Preliminary mission profile of Hera's Milani CubeSat
Fabio Ferrari, Vittorio Franzese, Mattia Pugliatti, Carmine Giordano, Francesco Topputo
PPreliminary mission profile of Hera’s Milani CubeSat
Fabio Ferrari ∗ , Vittorio Franzese, Mattia Pugliatti, Carmine Giordano,Francesco Topputo Department of Aerospace Science and Technology, Politecnico di Milano, Via La Masa 34,20156, Milan, Italy
Abstract
CubeSats offer a flexible and low-cost option to increase the scientific and tech-nological return of small-body exploration missions. ESA’s Hera mission, theEuropean component of the Asteroid Impact and Deflection Assessment (AIDA)international collaboration, plans on deploying two CubeSats in the proximity ofbinary system 65803 Didymos, after arrival in 2027. In this work, we discuss thefeasibility and preliminary mission profile of Hera’s Milani CubeSat. The Cube-Sat mission is designed to achieve both scientific and technological objectives.We identify the design challenges and discuss design criteria to find suitablesolutions in terms of mission analysis, operational trajectories, and Guidance,Navigation, & Control (GNC) design. We present initial trajectories and GNCbaseline, as a result of trade-off analyses. We assess the feasibility of the MilaniCubeSat mission and provide a preliminary solution to cover the operationalmission profile of Milani in the close-proximity of Didymos system.
Keywords:
Hera, AIDA, CubeSat, Didymos, asteroid, Milani ∗ Corresponding author
Email addresses: [email protected] (Fabio Ferrari), [email protected] (Vittorio Franzese), [email protected] (MattiaPugliatti), [email protected] (Carmine Giordano), [email protected] (Francesco Topputo)
Preprint submitted to Advances in Space Research February 3, 2021 a r X i v : . [ a s t r o - ph . E P ] F e b . Introduction Motivated by a great scientific interest and large accessibility to space missions,small celestial bodies represent the current frontier of space exploration. Theclose-proximity exploration of asteroids and comets entered a new era in 2000,as the NEAR-Shoemaker spacecraft entered into orbit around asteroid 433 Eros,achieving the first rendezvous with a small celestial body (Veverka et al., 2001).An important milestone was marked more recently, by ESA’s Rosetta (Ulamecet al., 2014) and later by JAXA’s Hayabusa 2 (Van wal et al., 2018; Tsudaet al., 2020) missions, which were able to release small probes and SmallSatson the surface and/or in the close-proximity of such objects. In this context,CubeSats offer a flexible and low-cost option to increase the scientific and tech-nological return of small-body exploration missions. Although many concepts ofinterplanetary CubeSats have been studied and/or are planned for future mis-sions (Walker et al., 2018; Franzese et al., 2019; Speretta et al., 2019; Topputoet al., 2020), very few of them have flown so far (Freeman, 2020; Lockett et al.,2020), and no CubeSat has ever flown in the proximity of a small-body yet.ESA’s Hera mission (Michel et al., 2018), the European component of theAsteroid Impact and Deflection Assessment (AIDA) international collabora-tion (Cheng et al., 2015), plans on deploying two CubeSats in the proximityof binary system 65803 Didymos, after arrival in 2027. The idea is supportedby several SmallSat/CubeSat studies that have been performed in the past fewyears with reference to Hera (formerly known as AIM), to study the feasibilityof deploying a small lander (Ferrari and Lavagna, 2018, 2016; Lange et al., 2018;C¸ elik et al., 2019) and possibly CubeSats (Kohout et al., 2018; Lasagni Manghiet al., 2018; Perez et al., 2018) in the close proximity of Didymos. These were an-ticipated by detailed studies of the dynamical environment near binary asteroidsystems (Tardivel and Scheeres, 2013; Tardivel, 2016; Ferrari et al., 2016, 2014;C¸ elik and S´anchez, 2017), some with direct application to the Didymos casestudy (Dell’Elce et al., 2017; Capannolo et al., 2019, 2016). Hera is currentlyin its phase-B design, on-track to be launched in 2024. Its payloads have been2ecently consolidated and, as mentioned, it will carry two 6U CubeSats, to bedeployed after rendezvous with Didymos. These are called Juventas (Karatekinet al., 2019) and Milani. Milani has been officially confirmed on mid 2020 andis currently in its phase-A design. Its flight readiness does reflect Hera schedule,foreseen in late 2024.In this work, we discuss the feasibility and preliminary mission profile of Hera’sMilani CubeSat. The Milani mission is designed to achieve both scientific andtechnological objectives. The first include the global mapping of Didymos (pri-mary) and Dimorphos (secondary) asteroids. This involves determining thecomposition difference between the bodies and the study of their surface prop-erties. In the context of the AIDA international collaboration, Milani will helpat determining the composition of the ejecta created after the impact of DARTspacecraft (Cheng et al., 2018) in 2022 on the surface of Dimorphos, and theirfallbacks on the surface of the asteroids. In terms of the technological objec-tives, the mission will be among the first to operate CubeSat technologies in deepspace and the first to use Inter-Satellite Link (ISL) network with the motherspacecraft in such challenging context.Milani is a 6U CubeSat with maneuvering capabilities both in terms of trans-lational and attitude motion (full 6-DOF). After release it will perform au-tonomous operations to reach its operational trajectories towards the fulfilmentof its mission goals. The main payload aboard Milani is the ASPECT hyper-spectral camera (Kohout et al., 2018). The characteristics of the ASPECTcamera are reported in Table 1. The payload has three channels, which arethe Visible (VIS), the Near-Infrared (NIR), and the Short Wavelength Infrared(SWIR). The three channels have different characteristics, especially in terms offield-of-view and sensor size. These quantities affect the allowed orbital rangesto the targets for scientific observations. The visible channel has the largest fieldof view and a 1 Mpx sensor size. The NIR is narrower than the VIS channel,while the SWIR is a mono-pixel circular FOV channel. In addition to ASPECT,which is used for scientific imaging only, Milani hosts two additional cameras,which are used for optical navigation. These cameras have not been selected yet:3 able 1: Characteristics of the ASPECT hyperspectral camera.
Parameter Unit VIS NIR SWIR
Field-Of-View deg 10 x 10 6.68 x 5.36 5Sensor Size pix 1024 x 1024 640 x 512 1Pixel Size µ m 5.5 x 5.5 15 x 15 1000Focal Length mm 32.3 81.7 11.7F-number - 3.3 6.0 0.9the properties and performance assumed for navigation cameras are reported inSection 4.4. As a seconday payload, Milani hosts the VISTA thermogravime-ter (Dirri et al., 2018), which will collect information on the dust environmentnear the asteroids. It is operated in background during the operational phasesof the Milani mission: it does not impose any further requirement and does notrequire a specific tayloring of the mission profile.After release in the proximity of Didymos binary asteroid, Milani independentlymakes its own way to its operational trajectory, optimized to observe the aster-oid system. In this work, we consider the CubeSat limitations given by minia-turized components, and address the challenges in deriving an optimal missionprofile which meets the mission and scientific objectives. The GNC architectureand design that allow to achieve such a mission are also shown. It is worthstressing that the initial results presented in this paper have been obtained inresponse to the relevant ESA call. As such, the preliminary profile here shownwill be revised as both mission and spacecraft design advance in later stages.The paper is organized as follows. Section 2 reports the design constraintsof the mission given by the environment and the payload. Section 3 showsthe mission profile with a detailed explanation of the mission phases. Then,the GNC architecture and preliminary design are shown in Section 4. Theoperational analysis of the payload is reported in Section 5. Finally, conclusionsand a summary of the results are given in Section 6.4 able 2: Didymos system characteristics and imaging constraints. Asteroid d m d p v GSD α θ /FOVDidymos 780 m 10 % 0.15 ≤ ≤ ≤ ≤
2. Design constraints
The constraints affecting the design of the mission and the CubeSat platformare presented in this Section. The Didymos binary system is composed of twoasteroids: the primary (Didymos, also called D1 in the following) and its satel-lite (Dimorphos, also called the secondary or D2 in the following). The primarybody has an estimated diameter of 780 m and an assumed albedo of 0.15. Thesecondary has an estimated diameter of 170 m and an assumed albedo of 0.15.Current estimates consider a 10 % size error for both asteroids. The require-ments applicable to the Milani CubeSat derive directly from both the missionobjectives and the ASPECT payload. To achieve the mission objectives withASPECT, the payload team has determined the following two main conditions:1) To map both asteroids with a ground resolution lower than 2 m/pixel withimages from both the VIS and the NIR channels; 2) To observe the asteroidswith a phase angle (Sun-asteroid-CubeSat angle) between 5 and 25 degrees.In order to ease the operations of Milani, Dimorphos is required to be imagedwithin a single picture, always inside the FOV of ASPECT, while the primarycan be imaged as a 4-images mosaic. These values are summarized in Table 2,where d is the equivalent diameter of the asteroids, m d the associated margin, p v the albedo, GSD the ground sampling distance, α the phase angle, and θ/ FOVthe ratio between the apparent dimension of the asteroid to the ASPECT field-of-view. Note that the limiting value for the FOV is given by the NIR channel,since it is narrower than the VIS channel. The SWIR channel is not consideredhere because it is a monopixel channel.With the values in Table 2, it is easy to verify that Dimorphos fills the FOV5f the VIS channel at 1069 m of distance and the FOV of the NIR channelat 1997 m of distance, while Didymos fills a 2 × Table 3: Mission design constraints.
Asteroid
Min Range Max Range Min Phase Angle Max Phase AngleDidymos 4572 m 10940 m 5 deg 25 deg
3. Mission profile
This section presents the preliminary mission profile for Hera’s Milani CubeSat,from its release in the proximity of Didymos system, up to its decommisioning.We discuss the design strategy to provide efficient release of Milani from Heraspacecraft and detail the operational trajectories during the CubeSat sciencephase. End-of-life options are proposed. The feasibility of the mission profile iseventually discussed. The overall design is compliant with constraints outlinedin Section 2. The dynamics of the CubeSat near the Didymos system are studiedusing a high-fidelity model, which includes the heliocentric motion of Didymossystem barycenter, the binary motion of the asteroids (provided by high-order6ntegration in ESA’s Hera Mission kernels ) and relevant perturbations, suchas the effects of the non-sphericity of asteroids (through a polyhedral modelof Didymos and ellipsoidal model of Dimorphos) and Solar Radiation Pressure(SRP). The Hera spacecraft plans on releasing Milani after arrival at Didymos system,in late spring 2027. In this work, we set the release date to May 1st, 2027. Atthis time the Didymos–Sun distance is 1.5 AU and increases up to 2.0 AU duringthe expected operational life of the CubeSat. The selection of Milani operationaldates is important to characterize the dynamical environment in the proximityof Didymos, as it affects the magnitude of the SRP, which is relevant. On theother hand, the release date does not affect the operations of Milani in termsof orbital determination and illumination conditions. The relative geometry ofHera trajectories and release point is set in terms of Milani/Hera, Didymos andSun position. At any epoch, the release will be performed when Hera is betweenthe binary system and the Sun direction, in order to have Didymos visible onits day side. Milani’s release conditions are carefully selected after an extensiveanalysis, involving the investigation of different release points on Hera’s Earlyand Detailed Characterization Phases trajectories , the analysis of geometricalconstraints at release, the dynamics of the CubeSat after release relative to Heramothercraft and Didymos system. In particular, the following criteria have beenconsidered in terms of release geometry and release trajectory: • Minimum angle between CubeSat release velocity direction and CubeSat-Sun direction of 45 deg; • Minimum safety factor C of the release trajectory of 0.4. , Last accessed: June 2020 see Hera Mission kernels documentation at > v peri = (1 + C ) v parab (1)with v peri and v parab defined as the velocity at pericenter on the release trajec-tory and the parabolic velocity at the release point, respectively. These con-ditions derive from the mother spacecraft requirements in terms of safety andillumination conditions. In addition, the release trajectory was selected to guar-antee consistent relative motion with respect to Hera spacecraft and Didymossystem for up to 7 days after release, in terms of: • Maximum CubeSat–Hera distance of 60 km, to ensure communicationwith the mothercraft; • Maximum phase angle of Didymos system (Sun-Didymos-CubeSat angle)of 90 deg, to ensure dayside visibility of the asteroids;Finally, we analysed the robustness to release uncertainties, related to both thedeployer mechanism and Hera’s GNC accuracy. These are quantified as: • Release velocity in the range 0-5 cm/s ( ± σ value) • Release direction accuracy of the deployer mechanism within 5 deg (3 σ value) • Release orientation accuracy of Hera spacecraft within 0.5 deg (3 σ value)The analysis performed is aimed at finding suitable release directions. In thiscase, pointing and release direction errors are the most important sources oferrors. Position and velocity errors of Hera play a minor role in detecting pre-ferred directions and, at the current stage they can be neglected. These will beadded at a later refinement of the design. Release points are chosen among Heraspacecraft trajectories, which are retrieved from ESA’s Hera Mission kernels.We performed an extensive Monte Carlo analysis of the parameter space (40kruns among eight difference release points) and, as a result, a release from30 km (distance from Didymos system barycenter) in the direction (Az=10 deg,el=60 deg), is selected as a design baseline solution. Directions are shown in8idymos equatorial plane, where Azimuth is the in-plane angle (Az=0 deg to-wards the projection of Sun’s position on Didymos equatorial plane), and ele-vation is the out-of-plane angle. Figure 1 shows the results of the analysis interms of release direction, for the 30 km distant release point. Each releasecondition is propagated forward for 7 days. The compliance to the aforemen-tioned constraints is checked at any time on the release trajectory. Feasiblerelease directions are identified by green markers, while red markers indicateconditions where the constraints are not satisfied. Unfeasible release directionin Figure 1 are characterized by a mix of green and red markers. This is dueto effect of the release velocity: these directions are typically unfeasible for highrelease velocities (close to 5 cm/s), but might be feasible for lower velocities. Infact, the higher the release velocity, the higher the probability of falling beyonda 90 deg phase angle or 60 km distance from Hera after a 7-day ballistic arc.The blue marker highlight the selected release direction.The release solution is shown in Figure 2. The trajectory of Milani and Heraspacecraft are shown for seven days after release. This solution is compliantwith design constraints, robust to uncertainties, and guarantees a safe 7-dayballistic arc after release. After release from Hera and commissioning, Milani will maneuver to performscientific operations. This section presents the selected operational orbit andmaneuvering strategy to accomplish Milani’s mission objectives. As summa-rized in Table 3, scientific operations are carried at a distance within the range4.572-10.940 km from Didymos system and when the phase angle (Sun-asteroid-CubeSat angle) of Didymos and Dimorphos is in the range 5-25 deg. Also, weenforce the CubeSat to have a non-zero elevation above Didymos equatorialplane, to ensure visibility of the asteroids poles. In terms of ∆ v cost, we consid-ered a budget of 10 m/s. In addition to constraints reported above, additionaldesign drivers were considered, namely: • Safety , in terms of orbital energy, quantified by the safety factor C. We9 igure 1: Release options in the Didymos equatorial plane. Green and red markers indicatecompliant and non-compliant solutions, respectively. The upper-left picture is the compositeof the other three pictures, plus the addition of geometrical constraints at release (forbidden ±
45 deg cone around CubeSat-Sun direction).
Azimuth is the in-plane angle (Az=0 deg towards the projection of Sun’sposition on Didymos equatorial plane), elevation is the out-of-plane angle.Yellow and black markers indicate the direction of the Sun and Didymos,respectively, as seen from the release point. The blue marker represents theselected release direction.give the highest priority to trajectories that are inherently safe, i.e. withC > < • Simplicity , in terms of reduced operational burden required to performactive operations on the CubeSat and optimization of the time allocated onHera to relay Milani operations. To accomplish this, we leverage naturaldynamics and perturbations of the asteroid environment to reduce thefrequency of manoeuvres. In particular, we consider this criterium moreimportant than ∆ v cost, which is less critical in our mission.10 igure 2: Nominal release trajectory in the Didymos equatorial frame. Milani’s and Hera’sorbital motion is shown for seven days after release. Geometrical constraints (release exclusionangle around Sun’s direction), and Didymos system are shown. • Robustness to uncertainties due to the system and dynamical environ-ment. This is tightly connected to safety and simplicity criteria. Inher-ently safe trajectories are typically more robust to uncertainties. On theother hand, long ballistic time of flights between consecutive manoeu-vres require robust trajectories, able to deal with uncertainties withoutjeopardizing the safety of the Hera mission or altering the mission profilestrategy. • Cost , in terms of ∆ v . Our analyses show that cost is not critical to ourmission. For this reason, safe, simple, and robust trajectories are preferred,at a cost of a slightly higher ∆ v .We performed an extensive trade-off analysis between several orbital strategiesand trajectory solutions, including hyperbolic arcs, closed orbits and three-body11roximity solutions. The results of the trade-off are summarized in Table 4. Inparticular, we show the suitability of each strategy in terms of available time forscience operations (time in the science admissible region), navigation constraints(check on phase angles and asteroid illumination), safety/risk of entering chaoticdynamics, simplicity of operations/maneuvering strategy, dynamical robustnessto uncertainties and ∆ v cost. The study clearly identifies the hyperbolic-arcstrategy as the most promising solution to host Milani scientific operations.This has several advantages in terms of safety, simplicity and robustness, andprovides the best option in terms of asteroid visibility. In particular, we imple-mented a patched-arc manoeuvring strategy that leverage the SRP accelerationto target pre-selected waypoints. To reduce the burden for active operations, weconsider a 4-3-4-3 maneuvering pattern, where maneuvers are performed aftera 4- or 3-day ballistic arc. This is similar to the strategy implemented by theHera spacecraft. Selecting such pattern has the advantage to ease operations atmaneuvering points, which will be fit within a fixed weekly schedule and alignedto Hera operations.After a thorough design process, where several hyperbolic-arc waypoint configu-rations have been investigated, the waypoints of the hyperbolic loop are selectedas shown in Figure 3. Left plots in Figure 3 show the ranges and admissiblescience regions (between dashed lines). Milani has science windows of 1-2 daysfor each arc. Projections of the trajectory on the Didymos equatorial plane areshown on the right. To maximize the time spent by the spacecraft within thescience admissible region, the orbital plane between consecutive hyperbolic arcsis tilted by a few degrees at each maneuvering point. This is clearly visible inthe y-z projection plot (lower-right). This allows Milani to fly within admissibleranges in terms of aspect angle and distance, when transiting near the pericen-ter of each hyperbola. Numbered labels indicate the maneuver sequence, underthe 4-3-4-3 day scheme, from maneuver 0 (insertion into science loop trajectory)up to maneuver 5. The waypoint design strategy is modular and can be fur-ther extended. As detailed in Section 5, six hyperbolic arcs (21 days in total)are enough to accomplish the scientific objectives of the mission. If needed,12 able 4: Science orbit trade-off matrix. Strategy Time forscience Navigation Safety/risk Simplicity Robustness Cost:monthlyLoop(C >
0) 1-2 daysper loop Always onasteroids’dayside Inherentlysafe Compliantto 4-3-4-3pattern 3-4 days 1.5 m/sLoop(C <
0) 2-3 daysper loop Always ondayside Moderaterisk Compliantto 4-3-4-3pattern 2-3 days 1.2 m/sClosedorbit(7 km) < < fewhours perorbit Daysidefor halforbit High risk Maneuverfrequency1-2 days < < < < < the science loop trajectory can be further extended at the cost of 1.5 m/s permonth. Eventually, we discuss two End-of-Life (EoL) options in terms of their conceptand feasibility in the broad context of the Hera mission, with the goal to identifybenefits and criticalities. No baseline solution was selected within the contextof this work.Option 1: Injection into a graveyard heliocentric orbit. This option is safe andcheap, and it does not require any additional trajectory design after the scientificphase (except for a long-term integration of the outgoing heliocentric orbit). As13 igure 3: Nominal science trajectory. Phase angle and distance time profile with respect toDidymos (D1) and Dimorphos (D2) are shown in upper and lower left plots. Science admissibleregion is highlighted (ranges between dashed lines). Projections on Didymos Equatorial framex-y and y-z plane are shown in upper and lower right plots, respectively. These show scienceadmissible regions in terms of distance from the binary system (green sphere is minimumdistance, red sphere is maximum) and phase angles (green cone is minimum value, red coneis maximum value). The Sun direction is also shown (orange arrow inside the green cone), aswell as the projection of Hera spacecraft’s trajectory (green lines in the upper right plot). discussed, the nominal science loop is built as a sequence of hyperbolic arcs.Missing one manoeuvre would safely bring Milani into an escape trajectoryfrom the Didymos system. In addition, the SRP accelerates the CubeSat furtheraway from Didymos, increasing its orbital energy. In this case, a safe graveyardheliocentric orbit can be achieved by missing the last manoeuvre of the scientificphase. After this, the spacecraft takes approximately 10 days to fly beyond a60 km distance from Hera spacecraft. This option is the safest possible andmay be preferred to avoid criticalities in terms of operational burden and costs.However, it does not provide any opportunistic science information in additionto those gathered during the science phase: it is a low risk-low gain solution.14ption 2: Landing attempt on Dimorphos. The second option is to attempta landing on D2. After the nominal scientific and technological objectives ofthe mission are accomplished, it might be worth to exploit Milani to provideadditional data on the Didymos system. To achieve this goal, a higher riskcan be accepted. In this context, we plan to get closer to the Didymos system,dropping the design driver of flying inherently safe hyperbolic trajectories. Asmentioned, orbiting the inner region of Didymos system poses several challengesin terms of navigation and robustness to manoeuvres. This is a high risk-highgain option. The knowledge analysis performed in Section 4.2 shows that, inprinciple, the current GNC baseline would be compatible with a soft-landingdesign for the CubeSat. However, a more detailed analysis will be required torigorously assess the feasibility of such option.
As mentioned, the SRP plays a fundamental role in assessing the dynamicsof the CubeSat in the close-proximity of Didymos. Also, it contributes in arelevant manner to the active maneuvering costs to be provided to control theattitude of the CubeSat. The momentum budget is estimated here by assessingthe impact of the SRP perturbation to the attitude dynamics of Milani. We usea cannonball model with an equivalent area of 0.5160 m , a reflection coefficient( C r ) of 1.1926, and a constant arm of 5 cm. These data are consistent for a 6UCubeSat with large solar arrays.As mentioned earlier, the baseline scenario considers that Milani is released inMay 2027, when the distance from the Sun is 1.5 AU, reaching 1.9 AU and2.2 AU after 3 and 6 months of operations, respectively. For comparison, weconsider here the backup launch option as well, which considers a CubeSatrelease on January 2031, when the distance from the Sun is 1.1 AU, reaching1.5 AU and 1.9 AU after 3 and 6 months of operations, respectively. The latteroption is considered since it is a worst case scenario: the CubeSat is closer tothe Sun and the effect of SRP is higher. The total momentum buildup due toSRP in the worst case scenario (backup launch and 6 months of operations)15 igure 4: SRP total momentum build up by the SRP on Milani after 6 months. The nominalvalue is shown with a red marker for C R = 1 .
19 and SRP arm=5 cm. is illustrated in Figure 4 as function of the key parameters of the cannonballmodel. With the nominal values a total momentum build up of 0.99 mNmsduring the whole mission is estimated.Assuming that the disturbance torque is building up on a single reaction wheel,two options are considered in terms of momentum capacity: 25 mNms and55 mNms. In the first case a total of 40 dumping manoeuvres would be requiredfor 6 months of operations (approximately 1 manoeuvre every 4.5 days) while inthe latter one the number drop to 18 for 6 months of operations (approximately 1manoeuvre every 10 days). The total ∆ V budget to be allocated for momentumdumping is therefore estimated to be around 1 m/s in the worst case scenario.The evolution of the ∆ v budget for desaturation as function of the missionlaunch and duration is illustrated in Figure 5.16 igure 5: Desaturation budget as function of mission duration for the nominal launch (bluecurve) and backup launch (red curve).
4. GNC strategy
The key driver for Milani’s GNC subsystem design is to maximize the opportuni-ties to observe the binary asteroid system. Also, it is paramount to complementthe Orbit Determination (OD) with optical navigation, to always track the tar-get asteroid, and to increase the efficiency of the operations by exploiting thepointing of the scientific observations for optical navigation. All in all, it isbeneficial for the mission to never lose the line-of-sight to the target asteroidwhile performing scientific but also housekeeping tasks.The GNC system architecture is shown in Figure 6. Milani is equipped with anon-board computer (OBC) where two modules are present, namely the ADCSprocessing module and the GNC processing module. These modules are re-sponsible for collecting and processing sensor inputs to elaborate commands forthe actuators. The ground segment is responsible for computing the nominalguidance, navigation, and control of the satellite. This information is sent tothe Hera spacecraft that is acting as a relay satellite and then sent back toMilani via the inter-satellite link (ISL). Apart from the ASPECT payload, weassume that Milani is equipped with a 21 ×
16 deg NavCam and a 40 ×
40 degWide Angle Camera (WAC). These are required for high-resolution imaging ofthe asteroids and optical navigation, as described in Section 4.4. The navigationmeasurements for Milani come from the navigation camera and ISL. The nav-17 era
IMUReaction Wheels ADCS Processing Module
OBC
Navigation Camera
Ground Segment
ISL TX/RX GNC Processing Module
X-bandRF linkISL link
Sun SensorsStar Trackers
CubeSat
OrbitControlAttitudeControl
Figure 6: System architecture. igation camera is used to acquire images of the two asteroids, while the ISL isexploited for range and range-rate measurements with respect to Hera. Milani isequipped with a Six Degree-of-Freedom Reaction Control System (6 DOF RCS)for trajectory and attitude control. The attitude measurements for Milani aregiven by an Inertial Measurement Unit (IMU), two sun sensors, and the startrackers. The attitude is also controlled by the reaction wheels.
The Differential Guidance (DG) strategy (Dei Tos et al. (2019); Park andScheeres (2006)) adopted for Milani’s guidance is detailed in this section. Inthe DG formulation, the whole trajectory is subdivided in different legs. Atthe extremal points of a single leg, two maneuvers are applied to cancel boththe position and velocity deviations on the final leg point. However, the finalimpulse is usually not applied in practice, since at the time of arrival at the finalpoint a new maneuver is calculated in a receding horizon approach. The ma-neuver can be computed by minimizing the deviations from the nominal state18t the final point in a least square residual sense. Thus, the maneuver that hasto be applied at the time t j in order to cancel out the deviations at time t j +1 is computed as Dei Tos et al. (2019)∆ v j = − (cid:0) Φ Trv Φ rv + Φ Tvv Φ vv (cid:1) − (cid:0) Φ Trv Φ rr + Φ Tvv + Φ vr (cid:1) δ r j − δ v j (2)where δ r j and δ v j are the (estimated) position and velocity deviation at time t j , Φ rr , Φ rv , Φ vr and Φ vv are the 3-by-3 blocks of the State Transition Matrix(STM) Φ ( t j , t j +1 ) from time t j to time t j +1 associated to the nominal trajectory. Errors in the dynamical propagation of the trajectories, e.g. inaccuracies instate determination or thrust misalignment, can lead to large deviations withrespect to the nominal trajectory. Hence, a knowledge analysis is required tocompute, through a covariance analysis, the achievable state knowledge. Sim-ulations of the radiometric data for range and range-rate coming from the ISLare performed, generating the pseudo-measurements as ρ = (cid:112) ρ T ρ + ε ρ , ˙ ρ = ρ T η ρ + ε η (3)where ρ is the range, ˙ ρ is the range rate, ρ = r − r H is the relative distancebetween Milani and Hera, while η = v − v H is the relative velocity with ε rep-resenting the error. r and v are position and velocity of Milani Cubesat, while r H and v H represent position and velocity of the Hera spacecraft. Pseudo-mesaurements are used to feed an Extended Kalman Filter (EKF, Schutz et al.,2004) in order to simulate a realistic Orbit Determination procedure. In ourcase, the Hera spacecraft is always in view and no assessment of visibility win-dows is needed. The overall navigation cost, necessary to keep the spacecraft on the nominalpath, is estimated in a closed-loop fashion, taking into account: 1) the knowledgeanalysis (as in Section 4.2) to estimate the deviation of the real trajectory from19he nominal trajectory at the target points; 2) the differential guidance (as inSection 4.1) to assess the stochastic cost, starting from the estimated deviations.The total navigation cost is estimated by means of a Monte Carlo simulation.Following this approach, an initial Gaussian distribution with mean ¯ x andcovariance P is identified and a set of samples x i is generated. Both thestate and the covariance matrix are propagated with the associated dynamicsup the first measurement epoch, where the estimated trajectory is updated.Proceeding in this way, the state estimates are sequentially updated as newmeasurements are processed, leading to the position and velocity knowledgeprofiles. This is repeated up to the final epoch of the Orbit Determinationphase, where the deviation from the nominal path is estimated. The deviationis then pushed forward using the STM up to the maneuver time and used tofeed the guidance law. The correction impulse is computed and applied. Thewhole process is repeated up to the final time for each initial state in the sampleset. The estimation of the total cost for each sample is obtained as the sum ofall maneuvers’ cost, i.e., ∆ v i = (cid:80) Nj =1 (cid:13)(cid:13) ∆ v ij (cid:13)(cid:13) . During the science phase, it is of paramount importance to acquire preciselyand track the nominal trajectory in order to achieve the mission objectives.An assessment considering a higher fidelity model, with the OD process in theloop, is performed. Some assumptions are made for this analysis and they arelisted below: • The guidance law is the standard differential guidance algorithm; • Correction maneuvers are given together with deterministic maneuvers; • No uncertainty in stochastic maneuvers is considered; • Due to technological constraints, correction maneuvers are not applied iftheir value is lower than 5 mm/s;20
An initial a-priori uncertainty of 10 m on position, 1 mm/s on velocity(3 σ ) is used; • To compensate for differences between physical model and real world, athrust misalignment of 1% in magnitude and 1 deg in pointing angle (3 σ )is considered; • The ISL is simulated taking into account an accuracy of 1 m in range and0.1 mm/s in range-rate. The error is modelled as Gaussian noise; • In order to allow Flight Dynamics estimations and reduce the operationalcosts, an interval of 1.5 days between the maneuver and the beginning ofthe OD phase is considered, while a cut-off time of 1 day is inserted beforethe maneuver; • The ISL performs a range measurement every 20 minutes and a range-rateevery 2 minutes; • Propagation is done linearly by means of the STM, while the estimationis done exploiting the EKF; • igure 7: Science orbit timeline (measurements dots are too close to be distinguished). quite precise knowledge at the final point. Indeed, 1 σ position total accuracyis 100 m, while the velocity accuracy is better than 1 mm/s. Furthermore, thecorrections are very effective in strongly reducing the dispersion. This leadsto errors of some meters in position and few tens of microns per second invelocity after the correction step. The overall error associated to the OD iscompatible with respect to the one assumed in the previous analyses when amechanization of the error was considered. The 95% confidence level for totalcorrection maneuver cost in the science phase is 0.069 m/s (Figure 10), whilethe position error one is 2.76 km, again mainly due to uncertainty in the finalmaneuver (Figure 11). As for the release trajectory, the approach described in Section 4.3 is exploited.The first day after release is fully allocated to commissioning. After that, a firstOD lasting 1 day for orbit acquisition is made. This is useful to reduce the hugedispersion given by the release. No correction maneuver is performed during thefirst 7 days. Then, a second Orbit Determination is performed from day 5 andday 6, where the deviation from the nominal path is estimated and then usedas input for the differential guidance algorithm. In the second transfer phaseleg, from the Injection Maneuver to the Science Orbit Acquisition Manuever(SOAM), the scheme similar to the science phase one is used: two correctionmaneuvers are given, the first after 4 days from the Injection Maneuver (IM)22 igure 8: Achievable position knowledge in the science phase. and the second after 7 days from the IM together with the SOAM. Differentlyfrom the science loop, the first correction maneuver is not associated with anydeterministic maneuver, but it is needed in order to cope with the deviationscaused by the Injection Maneuver and to target with an increased precision theScience Orbit Acquisition Maneuver point. In the second transfer phase leg acut-off time of 1.5 days is considered between the OD and the maneuvers, plusa period of 1 day is taken into account between the maneuver and the beginningof the OD. For the initial state uncertainty, the worst-case scenario is taken asreference (see Section 3.3.1 for detailed discussion). Thus, a deployer releasevelocity of 5 cm/s with an uncertainty of 1 cm/s (3 σ ) is used. The half conepointing error is 5 deg; on top of it the Hera pointing accuracy of 0.5 deg (3 σ )is considered.For clarity’s sake, the assumptions made for this analysis are summarized andlisted below: • The guidance law is the standard differential guidance algorithm; • Correction maneuvers are given with the IM, the SOAM and at day 4 ofthe second leg; 23 igure 9: Achievable velocity knowledge in the science phase. • No uncertainty in stochastic maneuvers is considered; • Correction maneuvers are not applied if their value is lower than 5 mm/s; • An initial uncertainty of 5 m on position is considered. The relative veloc-ity with respect to Hera has a mean of 5 cm/s and a standard deviationof 1 cm/s (3 σ ). A pointing error of 5 deg (3 σ , half cone) with a 0.5 degpointing accuracy is used; • A thrust misalignment of 1% in magnitude and 1 deg in angle (3 σ ) isconsidered; • The ISL is simulated taking into account an accuracy of 1 m in range and0.1 mm/s in range-rate. The error is modeled as Gaussian noise; • During the first leg, Orbit Acquisition is performed from day 1 to day 2,while Orbit Determination from day 5 to day 6; • In the second leg, a interval of 1.5 days between the maneuver and thebeginning of the OD phase is considered, while a cut-off time of 1 day is24 a) (b)
Figure 10: (a) Navigation cost probability distribution function for science phase. On they-axis the number of occurrences are shown. (b) Navigation cost cumulative distributionfunction for science phase. inserted before the maneuver; • The ISL performs a range measurement every 20 minutes and a range-rateevery 2 minutes; • Propagation is done linearly by means of the STM, while the estimationis done exploiting the EKF; • a) (b) Figure 11: (a) Final error probability distribution function for science phase. On the y-axisthe number of occurrences are shown. (b) Final error cumulative distribution function forscience phase .Figure 12: Transfer trajectory timeline (measurements dots are too close to be distinguished). sition phase is beneficial to enhance the knowledge analysis in the first transferleg, quenching the dispersion and helping in determine the correct orbit thespacecraft is on just after the release. The covariance analysis shows also thatthe navigation costs (Figure 15) can be represented as a Gaussian distributionof mean 0.01354 m/s and a standard deviation of 0.0039 m/s. The 95%-ile forcorrection maneuver cost in the transfer phase is 2.1 cm/s.
The baseline navigation strategy exploits information of range and range-ratewith respect to the mother spacecraft. In addition, the mission will perform anoptical navigation experiment by processing the images of the asteroids. This is26 igure 13: Achievable position knowledge in the transfer phase intended to validate the performances of optical navigation on-board, but willnot impact the baseline navigation strategy.
Different state-of-art strategies can be adopted for optical navigation. Theyrange from the landmark-based methods to centroiding and disk fitting meth-ods. The landmark navigation estimates the position of Milani based on thenatural landmarks on the asteroid surface de Santayana and Lauer (2015). It isaccurate, however is also heavy from a computational standpoint. The centroid-ing method with disk fitting exploits the acquisition of the center of brightnessof the figure to estimate the relative line-of-sight and the external horizon toestimate the apparent asteroid size, which is related to the relative range Gil-Fernandez and Ortega-Hernando (2018). This method can yield a good accu-racy, the image processing required is simple, and an accurate asteroid modelis not required. The horizon-based navigation is similar to landmark naviga-tion, but it compares the asteroid shape and dimension as seen in the imageswith an asteroid model Owen (2011). The correlation between the two yield an27 igure 14: Achievable velocity knowledge in the transfer phase information about the relative position and pose of Milani at a very high compu-tational cost, and an accurate asteroid shape model is required. We performeda trade-off analysis to select the most suitable method and the centroiding withdisk fitting resulted as the most promising one for optical navigation owing toits accuracy, robustness, simplicity, and independency from the asteroid modelknowledge. Thus, a navigation strategy exploiting the centroiding techniquewith disk fitting is baselined for navigation. During the occultation periods ofthe secondary by the primary body or shadow, the navigation strategy will stillbe robust, as Milani could either use ISL range and range-rate measurements oruse Didymos visual images (provided that the navigation NavCam field-of-viewwill be able to image Didymos fully within the frame) or relying on on-boardpropagation to avoid losing the tracking of the system. However, since the shapeof the asteroids and their features are not known, the centroiding method witha disk fitting has been chosen as the baseline for optical navigation. In order toassure accuracy, observability of the whole system, coverage, and efficiency ofoperations, the navigation strategy uses a different navigation camera which has28 a) (b)
Figure 15: (a) Navigation cost probability distribution function for transfer phase. On they-axis the number of occurrences are shown. (b) Navigation cost cumulative distributionfunction for transfer phase. a larger field-of-view and higher resolution than ASPECT. In this way, whileperforming scientific operations, it is still possible to acquire navigation infor-mation. Moreover, a separated wide-angle camera (WAC) is foreseen to grantthe full system visibility at any time. Thus, the adopted strategy for opticalnavigation exploits the same target of the scientific investigation with a nav-igation camera but keeps the observability of the two asteroids with a smallultra-wide angle camera. In this way, the pointing is shared among science andnavigation, the navigation observables are accurate because the navigation cam-era is dedicated to the asteroid, and the full binary system view is assured owingto the ultra-wide angle camera. This strategy is also beneficial during the safemode and targets acquisition mode. The parameters of the navigation camerasare reported in Table 5. Due to the early stage of the design process, the GNCbaseline has not been established yet in terms of hardware components. Thevalues in Table 5 are assumed based on typical performance of similar sensors,and do not refer to any existing camera. A representative image of the Didy-mos system with the three different cameras (ASPECT, NavCam, and WAC)is shown in Figure 16. 29 able 5: Navigation camera characteristics.
Camera FOV Sensor
NavCam 21 x 16 deg 2048 x 1536 pixWAC 40 x 40 deg 2048 x 2048 pix
Figure 16: The external frame represents the FOV of the WAC, the medium frame representsthe FOV of the NavCam, while the small asteroid is included in the small ASPECT field-of-view. The distance at which this image is simulated is about 8.5 km from Didymos.
The image processing steps and the optical navigation method are describedin this paragraph. The image, generated according to the CubeSat trajectory,pointing, and navcam specifications, is retrieved by Celestial Objects RenderingTool (CORTO), which is a tool developed at Politecnico di Milano (Figure 17,step 1). The image is pre-processed to compute a mean background noise whichis subtracted from the image, and the image is thresholded to highlight thebright objects in the frame (Figure 17, step 2). In this way, it is straightforwardto identify the two groups of connected pixels belonging to D1 and D2, whichcan be bounded by a green box (Figure 17, step 3).The center of brightness of each object can be easily computed by determiningthe centroid of the illuminated pixels inside the green boxes (Figure 18, step 4).The principal axes of each object can be determined, one of this axis will be30 igure 17: Steps 1-3; Image acquisition, pre-processing, and objects detection.Figure 18: Steps 4-6; Center of brightness (blue dot), center of mass (red dot), light directionand lit edge estimations. aligned with the light direction while the other in the direction orthogonal to it.In this way, the axis of the light direction can be estimated from the images butit can be also complemented by the sun sensor information (Figure 18, step 5).The center of mass can be then estimated as a displacement of the center ofbrightness along the negative light direction. The displacement between thecenter of brightness and the center of mass is inversely proportional to theobject phase angle (Figure 18, step 5). The image is then scanned along thelight direction to identify the pixels belonging to the lit edge of each body(Figure 18, step 6).Owing to the estimations of both the center of mass and the lit edge of eachobject in the images, a mean radius in pixels can be estimated from the centerof mass to the pixels constituting the lit edge. In this way a disk is fitted tothe object (Figure 19, step 7 for D1 and step 8 for D2). The center of mass,the center of brightness, and the dimensions of the two objects are the outputsthat can be extracted from the image processing algorithm.31 igure 19: Steps 7-9; D1 disk fitting and D2 disks fitting.
The optical navigation method accuracy is evaluated by processing 150 imagesrandomly chosen from the nominal orbit. The procedure extracts navigationinformation from the figures in a static way, thus no dynamic filtering is usedin this preliminary phase. The image processing steps extract the informationon the centroid of D1 and the apparent disk size. This information are givenin pixels and are compared to the actual ones to assess the errors involved withthe image processing. Figure 20 shows the mentioned errors, where the x and y directions are the horizontal and vertical pixel coordinates and COM refersto the center of mass. The error in the centroiding has a 3 σ std lower than10 pixels, while the error in the disk radius estimation has a 3 σ std lower than20 pixels.The NavCam has a 21 ×
16 deg FOV and a 2048 × igure 20: Center of mass error in horizontal and vertical pixel directions x and y and radiuserror as output of the image processing. Milani’s nominal control architecture is expected to be based on traditionalmethods. However, because of the unique operations of Milani, in concert withother spacecraft (Hera and Juventas) and the risk of collision with either ofthe asteroids, particular care is involved in the design of the Corrective Ac-tion Maneuver (CAM) strategy. The CAM is a semi-autonomous contingencymaneuver which is executable during nominal operations, in this section thestrategy involved in the evaluation, quantification and execution of the maneu-33 igure 21: High-level architecture of the CAM strategy. ver is explained.During operations Milani will be sharing the most valuable space around Didy-mos system with Juventas and Hera. To ensure safe operations, the CubeSatshall be capable to avoid collisions with the surrounding bodies. The safety ofMilani starts at mission analysis level with the design of trajectories that nom-inally do not encroach with the spacecraft and asteroids. However, a high-levelstrategy for the CAM is designed for unsafe deviations from nominal operations.Its schematics is shown in Figure 21. It is desirable to avoid both collisions withthe spacecraft and with the asteroids. However, it is also important to distin-guish between these two different events. The happening of the first one wouldproduce the loss of multiple systems, while the latter would involve Milani. Thecollision risk can be assessed directly with the ISL range and range-rate ca-pabilities for the spacecraft (Hera and Juventas, both active systems) while acombination of visual images from the NavCam and ISL data can be used withthe asteroids (Didymos and Dimorphos, both passive systems).The triggering mechanism of the CAM mode is based on the concept of riskranges, that are simply the estimated ranges from the spacecraft and the as-teroids. Whenever these quantities go below a certain threshold, a correctionmaneuver is considered necessary. Figure 22 shows the risk ranges associated toHera, Juventas and the Didymos system. Their evolution in time is describing34 igure 22: Example of risk tubes during the science phase of Milani mission. The trajectoriesof Hera (black rectangle), Juventas (inner magenta circle) and Milani (blue) are represented inthe Didymos Equatorial reference frame. The risk tubes for Hera and Juventas are representedwith radius respectively of 1 km and 500 m. A contingency spherical region of risk is assumedfor Didymos with a radius of 1.5 km. risk tubes.Once a corrective maneuver is requested, its orientation and magnitude arecomputed. The strategy to do that on-board is based on an hybrid between ageneric and a specific look-up tables. The generic one contains only the mag-nitude of the maneuvers as a function of the range of Milani from the collidingobject. The delta-V vector of the maneuver is directed towards the local radialdirection of Milani’s osculating orbit, opposite to the asteroid system. Thesemaneuvers are pre-computed on ground based on the dynamic environment ofthe asteroid in such a way to ensure Milani will get further away but will notescape the system before a certain amount of days to be specified. The specificone contains pre-computed maneuvers both in magnitude and direction that areevaluated with a certain timespan on the nominal trajectory. The specific oneare more accurate and can be relevant for small deviations from the nominaltrajectory, the generic one are less accurate but are designed to cover the entirespace around the colliding objects. 35 . Payload operations
In this section a detailed analysis of payload operations during the scientificphase of the mission is illustrated. In particular, we only focus on ASPECToperations, which is the only payload that impose observational requirementsto the mission profile. The driving requirements are in terms of phase angle andresolution. Together with resulting distances, these are summarized in Table 2and Table 3.A science orbit cycle of 21 days is considered in the analysis to assess the ca-pability to fulfill the payload objective to produce global maps of the asteroids.The time intervals within this cycle in which the constraints on the phase angle,distance and resolution are simultaneously satisfied are considered for potentialobservations.Further pruning is performed by assessing the illumination condition and view-ing geometry of each individual face of the asteroid shape models. Shadowingeffect of Didymos on Dimorphos are also taken into account. Considering allthese factors, it is estimated that a total cumulative time of 4.7 and 4.6 daysare available to perform scientific observations of, respectively, Didymos andDimorphos. There are however regions in both bodies near the south poles thatwill be permanently in shadow during the mission. These cannot be observedby ASPECT using visual imaging and are not caused by the choice of Milanitrajectories, and therefore are not accounted in the evaluation of the globalcoverage.Figure 23 and Figure 24 illustrate the faces that can be imaged during thepotential observation periods. In bot cases global coverage can be achievedwith the trajectory chosen. It is also estimated that a minimum number of4 images timed at the proper epochs will be needed for each body to achieveglobal coverage. The areas covered by them is illustrated in Figure 25 andFigure 26.This analysis is valid assuming ideal pointing and that the target body is entirelywithin the FOV of ASPECT. If the latter case is not true, especially in the case36
180 -135 -90 -45 0 45 90 135 180
Lambda [deg] -90-60-300306090 P h i [ deg ] M i n i m u m ang l e be t w een ASPE C T and l o c a l no r m a l [ deg ] Figure 23: ASPECT potential global coverage on Didymos. The map represents which facesof the shape model can be imaged by the payload given that the observation requirements aresatisfied. The color of each face represents the minimum angle between the ASPECT line ofsight and the face local normal during the science orbit cycle. -180 -135 -90 -45 0 45 90 135 180
Lambda [deg] -90-60-300306090 P h i [ deg ] M i n i m u m ang l e be t w een ASPE C T and l o c a l no r m a l [ deg ] Figure 24: ASPECT potential global coverage on Dimorphos. The map represents which facesof the shape model can be imaged by the payload given that the observation requirements aresatisfied. The color of each face represents the minimum angle between the ASPECT line ofsight and the face local normal during the science orbit cycle.
180 -135 -90 -45 0 45 90 135 180
Lambda [deg] -90-60-300306090 P h i [ deg ] I m age nu m be r [ - ] Figure 25: Simulation of an image acquisition sequence to achieve global coverage on Didymos.The colors represent the areas of the shape model covered by each image in a sequential order.Global coverage on the visible faces can be achieved with 4 images. -180 -135 -90 -45 0 45 90 135 180
Lambda [deg] -90-60-300306090 P h i [ deg ] I m age nu m be r [ - ] Figure 26: Simulation of an image acquisition sequence to achieve global coverage on Dimor-phos. The colors represent the areas of the shape model covered by each image in a sequentialorder. Global coverage on the visible faces can be achieved with 4 images. igure 27: Schematic of the angle used as metric to color the faces of the shape models inFigure 23 and Figure 24. The angle is the one between the line of sight vector from the facecenter to ASPECT (cyan) and the local normal of each face (black). of Didymos, a mosaic strategy is proposed. As far as the scientific orbit isconcerned, there seems to be plenty of opportunities in terms of observationtime to acquire a higher number of images. The bottle-neck in this case mightbe given by the overall data budget, which is expected in the range of few Gbits.
6. Conclusion
The paper presents the preliminary mission profile of Hera’s Milani CubeSat,during its operational lifetime after release in the proximity of Didymos binaryasteroid system. We provide a detailed analysis of the feasibility of such mis-sion, given the constraints arising from Hera mission scenario. We discuss thechallenges and driving design criteria in terms of mission analysis, trajectorydesign and GNC design. Finally, we provide a preliminary design solution, con-sistent with mission objectives and demonstrate its feasibility and suitability inmeeting science and technological obejctives of the Milani CubeSat mission.Although the preliminary mission profile suggests feasibility against the imposedrequirements and constraints, the initial results presented in this paper will besubject to changes as the Milani mission project evolves.39 cknowledgement
This work has been performed in response to ESA call AO/1-10258/20/NL/GLC:Hera Mission “Second CubeSat” Phase A/B C/D & E1. Fabio Ferrari acknowl-edge funding from the European Union’s Horizon 2020 research and innovationprogramme under the Marie Sk(cid:32)lodowska-Curie grant agreement No. 800060.Mattia Pugliatti and Francesco Topputo acknowledge funding from the Euro-pean Union’s Horizon 2020 research and innovation programme under the MarieSk(cid:32)lodowska-Curie grant agreement no. 813644. The authors would like to ac-knowledge the support received by the whole Milani Team.
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