, Spirit and Opportunity) in 2004, Phoenix in 2008 and MSL Curiosity in 2012 (Table

Fig. 3

 3 Fig. 3 Mars atmospheric profile as measured by entry probes. The atmospheric profiles as retrieved from the EDL measurements of Mars' entry probes are plotted together with the surface values as measured by the landers ('circles'). The different profiles are relevant to different sites, seasons and local time: refer toTable 2 for details and further references. The plotted data have been retrieved from the relevant Planetary Data System (PDS) archives (PDS the Planetary Atmosphere Node: data archive for landers: http://atmos.pds.nasa.gov/data_and_servic es/atmospheres_data/MARS/mars_lander. html).

  ,[START_REF] Blanchard | Mars phoenix entry, descent, and landing trajestory and atmosphere reconstruction[END_REF][START_REF] Withers | Observations of atmopheric tides on Mars at the season and latitude of the Phoenix atmospheric entry[END_REF][START_REF] Withers | A smoothing technique for improving atmospheric reconstruction for planetary entry probes[END_REF]], and MSL-Curiosity[START_REF] Chen | Reconstruction of Atmospheric Properties from Mars Science Laboratory Entry, Descent, and Landing[END_REF], Kalgaard et al. 2014[START_REF] Holstein-Rathlou | Atmospheric studies from the Mars Science Laboratory Entry, Descent and Landing atmospheric structure reconstruction[END_REF].Within the AMELIA team, different approaches, algorithms, methods and data sets were employed for simulation and reconstruction of the Schiaparelli trajectory and attitude during the entry and the descent phases in order to retrieve and validate the most accurate atmospheric profile.The first step of the investigation is modelling of the dynamics of the EDM and the EDL sensors and measurements during the different phases of the EDL. These phases consistent of:•an entry phase, from the detection of the Entry Interface Point (EIP) down to the parachute deployment;• initial descent (Separation), from parachute deployment until the front shield is jettisoned;• mid-& terminal-descent, from jettison of the front shield down to the separation from the back shell;

Fig. 4

 4 Fig. 4 Schiaparelli EDM configurations at the different EDL phases.

  environmental and mission scenarios. Models were validated with data from previous entry probe missions [e.g. Van Hove & Karatekin 2014].The inputs for the simulations (and reconstruction) are the dynamical models of the EDM, the expected Mars' environment conditions (e.g. gravity and atmosphere models) and the state of the EDM at entry: namely position, velocity and attitude of the probe at the EIP. The EDL data recorded by the engineering sensors and derived from the GNC measurements are used as input, as is the Doppler tracking of the UHF signal.

Fig. 5

 5 Fig. 5 A schematic view of the AMELIA reconstruction approach. (A) Starting from the direct numerical integration of IMU data velocity, position and attitude are derived. (B) The aerodynamical data base (AeDB) is used in order to convert the sensed accelerations into atmospheric parameters; outputs are velocity, position, angle of attack (AoA), side slip angle (SSA) which give the density, pressure and temperature profiles. (C) IMU aided TPS pressure data processing provides the static and dynamic pressures which give density and temperature profile. (D) From the Doppler shift of the radio link received on ground and via the Mars Relay orbiters, it is possible to measure the EDM velocity in Line-of Sight and to derive position, and possibly winds. (E) The EDM radar altimeter provides a direct measurement of the EDM elevation with reference to the Mars ground. (F) The combined reconstruction is assessed by checking the agreement of the different techniques, using data assimilation and by Extended Kalman filtering.

Fig. 6

 6 Fig. 6 Tools to model Mars' environment. Typical Mars weather events related to dust lifting (top images + yellow strip), relevant spatial scales (middle blue arrow) and meteorological models for their analysis (bottom yellow strip) are reported. The outputs of the integrated models have been implemented into the Mars Climate Database (MCD www-mars.lmd.jussieu.fr) in order to forecast the mean environmental parameters at a specific place, season, time of the day, and altitude. Image credits, left: NASA-MGS-MOC, middle: NASA-MRO-MARCI, right: NASA-MRO-HIRISE; images retrieved from the NASA Planetary Data System PDS: Figure from Spiga and Lewis, 2010, modified with permission.

  predictions and weather forecasts, to monitor weather conditions and to assess the atmospheric context at entry. Predictions have been used in order to forecast the environmental conditions that Schiaparelli was likely to face for mission design, in order to manage and optimize the EDL sequence versus different expected atmospheric scenarios. An extended MonteCarlo simulation campaign has been performed by the EDM Prime contractor (Thales Alenia Space, Torino, Italy -TAS-I) using a combination of Global, Mesoscale and Large-Eddy simulations[START_REF] Forget | Portigliotti Characterizing the Martian atmosphere for the ExoMars 2016 Lander[END_REF]]. These simulations resulted in the reference Schiaparelli EDL trajectory that has been used for comparison with the AMELIA simulations/reconstruction. Finally, expertise in modelling and data assimilation is fundamental for the scientific analysis and interpretation of the AMELIA results. Remote sensing observations (e.g. NASA Mars Reconnaissance Orbiter -MCS and MARCI records and ESA MarsExpress -PFS) and in situ measurements (e.g. from MER-Opportunity PanCam) taken around the time of the ExoMars2016 mission at Mars (19 th Oct 2016 local solar time 13:16), provide additional data (e.g. inverted temperature profiles and dust opacities) to assess the atmospheric context through assimilation within models and for direct comparison with the AMELIA reconstructed profile.

  be assessed by a combination of measurements: atmospheric opacity (e.g. from solar flux measured by the sun sensors and COMARS+ radiometer on the back shield, from DECA images), and from the front shield ablation. Dust load and condensates (e.g. fog and clouds) could be detected as detached layers from the temperature inversions and as sources of extra opacity.AMELIA also had the ability to probe the Planetary Boundary Layer (PBL) of Mars, estimating the altitude of its top (e.g. by comparison with Large Eddy simulation model,Spiga et al. 2010) and, by measuring wind speeds and turbulence inside the PBL, observing the turbulence scale and intensity. Finally, AMELIA results could have been investigated in synergy with DREAMS[START_REF] Esposito | The DREAMS experiment onboard the Schiaparelli Module of the ExoMars 2016 mission: 1 design, performances and expected results[END_REF]] that should have provided meteorological and environmental measurements at the surface of Mars, in order to study the meteorology and climate of Mars.

Fig. 7

 7 Fig. 7 Artist's view of Schiaparelli at the touch-down with the surface of Mars. In the background at the left side the back shell is visible, with the parachute still partially inflated (Credit: ESA).

Fig. 8

 8 Fig. 8 ExoMars2016 Schiaparelli landing site in Meridiani Planum. The landing ellipse, centred at 6° West and 2° South, measured about 100 km East-West and 15 km North-South. It was located on a relatively smooth, flat region as evidenced by the overlaid topographic map (source data: Mars Odyssey -THEMIS Day-IR, MGS -MOLA). The actual Schiaparelli impact site, as detected in the MRO HIRISE images, is marked with a star. (Credit: IRSPS/TAS-I/ESA).

  The characterization and assessment of the landing site would have been improved by combining remote sensing and descent images DECA[Koschny et al. this issue], co-registering the descent images with MRO-HiRiSe by matching geological and geomorphological mapping also in order to study aeolian and sedimentary processes at the landing site.SCHIAPARELLI's ENTRY AND DESCENTSchiaparelli, the Entry Demonstrator Module (EDM) of the ESA ExoMars Program, entered into the martian atmosphere on 19 th October 2016. Although it did not complete a safe landing, it transmitted data throughout its descent to the surface, but the signal was lost about 1 minute before the expected touch-down on Mars' surface. Due to an anomaly in the guidance, navigation and control (GNC) loop, Schiaparelli crash-landed on the surface of Mars from an altitude of about 4 km. The crash was later confirmed by Mars Reconnaissance Orbiter images of the impact site (Figure9). Schiaparelli continuously transmitted telemetry that was received by the TGO (Trace Gas Orbiter), while the signal carrier was recorded by the Giant Metrewave Radio Telescope (GMRT) in Pune (India) and by MarsExpress until the loss of signal. The radio signal and essential telemetry data received from Schiaparelli during EDL were interrupted for about 1 minute as a result of the expected plasma blackout during the hypersonic entry, covering an altitude range from about 70-30 km above the surface.Radio contact with Schiaparelli was lost shortly after front shield release, which is where flight data end (at about 4 km from the ground). Because of the limitation on bit rate and data volume, the EDL flight data received by TGO contain only GNC measurements at reduced sampling rates, and decimated pressure data. The complete EDL data set, including data from the plasma black-out phase, the GNC data and sensor measurements at higher rates, and also DECA images, were recorded on board and should have been transmitted after landing. As a consequence of the crash, no data have been returned from the Mars relay orbiters during the planned subsequent passages.

Fig. 9

 9 Fig. 9 ExoMars2016 Schiaparelli impact site on Mars as recorded by the NASA Mars Reconnaissance Orbiter HiRISE camera (image taken on 25 October 2017). The locations of the surface platform crash site, parachute with back cover (at the lower left corner) and front heat shield (at the upper right corner) impact site on Mars' surface are marked. Close-up views of the related hardware components are provided in the zoomed insets. (Credit: NASA/JPL/UA/ESA)

The

  ExoMars Atmospheric Mars Entry and Landing Investigation and Analysis (AMELIA) experiment in 2016 aimed to exploit the engineering data recorded during the Entry, Descent and Landing (EDL) of the Schiaparelli descent module in order to perform scientific investigations of the atmosphere and surface of Mars along the descent track and at the landing site. The AMELIA scientific objectives and the intended investigations have been presented in the context of the ExoMars2016 Schiaparelli mission. The Schiaparelli EDL scenario and measurements have been described as they were planed, and some science may be recovered with the more limited data set returned following the events on 19 th October 2017. Beside the unfortunate conclusion of the Schiaparelli mission, the signal and data transmitted during the EDL provide unprecedented real-time data set for validating and assessing of the EDL sequence. We anticipate further scientific exploitation of the Schiaparelli EDL flight data for investigation of the martian atmosphere, and to contribute to the lessons learned for the upcoming ExoMars2020 mission and for a new EDLS opportunity.

6 Table 1 .

 61 Schiaparelli EDL Engineering sensors and data

	mission notes phase	EDL DECA, the Descent Camera was planned to record downward-looking images, as GNC processed data: valid at 100 Hz and down-sampled to 10 Hz EDL hibernation Antennas at the bottom of the EDM: 3 oriented on a circle separated by 120° for velocity measurement, 1 in the center of circle, perpendicular to EDM for slant measurement 3 accelerometer pairs: 1 axial, 1 tangential. Located at the edge of the DM platform at 120° Sensors located 1 at the stagnation point and 3 at 0.5m from the centerline, at 120°in triangular configuration, embedded into TPS: 7 on FS; 1 at stagnation and other 6 in triangular configuration at 2 different distances from the edge. 3 on the BC: on radial location on a single radius 3 J-type TC placed at 4,6 and 8-mm depth 1 for each thermal plug, placed on the structure down-looking; a burst of fifteen black and white, low resolution frames before touch-down. DREAMS, an environmental station monitoring meteorology for 2-4 sols at Mars' surface [Esposito et al. 2018], completed Schiaparelli's scientific payload. Schiaparelli was designed to communicate via the UHF antenna during the EDL as well as surface operations phases. The Schiaparelli telemetry data downlink concept was based on relay of data via the currently flying Mars orbiters (ESA Coasting Used by GNC in order to recover attitude after Terminal D L E E E E D TGO and MarsExpress, and NASA Mars Reconnaissance Orbiter, MAVEN, and Odyssey). During the EDL phases, only essential telemetry data were transmitted (Proximity) via the TGO owing to the reduced data rate available. In addition, the EDM UHF
	Subsystem / sensor Sensor type (#) measurement [unit] sampling frequency telemetry sampling rate / decimation	GNC Sensors carrier signal was recorded by the ESA Mars Express orbiter and by ground MIMU: Honeywell Miniature Inertial Measurement Unit YG9666NK Ring laser gyroscopes (3) angular rate [deg/s] 100 Hz 10 Hz Accelerometers (3) acceleration [m/s2] (mechanical load) 100 Hz 10 Hz SDS: Sun sensor a fully passive analog device, based on a quadrant photo detector solar aspect angles (sun vector) 10 Hz 10 Hz RT / 1 Hz No RT RDA: Radar Doppler Altimeter Customized radar altimeter with 4 independent beams/antennas velocity [m/s] and altimetry [m] relative to the terrain 20 Hz 1 Hz RT/ 10Hz No RT Landing ACC Endevco 2271 AM20 piezoelectric Accelerometers (6) 3 rotational and traslational acc. [m/s2] TPS sensors Pressure sensors FAD: Flush Airdata Sensing Kulite XTL-DC-123C-190M-250-mBAR-A (4) pressure [bar] (pressure field) 10 Hz 1 Hz Thermal plugs 7 on FS, composed of 3 J-type TC; 3 on BC, composed of 2 J-type TC temperature [K] (thermal loads) Thermocouples (TC) TC direct 12-J-150-118-0.5-21-3P2LA-3.5M-B40JX 10 Hz 0,1-1 Hz Thermistors PT200 MEAS PF0002413 (PF0002283 with a 2.5m cable) 10 Hz -stations on Earth (Direct to Earth link): the Giant Meterwave Radio Telescope 0,1-1 Hz DECA Descent Camera 60° field of view camera black & white images 15 frames at 1.5s (GMRT) in India. The Doppler shift and rate of the radio signal could be accurately measured during the EDL and represent a unique "signature" of FS: Front Shield, BC: Back Cover, TC: ThermoCouple, RT: Real Time; E: Entry, D: Descent, L: Landing the entry trajectory.

Table 2 .

 2 Comparison between EDL science of Mars' probes

	MSL-Curiosity				MSL	Aug 6, 2012	05:18 UTC	15:03 LMST	15:36 LTST	(-current >2287 sols)						MSL	Gale Crater	4.6°S 137.4°E,	-4.5 km				150.7°
	Phoenix	PHX			PHX	May 25, 2008	23:53:44 UTC	16.6 LTST	(+152 sols)							PHX	Green Valley,	Vastitas Borealis	68.21°N, 234.25°E	-4.45 km			76.6°
	Mars Exploration	Rovers:	MER1: Opportunity (O)	MER2: Spirit (S)	MER1-O (MER-b mission)	25 Jan 2004	04:55 UTC	13:13 LTST	+5111 sols)		MER2-S (MER-A mission)	Jan 4, 2004 ,	04:26 UTC	14:16 LTST	(+2210 sols)	MER1-O	Meridiani Planum	14.57°S, 354.47°E		MER2 -S	Gusev crater	1.95°S, 175.47°E	MER1-O: 339.1°	MER2-S: 327.7°
	Mars Pathfinder	MPF			MPF	Jul 4, 1997	02:58 LT nighttime:	(+83 Sols)								MPF	19.09°N, 326.74°E	-2.8 km					142.7°
	Vikings	VK1, VK2			VK1	Jul 20 1976	16:15 LT	(+2245 Sols)		VK2	Sep 3 1976	10:00 LT	(+1281 sols)			VK1	22.7°N, 312.05°E	-2.69 km		VK2	47.62°N, 134.23°E	4.23 km	VK1: 97.0°	VK2: 117.6°
	Mars 6 (USSR)				M6	12 March 1974	09:05:53 UTC	15:30 LT								M6	Pyrrhae Regio	23.90°S, 19.42°E					19.5°
					Time:	date, UTC,	local time (LT)	@EDL	(operational	sols@ Mars)						Landing	location					Season LS

ACKNOWLEDGEMENTS AMELIA is an experiment for scientific investigations of Mars' atmosphere and surface by means of the Schiaparelli measurements during its entry, descent and landing on Mars. The International AMELIA team built under the joint coordination of Principal Investigator: Francesca Ferri (Italy) and 3 Co-Principal Investigators (CoPIs): François Forget (France), Stephen R. Lewis (United Kingdom), Özgür Karatekin (Belgium). The team includes scientists from Italy, France, UK, Belgium, Finland, Germany, Australia and USA. The support of the national funding agencies of Italy (ASI, grant no. 2017-03-17 and I/018/12/3), Belgium (BELSPO and PRODEX), UK (UKSA, grant no. ST/M00306X/1) and France (CNES) is gratefully acknowledged.


Álvaro Marin Lujak
email: marin.lujak@imt-lille-douai.fr

Garcia Sánchez

Miguel Ortega Mier

Holger Billhardt
email: holger.billhardt@urjc.es

Álvaro Garcia Sánchez

Miguel Ortega Mier
email: miguel.ortega.mier@upm.es

An Overview of a Break Assignment Problem Considering Area Coverage

Keywords: eet scheduling, break assignment, emergency eets

published or not. The documents may come

Introduction

Usually, in emergency eets (such as police and ambulance eets), the relation between the dynamic spatio-temporal area coverage requirements and the number of breaks and their duration is not taken into account for break assignment and the breaks are regulated by (static) labor rules. Thus, it may happen that the eet is undersized and recurrently falls behind its performance expectations.

Even though a vehicle crew having a break can be assigned to assist an incident, its arrival time is delayed due to the preparation time necessary to stop the break and start the mission. This additional delay (often in terms of minutes) can mean the dierence between life and death both in the case of urgent out-of-hospital patients and rapidly evolving disasters.

To guarantee ecient and timely emergency assistance, a minimum number of stand-by vehicles with in-vehicle emergency crews must always be available to cover each area of interest, i.e., to assist a probable incident within a predened maximum delay in the arrival. This can be done by dynamically transferring stand-by vehicles to (time-and area-dependent) locations that maximize the coverage of a region of interest in each time period. These locations can be a set of strategically positioned depots, parking lots, terminals, garages, and similar.

In the emergency eet context with temporarily and geographically varying workload, if the eective number and duration of previous work breaks has not been taken into account in the assignment of vehicles to incidents, it may also happen that a vehicle crew has worked during extended periods of time without any break or with interrupted breaks that were insuciently long for effective crew's rest. Such a disparity between a too high workload and insucient breaks leads to increased fatigue that can have detrimental eects on emergency assistance. The consequence is the feeling of being drained with related deterioration of attention and performance that may be hazardous for emergency assistance. Hence, strategic eet dimensioning performed before the eet's deployment should consider expected workload dynamics to guarantee frequent and suciently long time for rest for the vehicles' crews.

In this paper, we formulate this problem under the name of the break assignment problem considering area coverage (BAPCAC). Based on the historical data, the BAPCAC problem consists in determining the vehicles with in-vehicle crews necessary for optimal eet's deployment in each time period of a workshift, and their breaks' type, number, and durations based on the legal constraints, and the forecasted workload dynamics in terms of the area coverage by the eet. By the area coverage, we consider that incidents appearing in the region of interest may be potentially assisted within a predened target delay in the arrival. Moreover, the BAPCAC model relocates vehicles at each time period to the locations that best cover the forecasted incident demand. The objective of the BAPCAC model is an ecient dimensioning and an eective choice of break coordination strategy in emergency vehicle eets based on historical data while increasing both the quality of service of emergency eets as well as the well-being of the vehicles' crew members while reducing their absenteeism due to fatigue.

The paper is organized as follows. In Section 2, we describe the state-of-theart practice in break scheduling and introduce the break assignment problem considering area coverage (BAPCAC) and its mathematical model. We conclude the paper with a discussion of the model in Section 3.

BAPCAC: Preliminaries and the model

Breaks in emergency eets are usually considered preemptive and in the case of an incident, the closest available vehicle having the required equipment is called to assist the incident independently of the past crew's break and workload dynamics and if it is momentarily in a break or not. This approach may induce a delay in arrival of up to several minutes, which in critical cases can be hazardous.

A review of the literature on personnel scheduling problems can be found in [START_REF] Van Den Bergh | Personnel scheduling: A literature review[END_REF]. Beer et al. [START_REF] Beer | An AI-based breakscheduling system for supervisory personnel[END_REF] address a complex real-world break-scheduling problem for supervisory personnel and present a scheduling system that can help professional planners create high-quality shift plans. Similarly, Di Gaspero et al. [START_REF] Gaspero | Automated shift design and break scheduling[END_REF] also consider the problem of scheduling breaks that fulll dierent constraints about their placement and lengths. Mesquita et al. [START_REF] Mesquita | A new model for the integrated vehicle-crew-rostering problem and a computational study on rosters[END_REF] present dierent models and algorithms for the integrated vehicle and crew scheduling problem, where crews can be assigned to dierent vehicles. In their algorithms, they consider several complicating constraints corresponding to workload regulations for crews. Defraeye and Van Nieuwenhuyse [START_REF] Defraeye | Stang and scheduling under nonstationary demand for service: A literature review[END_REF] provide a state-of-the-art overview of research in the period 1991-2013 on personnel stang and scheduling approaches for systems with a stochastic demand with a time-varying rate. Rekik et al. in [START_REF] Rekik | Implicit shift scheduling with multiple breaks and work stretch duration restrictions[END_REF] consider a break scheduling problem that includes dierent forms of exibility in terms of shift starting times, break lengths and break placement. In the BAPCAC problem, we consider the F |V |W break model. Here, F stands for the fractionable breaks with an upper and lower bound on the number of breaks that can be assigned to each vehicle crew; V stands for variable break lengths with an aggregated break length given, which may be split into sub-breaks for each vehicle crew. W stands for the workstretch duration that denes a lower and upper bound on the number of consecutive periods of uninterrupted work before and after each sub-break can start, see, e.g., [START_REF] Kiermaier | The exible break assignment problem for hierarchical tour scheduling problems[END_REF]. We also assume that the plan of vehicle crew shifts that make a work-day shift is given a priori.

We assume that incidents appear, w.l.o.g., in a 2D square environment Env = [0, l] 2 ⊂ R 2 of side length l > 0. Environment Env is divided in mutually exclusive and nonempty rectangular unit areas e ⊂ Env of equal size such that e i ∩ e j = ∅ for i = j and e∈Env e = Env. Vehicle agents are positioned and may move only within the subset J ⊆ Env of unit areas.

Let T be a set of consecutive time periods {1, . . . , |T |}, representing a vehicle crew shift, where |T | is the cardinality of T . For each time period τ ∈ T , D eτ represents incident density or demand at area e ∈ Env. I ⊆ Env is a subset of unit areas i ∈ I with positive incident density. Then, each vehicle a ∈ A can have one of mutually exclusive vehicle states: {idle, on -break, occupied}: idle -a vehicle is waiting for a new incident assistance; on-break -currently on a break. An idle vehicle is considered to be covering unit area i ⊂ I if it is located in any unit area from which it can arrive to unit area i within a predened and given target arrival time ∆t, while for the vehicles on-break, the arrival time is increased by an additional preparation delay. x aτ j valued 1 if agent a at time τ ∈ T is located at unit area j ∈ J ; 0 otherwise y aτ binary break assignment variable valued 1 if agent a ∈ A is assigned a break at time τ ∈ T ; 0 otherwise z aτ i real nonnegative coverage assignment variable representing the part of density at incident unit area i ∈ I assigned to idle agent a ∈ A at time τ ∈ T , where 0 ≤ z aτ i ≤ 1 zaτi real nonnegative coverage assignment variable representing the part of density at incident unit area i ∈ I assigned to on-break agent a ∈ A at time τ ∈ T , where 0 ≤ zaτi ≤ 1 δ iτ real nonnegative density of area i ∈ I uncovered at time τ ∈ T α abτ binary variable valued 1 if agent a ∈ A starts a break of type b ∈ B at τ ∈ T ; 0 otherwise (BAPCAC):

min w • i∈I,τ ∈T δ iτ + (1 -w) • a∈A,τ ∈T 1 -y aτ , (1)
such that:

a∈A z aτ i + zaτi = D iτ -δ iτ , ∀i ∈ I, τ ∈ T (2)
z aτ i ≤ j∈J |Nij =1 D iτ x aτ j , ∀a ∈ A, τ ∈ T , i ∈ I (3) zaτi ≤ j∈J | Nij =1 D iτ x aτ j , ∀a ∈ A, τ ∈ T , i ∈ I (4)
z aτ i ≤ D iτ (1 -y a,τ ), ∀a ∈ A, τ ∈ T , i ∈ I (5) zaτi ≤ D iτ y a,τ , ∀a ∈ A, τ ∈ T , i ∈ I (6) i∈I z aτ i ≤ 1, ∀τ ∈ T , a ∈ A (7) i∈I zaτi ≤ 1, ∀τ ∈ T , a ∈ A (8) j∈J x aτ j = 1, ∀τ ∈ T , a ∈ A (9)
x aτ j + x a(τ +1)j ≤ 1 + IM jj , ∀a ∈ A, τ = {1, |T | -1}, j, j ∈ J

α abτ = 1, ∀a ∈ A, b ∈ B, τ ∈ {1, T -M AX w b } (13) τ +M AX w bs τ =τ α absτ + τ +M AX w b l τ =τ α absτ ≤ 2, ∀a ∈ A, τ ∈ {1, T -M AX w b l } (14)
z aτ i , zaτi , δ iτ ≥ 0, x aτ j , y aτ , α abτ ∈ {0, 1}, ∀i ∈ I, j ∈ J , τ ∈ T , a ∈ A

3 Discussion

In (1), w is the weight assigned to the coverage mean such that 0 ≤ w ≤ 1.

Constraints (2) relate to the coverage of each unit area i by idle vehicles and vehicles on-break. Here, minimizing the arrival time to an incident has priority over the performance of a break in its totality. If we exclude zaτi from the above and other constraints, our model turns into a non-preemptive break model.

Constraints (3) and ( 4) limit the coverage of each idle agent and an agent on-break to at most density D iτ of unit area i if it is positioned within the travel time dened by adjacency matrix N ij and Nij , respectively. These constraints ensure that part z aτ i and zaτi of the coverage of area i by an idle agent and an agent on-break a respectively, is at most the sum of the densities of the areas j ∈ J within its reach at time τ ∈ T . Furthermore, constraints (5) and ( 6) limit idle coverage and the coverage on-break only to idle agents and the agents at break, respectively. Moreover, constraints [START_REF] Rekik | Implicit shift scheduling with multiple breaks and work stretch duration restrictions[END_REF] guarantee that the incident density covered by each idle agent sums up to at most 1. Similarly, constraints (8) capacitate the coverage for each agent on-break.

Constraints (9) assign to each agent a at each time period τ a unique location j ∈ J , by means of x aτ j , while constraints (10) relate agents' positions x aτ j in two consecutive time periods t, t + 1 based on the maximum distance travelled established in IM jj . Moreover, minimal and maximal break durations are imposed by constraints (11) and (12). Constraints (13) assure that short and long breaks start at latest after a maximum uninterrupted work time M AX w b of consecutive time periods without a break. Additionally, (14) species that long and short breaks are coordinated within the maximum allowed working times.

Finally, constraints (15) are non-negativity constraints on the decision variables.

  Let B = {b s , b l } be a set of short and long breaks respectively. The minimum number of short and long breaks is related to the duration of the shift, labor rules, and legal requirements. We track accumulated workload of each vehicle crew since the last break at each time period τ ∈ T to comply with a given maximum allowed work time M AX w b before the start of a break b ∈ B. Each break has a minimal duration ∆ M IN b and a maximal duration ∆ M AX b , that specify the required amount of break time based on legal requirements. Since the problem of area coverage is interconnected with the break assignment problem in the emergency eet context, we approach it by a unique math-ematical programming model in which the decisions on the number of vehicles necessary for the coverage, their locations, identities, and the break assignments are decided all at once for the whole workshift. Sets and indices T time horizon; a set of time periods in a work shift; τ ∈ T A set of agents a ∈ A representing |A| capacitated vehicles with vehicle crews B set of break types for example, {b s , b l }, where b s stands for short breaks, whereas b l stands for long breaks I set of unit areas i ∈ I with positive incident density J set of unit areas j ∈ J , apt for vehicle locations Parameters D iτ estimated demand and, thus, required minimum proportion of vehicles for unit area i ∈ I at time τ ∈ T ∆ M IN b minimal duration of break b ∈ B ∆ M AX b maximal duration of break b ∈ B IM jj valued 1 if an agent can move from j ∈ J to j ∈ J based on the maximum transport time between 2 consecutive periods; 0 otherwise N ij 1 if an idle vehicle in j ∈ J can assist an incident at i ∈ I within a given target arrival time, 0 otherwise Nij 1 if a vehicle on a break located at j ∈ J can assist an incident at i ∈ I within a predened target arrival time, 0 otherwise M AX w b maximum allowed work time before assigning break b ∈ B usual this time will be 3 hours for short and 4-6 hours for long breaks Decision variables

y

  aτ ≥ ∆ M IN b α abτ , ∀a ∈ A, b ∈ B, τ = {1, |T | -∆ M IN b } (11) y a (τ +∆ M AX b +1) + α abτ ≤ 1, ∀a ∈ A, b ∈ B, τ = {1, |T | -∆ M AX b

Acknowledgements This work has been partially supported by an STSM Grant from COST Action TD1409 Mathematics for Industry Network (MI-NET).


Redouane Beniazza

Clément Poittevin

Jonathan Lusseau

Stéphane Massip

Frédéric Robert

Yannick Landais
email: y.landais@ism.u-bordeaux1.fr

A Unified Strategy Toward 5-, 6-, and 7-Membered Nitrogen Heterocycles Through Free Radical then Metal-Mediated Functionalization of Ene-carbamates

Keywords: Heterocycle, Heck reaction, Grignard, Vinylsulfones, Cyclization

Free-radical carbo-alkenylation of N-aryl, N-benzyl, and N-phenethyl-ene-carbamates with a disulfone provides vinylsulfones which may then be functionalized and engaged in Heck-type coupling to furnish highly substituted 5-, 6-and 7-membered nitrogen heterocycles. Grignardmediated cyclization starting from the same substrates further allowed a nucleophilic cascade process, affording a straightforward access to hydrocarbazoles, which may be regarded as potent intermediates for the synthesis of alkaloids of the aspidosperma family.

Introduction

Nitrogen-containing heterocycles are widely distributed in nature and among biologically relevant targets. [1] Because of their importance to pharmaceutical and agrochemical industries, [2] organic chemists have explored numerous strategies to access them in a straightforward manner. [START_REF] Clark | For selected examples[END_REF] Transitionmetal catalyzed processes [4] (Heck coupling, ring-closing metathesis, ….), ionic cyclizations [5] (halonium-mediated ring closure,….) or free-radical cyclizations [6] hold a prominent place in this context, allowing a straightforward access to heterocycles of various ring size, from simple precursors under mild conditions. Despite the numerous methods reported to date, there is still a need for more straightforward methodologies to elaborate nitrogen heterocycles, allowing a fine tuning of the ring size, the installation of several stereogenic centers and a good compatibility with resident functional groups. Finally, unified strategies offering an access to heterocycles with various ring sizes are attractive, leading, through a minor modification of a common framework, to structures as diverse as those found in alkaloids depicted in Figure 1. [7] In the course of our ongoing studies on free-radical processes, we have developed several carbofunctionalization of olefins, [8] affording polyfunctional systems, which we anticipated, could be useful precursors in the preparation of nitrogen heterocycles, intermediates in the synthesis of more complex targets (Figure 1). For instance, we showed that the carbo-alkenylation of electron-rich olefins leads to the formation of two new carbon-carbon bonds with the installation of two new functional groups. [8b,c,g] Ketones, esters, amides, thioesters are amongst the functional groups that may be added, starting from the corresponding xanthates or iodides. [8] The second component is an olefin issued from a vinylsulfone (i.e. 3). A broad variety of addition adduct is thus available, changing the nature of the radical precursor and that of the sulfonyl trap. The free-radical carbo-alkenylation process is particularly efficient with electron-rich olefins as this radical chain is governed by polar effects. Ene-carbamate and enamides are thus excellent olefinic partners for this reaction and provide the addition products with generally high yields (Scheme 1).

Scheme 1. Carbo-alkenylation of ene-carbamates.

The occurrence of a nitrogen center and a nearby unsaturation in compounds 4a-b led us envisaged their further elaboration to access 5-, 6-and 7-membered heterocycles in a limited number of steps. Scheme 2 depicts a general strategy to access these medium-size heterocycles, starting from a common structural motif I, resulting from the carbo-alkenylation of ene-carbamates bearing an N-alkylaryl moiety. The C-C bond formation and ring-closure of these precursors would then be carried out relying on two organometallic processes, i.e. an intramolecular Heck reaction and a conjugate addition of a Grignard reagent. Depending on the position of the olefinic appendage and the length of the carbon chain between N and the aryl moiety, various heterocycles would thus be accessible. Scheme 2. A general strategy to access nitrogenated 5-, 6-and 7-membered heterocycles.

We report here our efforts to generate, from 3-component carbo-alkenylation products, 5-, 6-and 7membered heterocycles through the intramolecular addition of an aryl-metal species (X = Pd or Mg, Scheme 2) onto the unsaturated sulfone. Tandem nucleophilic cyclizations were also carried out on the same substrates, leading to polycyclic systems with good stereocontrol.

Results and Discussion

The study started with the preparation of the desired three-component adducts through the free-radical carbo-alkenylation of enamides 6a-g, using xanthates 5a-c and vinyldisulfone 3 under conditions reported previously. [8g] Conjugated sulfones 7a-j were thus obtained in generally high yields as the Eisomer (Table 1). Interestingly, the reaction conditions were compatible with substrates bearing a bromine substituent on the aromatic ring, as in 7f and 7j. Finally, scaling up is allowed as 7b was for instance prepared on a 6.7 mmol scale leading to 3.4 g of product.

Table 1. Free-radical carbo-olefination of enamides.

Iodination of the aryl substituent in 7b-i was then carried out using I2 and Ag2SO4 in MeOH. [9] Iodoarenes 8a-c and 8e-f were obtained in good yields and excellent regioselectivity, except for arylamine 7g, which led to an inseparable mixture of two ortho-iodoarenes 8d-d' in a 68% overall yield (Table 2). 8d-8d' [b] 68 5 7h 2 h 8e 92 6 7i 0.7 h 8f 92 [a] Isolated yields. [b] 3:2 mixture.

With the iodoarenes 8a-f in hands, we then evaluated their reactivity in Heck-type processes. [START_REF] De Meijere | For general reviews on Heck reaction[END_REF] Preliminary attempts were carried out using precursor 8a, using Pd(OAc)2 and PPh3 with DBU as a base (Table 3, Conditions A, entry 1). [11] Under these conditions, the expected 7-membered ring compound was not formed, but instead we observed the isomerization of the double bond to afford ene-carbamate 10. Changing the palladium source to Pd2(dba)3 and heating in dimethylacetamide (DMA) [12] forced the cyclization and led to the desired 7-membered ring carbamate 9a in reasonable yield as a E/Z mixture of isomers (Table 3, Conditions B, entry 2). Addition of P(o-Tol)3 (60 mol%) to the previous conditions had a dramatic effect, [13] leading to the same carbamate 9a but in a 94% yield as a single Z-isomer (Table 3, Conditions C, entry 3). When these conditions were applied to 8b, the same observations were made and better yield and selectivities were obtained using the combination Pd2(dba)3/P(o-Tol)3/NEt3 in DMA (entry 5). Produc t E/Z ratio Yield (%) [b] 1 8 a NEt3 (3 eq), PhMe, 110 °C, 2 h. [b] Isolated yields.

A
Removal of the Boc protecting group in 9a led to the corresponding amine which was not isolated, but directly treated with camphorsulfonic acid in toluene to provide, in high overall yield, the lactam 11, possessing the tricyclic structure of hainanensine (Figure 1). [7b,14] The structure and stereochemistry of 11 was unambiguously assigned through X-ray diffraction studies. The stereochemistry of 9b was assigned accordingly (Scheme 3). The isomerization of the vinylic 8a into the allylic sulfone 10 could easily be carried out by treatment with DBU, [15] which led us examine the behavior of 10 under the above Heck reaction conditions. Treatment of 10 under conditions C led to no reaction, likely as a result of the important steric hindrance around the olefinic moiety. However, when conditions B, without ligand, were tested, 10 was converted, in good yield, into a 8:2 mixture of cyclized products 12a and 12b (Scheme 4). These compounds result from a 6-exo Heck cyclization, [16] to nitrogen, which delivers the corresponding alkyl-Pd species, undergoing a -hydride elimination to form predominantly tetrahydroisoquinoline 12a. A low amount of 12b was also formed resulting from the competitive elimination of the sulfonyl group. [17] The structure of 12b was confirmed through X-ray diffraction studies, while that of 12a, was secured after removal of the Boc group and subsequent lactamization under acidic conditions, leading to 13 in excellent overall yield. The isoquinoline 6-membered ring may also be accessible directly starting from the iodoaryl benzylamine, as shown for 8c (Scheme 5). Treatment of the latter, under conditions B, thus led to the formation of the 6-membered ring system 14. The latter may be formed through a 6-exo Heck cyclization, followed by the isomerization of the cyclization product. Isomerization of 8c in the basic medium prior to a 6-endo Heck reaction might also be some precedent in the literature. [18] However, when 8c was first isomerized into the ene-carbamate 15, then cyclized under conditions B, the corresponding isoindolines 16a and 16b were formed in reasonable yields instead of 14, thus ruling out the alternative isomerization/6-endo process. This also establishes that the 5-exo Heck cyclization is possible, [19] even with sterically hindered ene-carbamate such as 15. As above, desulfonylation also occurred in small amount to produce 16b. A 6-exo reaction was also observed with aryl bromide 7j, leading to 16c as a single Z-isomer using conditions C (Scheme 5). Removal of the N-Boc group and lactamization afforded tricyclic 16d in good overall yield and only 4 steps from the corresponding enamide. NOESY experiments (supporting information) establish the Zconfiguration of the vinylsulfone moiety in 16d as well as in its precursor 16c, in good agreement with observations made during the transformation of 8a into Z-9a (Table 3)

Scheme 5. Heck reaction on bromo-and iodoarylbenzylamine 7j and 8c.

The 5-exo Heck cyclization was then extended to iodoarylamines 8e-f, using again conditions B. As described for the analogue 8c, the cyclization was effective, leading directly to the fully substituted indole products after isomerization of the intermediate formed upon cyclization (Scheme 6). Under conditions B, the Heck cyclization is thus followed by an isomerization and the removal of the Boc protecting group to give 17a. [20] Under milder conditions (110°C instead of 140°C), 8f led to the Bocprotected indole 17b in excellent yield. Bromide 7f was reactive under conditions C (with a phosphine) and led to a mixture of the protected and unprotected indoles 18a and 18b in good overall yield. This sequence thus provides a straightforward access to functionalized indoles in only two or three steps starting from simple ene-carbamates.

Scheme 6. An access to the indole skeleton through Heck reaction on haloarylamines 7f and 8e-f.

As shown above, the free-radical olefin carbo-alkenylation-Heck cyclization sequence provides a straightforward entry to a variety of 5-, 6-and 7-membered nitrogen heterocycles in generally good yields. The carbo-alkenylation of olefins also allows the incorporation of a second functional group, which might be useful for further functionalization, including cascade processes. It was thus anticipated that iodides 8a-f might be involved in a double cyclization, resulting from the addition of an aryl-metal onto the unsaturated sulfone, followed by a second cyclization on the ester or nitrile of the side chain (Scheme 7).

Scheme 7. Nucleophilic cascade processes as a route to hydrocarbazoles.

Preliminary attempts were carried out starting from aryl iodide 8f. A Grignard reagent was thus generated from the latter using Knochel reagent [21] (i-PrMgCl-LiCl in THF), then transmetallation of the organomagnesium intermediate with a stoichiometric amount of CuCN (Table 4, entry 1). Two cyclized products 19 and 20 were thus formed; i.e. a keto-sulfone 19 resulting from the expected double cyclization depicted in Scheme 7, and a second tricyclic system 20, likely formed through further reduction of 19 under the reaction conditions. Each compound was formed as a single diastereomer, with stereochemistry as shown. A second experiment (entry 2), without the addition of the copper salt, afforded the same products in a similar ratio, showing that the Grignard reagent alone was adding to the vinyl sulfone and that the resulting -sulfonyl carbanion was reactive enough to add to the ester group. [START_REF] Simpkins | Sulphones in Organic Synthesis[END_REF] Several conditions were then tested to decrease the amount of alcohol formed during the process. Adding i-PrMgCl-LiCl slowly, using a syringe pump (entry 3), slightly improved the ratio in favor of the ketone 19. Changing the solvent from THF to benzene did not modify the ratio (entry 4), in contrast with earlier work suggesting that when benzene was used as a solvent, the reduction by i-PrMgCl-LiCl could be minimized. [START_REF] Canonne | [END_REF] Finally transmetallation with ZnCl2 led to the same results (entry 5). [24] Interestingly, monitoring of the reaction mixture (TLC analysis) after 1 h at -90°C showed that, even at this low temperature, formation of the Grignard reagent and the double cyclization were occurring and were faster than the transmetallation. [f,g] Yield 20 (%) [f,g]

1 i-PrMgCl-LiCl, CuCN [a]
37 37 2 i-PrMgCl-LiCl [b] 30 30 3

i-PrMgCl-LiCl, Cond A [c] 52 20 4 i-PrMgCl-LiCl, Cond B [d] 48 27 5 i-PrMgCl-LiCl, ZnCl2 [e] 51 22 [a] i-PrMgCl-LiCl (2 equiv.), THF, 6.5 h at 0°C then RT, 12h, then CuCN-2 LiCl (1.2 equiv.), -25°C, 2.5 h. [b] i-PrMgCl-LiCl (2.8 equiv.), THF, 6.5 h at -40°C. [c] Cond. A: i-PrMgCl-LiCl (2.8 equiv.) added with a syringe pump over 12h, THF, 0°C. [d] Cond. B: i-PrMgCl-LiCl (4.8 equiv.) added with a syringe pump over 12h, benzene, RT. [e] Cond. C: i-PrMgCl-LiCl (3.8 equiv.), THF, -90°C, then ZnCl2, THF, -90°C, to RT, 4 h. [f] Isolated yields after chromatography. [g] 19 and 20 were obtained as single diastereoisomers (supporting information).

Treatment of the ketone 19 with i-PrMgCl-LiCl led to the alcohol 20 in 47% yield with complete diastereocontrol, along with 43% of the recovered starting material, thus demonstrating that 20 was formed through reduction of 19 with the excess of i-PrMgCl-LiCl (Scheme 8). 19 was also reduced more efficiently with NaBH4 affording 20 in high yield and complete diastereocontrol. The stereochemistry of 19 and that of the reduced product 20, assigned through 1 H NMR studies (for extensive NMR experiments, see supporting information), indicates that epimerization at the chiral center bearing the sulfonyl group has occurred. This isomerization likely took place prior to the reduction, as enolization of the -sulfonylketone 19 into its epimer 19' (which has not been isolated) (Scheme 9) should be relatively easy under the reaction conditions, considering the acidity of the proton to the carbonyl group (pka ranging between 11-15 in DMSO). [START_REF] Simpkins | Sulphones in Organic Synthesis[END_REF]25] DFT calculations showed that 19 and 19' display lowest energy twist-boat conformations, with energy difference (computed at the M06-2X/6-31G (d,p) level) of 3.5 kcal/mol. Closer examination of these conformations however revealed that axial and equatorial approaches of the reductive agent onto the carbonyl group of 19 are both hindered, while the equatorial position is more easily accessible in the least stable 19', rationalizing the stereochemical outcome. [26] The strong interaction between the PhSO2 moiety and the ortho-OMe substituent of the aromatic substituent in 19' explains its higher energy as compared to 19. The reduction of 19 thus proceeds under a Curtin-Hammett regime, through the least stable, but more reactive epimer 19'. It is finally worth noticing that when alcohol 20 was oxidized using Dess-Martin periodinane, ketone 19 was obtained in 78% yield as a single isomer. Oxidation of 20 likely provides first the ketone isomer 19', which then epimerizes into the thermodynamically more stable epimer 19. The double anionic cyclization cascade was then extended to nitrile 8e (Scheme 10). This led to a tricyclic product 21, obtained as a single cis-isomer, and exhibiting an enamine function resulting from the tautomerization of the -sulfonylimine product.

10. Double anionic cyclization of nitrile 8e.

Finally, the strategy was applied to the cyclization of cyclic enamide 24, easily obtained through the free-radical carbo-olefination of enamide 22, followed by the iodination of the resulting threecomponent adduct 23 (Scheme 11). Iodoaryl-enamide 24 was thus treated with i-PrMgCl-LiCl under above conditions, leading to the expected tetracyclic product 25, as a single isomer, albeit in poor yield. No trace of the ketone precursor was detected under such conditions. The poor yield is probably due to the important strain and the trans-stereochemistry in precursor 24, which disfavors the successive cyclizations. The structure of 25 was unambiguously established through 1 H NMR studies (Supporting information). Although the yield of the cyclization step is low, the unusual structure of 25 is noteworthy, with 3 stereogenic centers created in a single pot.

Conclusion

In summary, we reported here on the straightforward access to a series of nitrogen heterocycles through a sequence of 3 consecutive reactions, including a free-radical olefin carbo-alkenylation, followed by a regioselective iodination of an arene, and finally an organometallic-mediated cyclization. Intramolecular Heck reaction and anionic (Grignard) processes were used to close the ring and generate the heterocycles. 5-, 6 and 7-membered rings are thus accessible through this sequence, offering an efficient and unified access to precursors of various alkaloids (Figure 1). [7,27] The initial carbo-alkenylation of olefins may also be performed on compounds bearing an aryl bromide, thus allowing the elaboration into a given heterocycle in only 2 steps (7j and 7f, scheme 5-6). The use of the Knochel "turbo Grignard" reagent led to double anionic cyclization affording polycyclic systems in generally good yields and high stereocontrol. Interestingly, further stereoselective reduction of the resulting ketone was also observed under these conditions. Finally, it is worth adding that an access to enantioenriched 5-and 6-membered heterocycles is at hand starting from precursors 10 or 15 using Pd catalysts and chiral ligands. Work along these lines is currently under progress and will be reported in due course.

Experimental Section

General procedure A for the Free-radical carbo-alkenylation of ene-carbamates.

To a solution of xanthate 5a (1 equiv.) in dry 1,2-DCE (2.5 to 15 mL) were added ene-carbamate 6 (1 to 2 equiv.), vinyldisulfone 3 (1.2 equiv.) and di(tributyltin) (1 to 1.5 equiv.). The reaction mixture was degassed, then 15 mol% of DTBHN were added and the reaction mixture was stirred for 1.5 h at 65°C. The yellow reaction mixture was then concentrated under reduced pressure and purified by chromatography on silica gel (Petroleum ether (PE)/EtOAc). 4, 156.6, 149.0, 147.7, 144.1, 139.9, 133.6, 132.2, 131.0, 129.4, 127.7, 120.7, 111.9, 111.4, 60.7, 56.2, 55.9, 52.9, 46.9, 36.1, 30.4, 26.4, 14.2; HRMS (ESI) Calcd.

for C26H33NO8NaS [M+Na] + 542.1819, found 542.1819.

General procedure C for the Heck reaction.

To a stirred solution of iodoarylamines 8 (1 equiv.), (o-tol)3P (conditions C) and Pd2(dba)3 (0.15 equiv.) in toluene (conditions C) or DMA (conditions B) were added Et3N (3 equiv.) at room temperature and the resulting mixture was stirred under reflux for 2 h. The reaction mixture was quenched with saturated NH4Cl aq. and partitioned between CH2Cl2 and water. The organic phase was collected and the aqueous phase extracted with CH2Cl2 (2 x 30 mL). The combined organic extract was dried over Na2SO4, filtered and concentrated in vacuo. The residue was purified by flash chromatography on silica gel (EP/EtOAc) to afford the desired compound. (2.1 g, 3.06 mmol, 1 equiv.) in PhMe (30 mL), (o-tol)3P (558.1 mg, 1.836 mmol, 0.6 equiv.), Pd2(dba)3 (420.3 mg, 0.459 mmol, 0.15 equiv.) and Et3N (1.29 mL, 9.18 mmol, 3 equiv.). Purification by flash chromatography on silica gel, (70/30 to 60/40 PE/EtOAc) afforded compound 9a (1.601 g, 94%) as a yellow oil. Rf = 0.23 (PE/AcOEt 60/40); IR (ATR) νmax (cm -1 ) = 2972, 1729, 1694, 1514, 1446, 1264, 1143, 1082, 731; 1 H-NMR (400 MHz, CDCl3) δ (ppm) = 8.05-7.92 (m, 2H), 7.61-7.46 (m, 3H), 6.59 (s, 1H), 6.57 (s, 1H), 6.38 (s, 1H), 6.33 (t, J = 7.2 Hz, 1H), 4.05 (q, J = 7.2 Hz, 2H), 3.82 (s, 3H), 3.79 (s, 3H), 3.74-3.64 (m, 1H), 3.55-3.41 (m, 1H), 2.86-2.73 (m, 2H), 2.28-2.18 (m, 2H), 2.11-2.00 (m, 1H), 1.78-1.67 (m, 1H), 1.48 (s, 9H), 1.20 (t, J = 7.2 Hz, 3H); 13 C-NMR (100 MHz, CDCl3) δ (ppm) = 172. 6, 156.3, 155.1, 150.7, 148.2, 142.2, 133.4, 132.0, 131.5, 129.3, 127.6, 114.7, 113.4, 80.8, 60.4, 56.7, 56.2, 52.1, 41.5, 36.0, 31.1, 28.5, 28.0, 14.2

General procedure D for anionic cascade using Knochel Grignard reagent.

To a solution of iodide (1 equiv.) in THF was added dropwise, using a syringe pump, a 1.18 M solution of i-PrMgCl-LiCl in THF (1.3 to 4 equiv.) at 0°C. The yellow reaction mixture was stirred 1-2 h at 0°C, then 1-2 h at room temperature and finally quenched with an aqueous ammonium chloride solution. The aqueous layer was extracted with EtOAc. The combined organic layers were washed with brine, dried over sodium sulfate and concentrated under reduced pressure. The crude mixture, after purification by column chromatography (silica gel), gave tricyclic ketones and corresponding alcohols. Ketone (19) and alcohol (20). Synthesized according to general procedure D from iodide 8e (205.7 mg, 0.30 mmol, 1 equiv.) in THF (3 mL) and 1.18 M solution of i-PrMgCl-LiCl in THF (0.56 mL, 0.66 mmol, 2.2 equiv.) added via syringe pump for 12 h at 0°C. Purification by flash chromatography on silica gel (PE/EtOAc 80/20 to 72/18) afforded the ketone 19 (80.3 mg, 52%, d.r. > 95:5) , 1701, 1604, 1484, 1394, 1323, 1168; 1 H-NMR (600 MHz, 328.2 K, CDCl3) δ (ppm) = 7. 97-7.93 (m, 2H), 7.71-7.67 (m, 1H), 7.63-7.58 (m, 2H), 7.24 (brs, 1H), 4.98-4.90 (m, 2H), 4.71 (d, J = 10.0 Hz, 1H), 3.84 (s, 3H), 3.72 (s, 3H), 3.71 (s, 3H), 2.74 (ddt, J = 15.1 Hz, J = 13.7 Hz and J = 4.2 Hz, 1H), 2.55 (dt, J = 17.8 Hz and J = 4.1 Hz, 1H), 2.40-2.33 (m, 1H), 2.21 (ddd, J = 18.0 Hz, J = 13.6 Hz and J = 4.5 Hz, 1H), 1.59 (s, 9H); 13 C-NMR (50 MHz, CDCl3) δ (ppm) = 200.7, 154.8, 152.1, 149.7, 139.5, 139.2, 137.3, 134.3, 129.5 , 128.5, 111.5, 95.8, 81.8, 71.8, 61.2, 60.7, 56.6, 56.2, 38.2, 34.7, 28.6, 24.8 1699, 1596, 1478, 1332, 1146, 914; 1 H-NMR (300 MHz, CDCl3) δ (ppm) = 8. 10-7.99 (m, 2H), 7.74-7.55 (m, 3H), 7.43-7.10 (brs, 1H), 4.94 (d, J =4.0 Hz, 1H), 4.85-4.66 (m, 1H), 4.46-4.16 (brs, 1H), 4.08-3.93 (m, 1H), 3.89 (d, J = 7.9 Hz, 1H), 3.82 (s, 3H), 3.70 (s, 3H), 3.37 (s, 3H), 2.53-2.37 (m, 1H), 2.30 (dq, J = 3.8 Hz and J = 13.0 Hz, 1H), 1.98-1.83 (m, 1H), 1.62-1.37 (m, 10H); 13 C-NMR (50 MHz, CDCl3) δ (ppm) = 154. 1, 151.8, 150.5, 139.9, 137.6, 137.2, 134.1, 129.5, 128.2, 111.3, 96.7, 81.2, 70.1, 64.3, 61.0 , 60.2, 57.1, 56.2, 41.0, 28.5, 28.0, 27.6; HRMS (ESI) Calcd. for C26H33NO8NaS [M+Na] + 542.1825 found 542.1821.

Figure 1 .

 1 Figure 1. Nitrogen heterocycle formation

  Cond. A: Pd(OAc)2 (15 mol%), PPh3 (60 mol%), NEt3 (3 eq), DBU (1.5 eq), PhMe then 70 °C, 3 h; Cond. B: Pd2(dba)3 (15 mol%), NEt3 (3 eq) DMA, 140 °C, 2 h; Cond. C: Pd2(dba)3 (15 mol%), P(o-Tol)3 (60 mol%)

Scheme 3 .

 3 Scheme 3. Deprotection and lactamization of 9a.

Scheme 4 .

 4 Scheme 4. Heck reaction on iodoaryl-ene-carbamate 10.

Scheme 8 .

 8 Scheme 8. Reduction of ketone 19.

Scheme 9 .

 9 Scheme 9. Epimerization and computed models for the reduction of ketone 19.

Scheme 11 .

 11 Scheme 11. Double anionic cyclization of 24.

  Synthesized according to general procedure C (conditions C) from iodide 8a

  as a colorless oil and alcohol 20 (31.4 mg, 20%, d.r. > 95:5) as a white solid. (4S,4aR,9aR)-Tert-butyl 5,6,7-trimethoxy-3-oxo-4-(phenylsulfonyl)-2,3,4,4a-tetrahydro-1H-carbazole-9(9aH)carboxylate (19). Rf = 0.44 (PE/EtOAc 70/30); IR (ATR) νmax (cm -1 ) = 2969

  ; HRMS (ESI) Calcd. for C26H31NO8NaS [M+Na] + 540.1668 found 540.1665. = 0.22 (PE/EtOAc 70/30); Mp = 120°C (PE/EtOAc); IR (ATR) νmax (cm -1 ) = 3497, 2974,

Table 2 . Iodination of arylamines 7b-i.

 2

	Entry Arene	Time Iodoarene Yield (%) [a]
	1	7b	0.5 h	8a	80
	2	7c	2 h	8b	70
	3	7d	2 h	8c	74
	4	7g	2 h

Table 3 . Heck reaction on iodoarylamines 8a-b.

 3

	Entr	A	Condition
	y	rI	s [a]

Table 4 .

 4 Anionic cascade using i-PrMgCl-LiCl reagent.

	Entr	Conditions	Yield
	y		19
			(%)

;

  HRMS (ESI) Calcd. for C29H37NO8NaS [M+Na] + 582.2288 found 582.2286.