Contingency Trajectory Planning for the Asteroid ...

Contingency Trajectory Planning for the Asteroid Redirect Crewed Mission Jacob Williams∗ ERC Inc., JETS Contract, Houston, TX, 77058, USA

Gerald L. Condon† NASA, Johnson Space Center, Houston, Texas, 77058, USA This study addresses the abort contingency options due to a failure of the Orion MultiPurpose Crew Vehicle (MPCV) service module main engine during the Asteroid Redirect Crewed Mission (ARCM). In the case of a main engine failure, the set of auxiliary (AUX) engines is used to return the Orion spacecraft to Earth in minimum time using the available propellant remaining. Results are shown for different cases depending on when the main engine fails. It is found that the AUX engine set has the performance needed to successfully complete the abort contingency mission for each of the cases studied.

Nomenclature ARCM

Asteroid Redirect Crewed Mission

ARM

Asteroid Redirect Mission

ARRM

Asteroid Redirect Robotic Mission

ARV

Asteroid Return Vehicle

CR3BP

Circular Restricted Three Body Problem

DRO

Distant Retrograde Orbit

EI

Entry Interface

ICPS

Interim Cryogenic Propulsion Stage

JPL

Jet Propulsion Laboratory

JSC

Johnson Space Center

KISS

Keck Institute for Space Studies

LGA

Lunar Gravity Assist

LOI

Lunar Orbit Insertion

MECO

Main Engine Cutoff

MPCV

Orion Multi-Purpose Crew Vehicle

NASA

National Aeronautics and Space Administration

NEA

Near Earth Asteroid

TLI

Trans-Lunar Injection

PRM

Perigee Raise Maneuver

TDB

Barycentric Dynamical Time

∗ Aerospace Engineer, Engineering Department, Aerosciences Flight Dynamics & GN&C Section (JE23), 2224 Bay Area Blvd., Houston, TX 77058, AIAA Senior Member † Senior Aerospace Engineer, Aeroscience and Flight Mechanics Division (EG5), 2101 NASA Parkway, Houston, TX 77058

1 of 17 American Institute of Aeronautics and Astronautics

I.

Introduction

Figure 1. Artist’s Rendition of the MPCV Docked with the ARV (with Captured Asteroid). Image credit: Analytical Mechanics Associates – Johnson Space Center Advanced Concepts Lab (JSC ACL).

A spacecraft mission to capture a small Near Earth Asteroid (NEA) and return it to the Earth-Moon system was proposed in a report from the Keck Institute for Space Studies (KISS) at the California Institute of Technology in early 2012.1 A year later, a robotic asteroid capture mission, along with a subsequent crewed visit, was added to the 2014 NASA budget request, and is known as the Asteroid Redirect Mission (ARM) concept.2, 3 It has two components. Firstly, in the robotic component, known as the Asteroid Redirect Robotic Mission (ARRM), the asteroid is captured and placed in a highly-stable Moon-centered Distant Retrograde Orbit (DRO). Secondly, a round-trip crewed mission, known as the Asteroid Redirect Crewed Mission (ARCM), is conducted to the asteroid in the DRO using the Orion Multi-Purpose Crew Vehicle (MPCV) spacecraft. An artist’s rendition of Orion docked with the Asteroid Return Vehicle (ARV) spacecraft (with captured asteroid) is shown in Fig. 1. A DRO is a class of stable periodic orbits in the Circular Restricted Three Body Problem (CR3BP) (they are family f in Henon’s 1969 survey4 ). In the two-body rotating frame, DROs move in the retrograde direction around the secondary body, appearing as large quasi-elliptical orbits. In the context of this study, since the Earth-Moon system is the one being considered, the DROs discussed here are centered at the Moona . In a realistic force model, the orbits are quasi-periodic, but still remain very stable over long periods of time. The long-term stability of the orbit makes it an ideal candidate for asteroid storage, since orbit maintenance maneuvers would not be required to keep the asteroid in the orbit. This paper is a companion to earlier studies that describe the details of the trajectory design for the crewed segment of the ARM.7, 8 It is noted that the Orion vehicle was not originally designed or sized with this mission in mind. Under the Constellation program (2005-2010), the vehicle was designed as part of a lunar surface access architecture that included a lander that performed the Lunar Orbit Insertion (LOI) maneuvers.9, 10 For the ARCM, Orion would be required to perform all maneuvers after the Interim Cryogenic Propulsion Stage (ICPS) Earth departure maneuver, which requires longer mission durations and a more complicated trajectory design with previously unconsidered abort modes. The current baseline ARCM requires two powered flybys of the Moon to reduce the overall Orion propellant cost. In total, the vehicle is required to perform at least seven key deterministic translational maneuvers: at Earth departure, outbound lunar flyby, DRO insertion, rendezvous (2 maneuvers), DRO departure, and return lunar flyby.7 The complexity of this mission design necessitates a detailed study of the potential off-nominal and abort a Other types of DROs include, for example, Earth-centered orbits in the Sun-Earth system5 and Europa-centered orbits in the Jupiter-Europa system.6 The term “distant retrograde orbit” was apparently first applied in the context of the Sun-Earth system.5


contingency situations which may occur.

II. II.A.

ARCM Mission Design

Vehicle and Engine Assumptions

The Orion mass and engine assumptions are shown in Table 1. The vehicle tanks are assumed to be fully loaded with propellant. The main engine is used to perform the nominal mission, and the AUX engine is used for this abort study. There are 8 AUX engines, with a thrust magnitude of 489.3 N each. Accounting for reductions due to thrust plume and engine canting, the combined thrust of these engines is 3662.468 N. Table 1. Orion Vehicle Assumptions

Initial mass at ICPS TLI Total translational propellant Main engine Isp Main engine thrust AUX engine Isp AUX engine thrust (8 engines) Pre-flyby mass drop

II.B.

26,390 kg 8,086.3 kg 315.1 sec 26,689 N 309.939 sec 3,662.468 N -92.1 kg

Mission Design Options

Figure 2. Mission Modes (Earth-Moon Rotating Frame). Both direct (one-impulse) or flyby (two-impulse) modes are possible on both the outbound and return phases of the mission. The illustrative impulsive transfers shown here use the CR3BP model, minimize the total ∆v, and limit the one-way transfer time to no more than 10 days. The DRO departures and insertions are allowed to occur at the optimal locations on the DRO. For real missions, the actual phasing location of the asteroid in the DRO must be accounted for.


A round-trip crewed mission between Earth and a DRO includes an outbound phase and a return phase, each of which has various options to consider when designing the integrated mission and analyzing the abort contingency options. For either mission phase, a gravity-assist flyby of the Moon can be employed to reduce the overall Orion propellant cost. Powered flybys will be considered in this study, where the Orion performs a maneuver at the periapsis of the Moon flyby (for a two-impulse arrival or departure). While the overall propellant can be reduced in this way, it does add to the mission complexity and the number of large critical maneuvers that the vehicle must perform. A flyby is possible both during the outbound phase (between Earth departure and DRO arrival), and the return phase (between DRO departure and Entry Interface (EI)). If no flyby is performed it is known as a direct (outbound or return) trajectory, and only one maneuver is performed (a one-impulse arrival or departure). Example trajectories for each of these cases is shown in Fig. 2. Thus, there are four possible mission permutationsb for a round-trip mission: 1. Direct Outbound / Direct Return 2. Direct Outbound / Flyby Return 3. Flyby Outbound / Direct Return 4. Flyby Outbound / Flyby Return Earlier studies concluded that Orion does not have the propellant capability for the direct/direct option. The flyby/direct and direct/flyby options are possible under some circumstances (depending on the departure epoch, the maximum allowable total mission duration, the phasing of the ARV in the DRO, and the desired stay time at the asteroid). The flyby/flyby option generally provides the most flexibility in terms of stay time and DRO phasing while maintaining reasonable propellant cost and flight times, as well as early-return contingency options, and is the mission design option used for the baseline nominal mission described in this study. Two performance indexes are available to be minimized when optimizing the nominal mission trajectory: mission duration or propellant usage. When minimizing the total mission duration, all the Orion propellant is generally used. Minimizing the Orion propellant instead will result in a longer mission (but only around 1-2 days more). The strategy adopted in this study is to use the minimum propellant case, which has an increased nominal mission duration, but allows for retaining additional propellant in reserve in order to deal with abort contingencies. II.C.

Nominal Mission Overview

The nominal ARCM trajectory used for this study is shown in Fig. 3. It is a flyby/flyby type trajectory. The Main Engine Cutoff (MECO) epoch for this mission is 2024-May-16 14:38:57 TDB, and the total mission duration is 25.6 days. This is one of many nominal missions cases that have been generated as part of ARCM mission design and performance trades at the Johnson Space Center (JSC). It is not considered a best or worst case mission, but is merely a representative example case for the purposes of this study. The ARV target DRO for this mission is based on an ARRM example reference trajectory provided by the Jet Propulsion Laboratory (JPL) for the asteroid 2009 BDc . The nominal mission was optimized using the Copernicus spacecraft trajectory optimization tool,11, 12 and minimizes the total Orion propellant used for a total mission duration of no more than 26 days. Only 6,687 kg of the Orion propellant is used for this mission. For the abort cases, the full propellant load of the vehicle will be available for use. Details on the nominal mission design have been addressed in a previous study.7 After the launch vehicle MECO, the ICPS performs a Perigee Raise Maneuver (PRM) maneuver, followed by most of Trans-Lunar Injection (TLI). The Orion vehicle main engine then performs seven major maneuvers over the course of the mission: the remainder of TLI, Outbound Lunar Gravity Assist (LGA), DRO Arrival, Rendezvous 1, Rendezvous 2, DRO Departure, and Return LGA. The maneuvers and timeline b For the outbound mission phase, it is also possible to include a free-return condition, where, at the conclusion of the Earth departure maneuver, the vehicle is on a circumlunar free-return trajectory back to Earth if no additional maneuvers are performed. At some point after Earth departure, Orion would then perform an additional maneuver to leave the free-return trajectory and target the first lunary flyby for the DRO insertion. This is known as a hybrid outbound trajectory, and provides a built-in abort option for a period of time post-TLI, at the cost of a higher propellant requirement. The hybrid options are not considered for the missions described in this study. c The asteroid capture trajectory was generated by Gregory Lantoine at JPL. Asteroid 2009 BD (SPICE ID 3444297) is a NEA in the Apollo group.


Figure 3. ARCM Nominal Mission. The nominal mission is a round-trip Orion trajectory from Earth to the ARV in a Moon-centered DRO. The total mission duration is 25.6 days, and Orion performs seven significant maneuvers, including two powered lunar flybys.

are shown in Table 2 (note that the ICPS maneuvers from MECO to Orion TLI are not shown here, as they are not relevant to this study). All trajectory segments were integrated explicitly using the DDEABM integration method (a variablestep size variable-order Adams-Bashforth-Moulton implementation) with a 10−11 error tolerance.13 The JPL DE 421 ephemeris14 was used for the celestial body ephemeris, with all bodies modeled as pointmasses (except for the Earth departure phases which used an 8×8 GGM02C Earth gravity model15 ). The pointmass gravitational parameters that were used are given in Table 3. This nominal mission is used for performance studies only, and does not include higher-order effects such as navigation or maneuver execution errors, or detailed Orion-ARV rendezvous maneuvers.16 II.D.

Earth Entry Interface

The target condition for both the nominal and abort missions is an Earth EI for a long range skip entry and splashdown off the coast of San Clemente Island (32.75◦ N, 120.75◦ W).17 See the example in Fig. 4. The EI constraint used for this study is a target line developed for the Orion program.18 The target line (shown in Fig. 5) consists of two 6th order polynomials for longitude and azimuth as functions of geodetic latitude. It represents an approximation for the set of acceptable skip-entry EI points which better lends itself to numerical optimization. The two polynomials can be expressed as: λ(φ) = a0 + a1 φ + a2 φ2 + a3 φ3 + a4 φ4 + a5 φ5 + a6 φ6 2

3

4

5

ψ(φ) = b0 + b1 φ + b2 φ + b3 φ + b4 φ + b5 φ + b6 φ


6

(1) (2)

Figure 4. Example EI Trajectory. The Orion outbound flyby maneuver targets an EI state that is on the target line for a skip entry and splashdown off the coast of San Clemente Island.

40

30

20

Latitude (deg)

10

0

−10

EI Locations

−20

Target Line Azimuth Directions −30

Enclosed EI Area San Clemente Landing Site

−40

−50 −240

−220

−200

−180

−160

−140

−120

−100

−80

Longitude (deg) Figure 5. Entry Target Line Constraints. Sixth-order polynomials for longitude and azimuth as functions of latitude are used to impose entry constraints for splashdown off the coast of San Clemente Island. The target line is an approximation to the entry interface points.


Table 2. Nominal Mission Summary

Event

Timeline [D:H:M:S from MECO] Start End

Burn Time [M:S]

Prop Used [kg]

Effective ∆v [m/s]

MECO Orion TLI

00:00:00:00 00:02:00:09

00:02:03:24

3:15

1684.63

203.835

Outbound LGA

06:01:36:29

06:01:39:08

2:39

1372.078

176.565

DRO Arrival

08:06:47:28

08:06:50:32

3:04

1587.358

217.709

39.765

5.656

Rendez. 1

08:06:51:32

08:06:51:37

0:05

Rendez. 2

09:06:51:37

09:06:51:41

0:05

38.877

5.539

DRO Departure

14:06:51:41

14:06:52:55

1:14

639.433

92.565

3:29

1803.195

277.038

13:50

7165.335

978.908

Return LGA

19:19:30:58 19:19:34:26 25:15:43:28 Totals

EI

Table 3. Gravitational Parameters

Body

µ (km3 /s2 )

Sun Earth Moon

132712440040.944 398600.436233 4902.800076

Where λ is longitude, φ is geodetic latitude, and ψ is geocentric azimuth (all in degrees). The coefficients for these two polynomials are given in Table 4. Two additional constraints are also imposed: h = 121.92 km γ = −5.86◦

(3) (4)

where h is geodetic altitude, and γ is geocentric flight path angle. These EI constraints are expressed in the Earth-centered Copernicus EPM OF DATE (inertial) reference frame at the EI epoch. The EI velocity is a free parameter (for the trajectories considered in this study, the EI velocity is typically around 10.99 m/s).

III.

Abort Strategy

The nominal mission design sets the backdrop for an abort analysis. In this scenario, the nominal mission is conducted using the main engine up to the point of the abort. The abort assumes that at the point of a planned nominal burn, the main engine fails. Fig. 6 shows the result of failed maneuvers if no additional Table 4. EI TARGET LINE COEFFICIENTS

i

ai

bi

0 1 2 3 4 5 6

-1.572813608817330E+02 -2.300334009252671E+00 -1.714730230987080E-02 1.047974416084420E-03 1.536774992582680E-05 -1.321600916935530E-08 -2.060032727268820E-10

4.370340479358631E+01 2.066083167052490E+00 -4.058829563109179E-02 -2.580839644551380E-03 2.643376297217353E-05 2.095919249545260E-06 2.120366586408750E-08


Figure 6. Propagated States After Failed Maneuvers. This figure shows the propagated states for 2 days after each of the failed main engine maneuvers.

recovery maneuvers are performed. After the failed maneuver, the AUX engines are subsequently used to return the crew to Earth. The maximum mission duration (i.e. active Orion lifetime) is 26 days for a nominal mission and 30 days for an abort mission. Both outbound and inbound aborts are designed to return the vehicle and crew to Earth as quickly as possible for early mission conclusion (i.e., the total mission duration is minimized). As part of the abort design, all available propellant may be used for aborts, and return time may employ all available remaining Orion vehicle active lifetime. The amount of propellant available for the abort maneuvers is the total propellant load minus the propellant already used up to that point by the main engine (see Fig. 7). A “failed maneuver” indicates that no part of the maneuver was performed by the main engine. Main engine failure for six cases are examined for this analysis: 1. Failed Orion TLI: The ICPS successfully completes its portion of the TLI burn, but then the Orion main engine fails to perform its portion of the TLI burn. 2. Failed Outbound LGA Flyby: The Orion main engine fails to perform the outbound LGA flyby maneuver. 3. Failed DRO Insertion: The Orion main engine fails to perform the DRO insertion burn. 4. Failed DRO Departure: The Orion main engine fails to perform the DRO departure burn. 5. Failed Inbound LGA Flyby: The Orion main engine fails to perform the inbound LGA flyby maneuver. 6. Early/Late Returns: Early (before nominal DRO departure) and late (after nominal DRO departure) returns are considered after a main engine failure during the stay time in the DRO.


M PC V Pro pella nt Rem aining [kg]

9000 mMPCV = 25,698 kg, mProp = 6687 kg

8000

m

= 26,390 kg, m

= 7165 kg

m

= 27,000 kg, m

= 7590 kg

MPCV

7000

MPCV

Prop Prop

mMPCV = 27,500 kg, mProp = 7940 kg 6000 5000 4000 3000 2000 1000 0

TLI

Outbound LGA

DRO Insertion

DRO Departure

Return LGA

Figure 7. Remaining Propellant for Aborts if Main Engine Fails Before Maneuver is Executed. This chart shows the values for various Orion reference design masses. Each mass case represents a different nominal mission, with a different abort space. All have the same total available translational propellant, but a different total initial mass (mM P CV ) and a different propellant requirement to complete the nominal mission (mP rop ). Only the second one (mM P CV = 26, 390 kg) is considered in this study.

The EI constraints for the abort mission are identical to the nominal mission. The target line return is more constrained and will generally present a greater performance impact than targeting h and γ only. The constrained longitude of the target line also limits the flight time to specific ranges. For faster returns, these additional constraints could be relaxed (for example, the minimum set of survival constraints would be h and γ, with λ and φ values corresponding to a point over any ocean). These relaxed EI constraints are not considered in this study. A single AUX maneuver abort is preferred, but this is not always possible. If a single burn cannot accomplish the abort with the remaining propellant, a second abort burn can be added. It is assumed that at least 10 minutes are needed after the failed maneuver before the AUX engines can be ignited. Once the main engine has failed, the AUX abort maneuver(s) return the crew to Earth as expeditiously as possible. This analysis does not examine the possible use of the AUX engines to continue with a nominal mission, though that scenario could be examined in future work.

IV.

Trajectory Optimization

The abort trajectory optimization problems were solved using Copernicus with the SNOPT optimization method.19 The objective function is the total mission duration (i.e., the abort returns are minimum time solutions, as compared to the minimum propellant nominal trajectory). Copernicus makes use of a multipleshooting approach where missions can be designed using any number of trajectory segments that can be integrated both backwards and forwards in time. For the abort analysis, the nominal trajectory segments are held fixed, and the abort segments form a separate optimization problem. The force models and segment integration parameters for the abort trajectories were the same as for the nominal trajectory. The AUX maneuver thrust direction is modeled by the spherical angles α (right ascension) and β (declination), as functions of time:20 α(t) = α0 + α˙0 (t − t0 ) β(t) = β0 + β˙0 (t − t0 )


(5) (6)

ˆ at time t is given by: Where t0 is the burn start time, and the direction of the thrust vector u ˆ (t) = [cos α(t) cos β(t)]ˆ u ev + [sin α(t) cos β(t)]ˆ eu + [sin β(t)]ˆ eh

(7)

ˆh = h/khk, e ˆu = The maneuver is expressed in the Copernicus “VUW” controls frame (ˆ ev = v/kvk, e ˆh × e ˆv ). e The optimization problem setup is slightly different for the different cases. In general, the optimization variables are: • The finite burn control law parameters α0 , β0 , α˙0 , and β˙0 for each of the AUX maneuvers. • The burn time ∆t for each of the AUX maneuvers. • The wait time from the failed maneuver to the start of the first AUX maneuver (this parameter is bounded to be no less than 10 minutes). • The various intermediate flight times (e.g., for the failed TLI case, the time between the conclusion of the AUX maneuver and EI is an optimization variable). • Flyby epoch (if the case contains a flyby). • Flyby state parameters (energy, periapsis radius, inclination, ascending node, and argument of periapsis). The flyby states are parameterized using the Copernicus universal element set.21 The flyby maneuvers are specified to occur at periapsis of the flyby. The flyby periapsis radius is bounded to be no less than 100 km above the lunar surface. • The EI epoch. • The EI longitude, latitude, velocity, and azimuth. The EI state is integrated backwards and constrained to provide state and time continuity with the forward-integrated abort return trajectory (this allows for specifying the EI altitude and flight path angle directly rather than being imposed as nonlinear constraints). and the main problem constraints are: • The Orion propellant limit (8,086.3 kg). • The total flight time limit (30 days). • The various time and state continuity conditions along the trajectory. • The EI target line polynomial constraints for longitude and azimuth (Equations 1-2). It is important to note that the EI state is parameterized in an Earth-fixed reference frame, which will produce locally-optimal solutions roughly every day for the EI epoch. Thus, it is necessary to check the EI epoch to ensure that the globally-optimal solution has been obtained. The Copernicus problem setup (i.e., propagating backwards in time from EI) makes it straightforward to vary the EI epoch by one day and quickly re-converge the solution.

V.

Results

A summary of the abort case results is shown in Table 5. The following sections provide details and plots for each case. The trajectory plots (which are screenshots from Copernicus) are shown in an Earth-Moon rotating-pulsating reference frame. The part of the nominal mission that is completed is shown as a solid black line, the uncompleted nominal mission is shown as a dashed black line, and the abort return is shown as a solid red line. V.A.

Failed Orion TLI

The failed Orion TLI trajectory is shown in Fig. 8. For this case, a single AUX maneuver will provide an Earth return to the target line EI. The optimal wait time to initiate this maneuver is about 10 hrs after the failed TLI. The return time from abort to EI is 1.26 days, for a total mission duration of 1.35 days. 10 of 17 American Institute of Aeronautics and Astronautics

Table 5. Abort Summary

Orion TLI

Outbound LGA

DRO Insertion

DRO Departure

Return LGA

Number of AUX Abort Burns

1

2

2

2

1

AUX 1 Prop [kg]

8086.3

2026.0

1989.7

956.8

2269.3

4375.5

3039.8

2406.7

8086.3

6401.6

5029.5

3363.5

2269.3

0

1684.6

3056.7

4722.7

5362.1

8086.3

8086.3

8086.3

8086.3

7631.4

10 hr 5 min

15 min

2.67 days

10 min

10 min

1.26

11.51

18.32

9.32

4.84

1.35

17.58

26.61

23.6

24.65

AUX 2 Prop [kg] Total Orion Prop Used for AUX Engines [kg] Total Orion Prop Used for Main Engines*[kg] Total Orion Prop Used [kg] Optimal Wait Time from Failed Maneuver to AUX Startup (≥ 10 min) Time from Failed Maneuver to EI [days] Total Mission Duration [days] * Prior

V.B.

to the abort.

Failed Outbound LGA Flyby

The failed outbound LGA trajectory is shown in Fig. 9. For this case, the AUX abort sequence consists of two separate AUX burns, because a single burn cannot accomplish the abort within the given Orion propellant limit. The first maneuver begins 15 minutes after the failed LGA maneuver, and the return time to EI is 11.51 days, for a total mission duration of 17.58 days. V.C.

Failed DRO Insertion

The failed DRO insertion trajectory is shown in Fig. 10. This case also requires two AUX maneuvers to accomplish the abort. The first AUX maneuver takes place 2.67 days after the failed insertion maneuver. The second AUX maneuver is a powered lunar flyby. The total time between the failed maneuver and EI is 18.32 days, resulting in a total mission duration of 26.61 days. This is the longest of all the abort cases, and is the only one longer than the nominal mission. V.D.

Failed DRO Departure

The failed DRO departure trajectory is shown in Fig. 11. This case also requires two AUX maneuvers to accomplish the abort. The first AUX maneuver begins 10 minutes after the failed departure maneuver. The total time between the failed maneuver and EI is 9.32 days, resulting in a total mission duration of 23.6 days. V.E.

Failed Return LGA Flyby

The failed return LGA trajectory is shown in Fig. 12. For this case, only one AUX maneuver is required to accomplish the abort, which begins 10 minutes after the failed maneuver. The total time between the failed maneuver and EI is 4.84 days, resulting in a total mission duration of 24.65 days. Note that this is the only case that does not use all the Orion propellant (about 455 kg remains unused). As was mentioned, a locally-optimally solution exists at approximately 1 day increments of the EI epoch. For this case the previous day’s solution required slightly more propellant than was available and so was not considered a feasible solution.


Figure 8. Failed TLI Abort. After the failed Orion TLI maneuver, a single AUX maneuver targets a return to Earth EI for a total mission duration of 1.35 days.

V.F.

Early/Late Returns

The early/late return cases are shown in Fig. 13. An early return occurs before the nominal planned DRO departure and a late return after the nominal DRO departure time. For the range of stay times from 0-8 days, the Orion vehicle has enough propellant to return using the AUX engines, using a two-maneuver return sequence (DRO departure and powered LGA flyby). Each case uses all the remaining Orion propellant. A single AUX maneuver return solution is generally not possible at this point in the mission with the propellant remaining. The total mission duration and return times for each case are shown in Fig. 14. It is noted that the total mission duration can be reduced by no more than 2 days when leaving at any point during the stay.

VI.

Conclusions

The Orion AUX-engine-based aborts provide a backup in the case of a failed main engine during the ARCM. This study examined the performance cost to recover from the failure of five primary critical space maneuvers nominally executed by the main engines: Orion TLI, outbound LGA flyby, DRO insertion, DRO departure, and return LGA flyby. Also examined was the cost of an early or late Earth return while Orion is docked with the ARV. Failure of the main engine to execute any of these maneuvers resulted in a one or two AUX burn sequence to return the crew to Earth EI as quickly as possible using all available remaining propellant. The results show that each of the return abort cases are feasible using the assumed vehicles and nominal mission, though not all were possible using a single abort maneuver. In general, all AUX aborts, with the exception of the failed DRO insertion case, provide an overall mission duration that is lower than the nominal mission (the failed DRO insertion case increases the nominal mission duration by about a day). Early returns from the DRO are also shown to be feasible using a two-maneuver AUX sequence.

VII.

Acknowledgments

This work was produced under the National Aeronautics and Space Administration (NASA) contracts NNJ05H105C and NNJ13HA01C. The authors would like to acknowledge the following people for their


Figure 9. Failed Outbound LGA Abort. A failed outbound LGA requires two AUX maneuvers to complete the early return abort, resulting in a total mission duration of 17.58 days.

contributions to this research: Juan Senent (JSC), Jeff Gutkowski (JSC), Cesar Ocampo (JSC), and Gregory Lantoine (JPL).

References 1 Brophy, J., Culick, F., Friedman, L., et al., “Asteroid Retrieval Feasibility Study,” Technical Report, Keck Institute for Space Studies, California Institute of Technology, Jet Propulsion Laboratory, April 2012. 2 “NASA Administrator Bolden’s Statement on the NASA FY 2014 Budget Request,” http://www.nasa.gov/home/hqnews/ 2013/apr/HQ_13-104_Bolden_FY14_Budget_Statement.html, April 2013. 3 Gerstenmaier, W., “Asteroid Redirect Mission and Human Exploration,” http://www.nasa.gov/pdf/756161main_ Gerstenmaier_Presentation.pdf, NASA Asteroid Initiative Industry and Partner Day, June 2013. 4 H´ enon, M., “Numerical Exploration of the Restricted Problem. V. Hill’s Case: Periodic Orbits and Their Stability,” Astronomy & Astrophysics, Vol. 1, February 1969, pp. 223–238. 5 Ocampo, C. A. and Rosborough, G. W., “Transfer Trajectories for Distant Retrograde Orbiters of the Earth,” Advances in the Astronautical Sciences, Vol. 82, 1993, AAS 93-180. 6 Lam, T. and Whiffen, G. J., “Exploration of Distant Retrograde Orbits Around Europa,” Advances in the Astronautical Sciences, Vol. 120, 2005, AAS 05-110. 7 Williams, J., “Trajectory Design for the Asteroid Redirect Crewed Mission,” JETS-JE23-13-AFGNC-DOC-0014, NASA JSC Engineering, Technology and Science (JETS) Contract, July 2013. 8 Condon, G. L. and Williams, J., “Asteroid Redirect Crewed Mission Nominal Design and Performance,” AIAA SpaceOps 2014 , May 2014. 9 Garn, M., Qu, M., Chrone, J., Su, P., and Karlgaard, C., “NASA’s Planned Return to the Moon: Global Access and Anytime Return Requirement Implications on the Lunar Orbit Insertion Burns,” AIAA/AAS Astrodynamics Specialist Conference and Exhibit, 2008, AIAA 2008-7508. 10 Condon, G. L., Stewart, S., and Williams, J., “Mission Design and Performance Assessment for the Constellation Lunar Architecture,” Advances in the Astronautical Sciences, Vol. 136, 2010, AAS 10-127.


Figure 10. Failed DRO Insertion Abort. A failed DRO Insertion maneuver requires two AUX maneuvers to complete the early return abort, resulting in a total mission duration of 26.61 days. This is the only case where the abort mission duration is longer than the nominal mission.

11 Ocampo, C., “An Architecture for a Generalized Trajectory Design and Optimization System,” Proceedings of the Conference: Libration Point Orbits and Applications, edited by G. G´ omez, M. W. Lo, and J. J. Masdemont, World Scientific Publishing Company, June 2003, pp. 529–572, Aiguablava, Spain. 12 Williams, J., Senent, J. S., and Lee, D. E., “Recent Improvements to the Copernicus Trajectory Design and Optimization System,” Advances in the Astronautical Sciences, Vol. 143, 2012, AAS 12-236. 13 Shampine, L. F. and Watts, H. A., “DEPAC - Design of a User Oriented Package of ODE Solvers,” Technical Report SAND-79-2374, Sandia National Labs, September 1980. 14 Folkner, W. M., Williams, J. G., and Boggs, D. H., “The Planetary and Lunar Ephemeris: DE 421,” Memorandum IOM 343R-08-003, Jet Propulsion Laboratory, California Institute of Technology, March 2008, http://naif.jpl.nasa.gov/ pub/naif/generic_kernels/spk/planets/. 15 Tapley, B., Ries, J., Bettadpur, S., Chambers, D., Cheng, M., Condi, F., Gunter, B., Kang, Z., Nagel, P., Pastor, R., Pekker, T., Poole, S., and Wang, F., “GGM02: An Improved Earth Gravity Field Model from GRACE,” Journal of Geodesy, Vol. 79, 2005. 16 Hinkel, H. D., Cryan, S. P., D’Souza, C., Dannemiller, D. P., Brazzel, J. P., Condon, G. L., Othon, W. L., and Williams, J., “Rendezvous and Docking Strategy for Crewed Segment of the Asteroid Redirect Mission,” AIAA SpaceOps 2014 , May 2014. 17 Gay, R. S. and Bihari, B. D., “Challenges of Roll Orientation With Respect to Vehicle Heading at Touchdown for the Orion Command Module,” Advances in the Astronautical Sciences, Vol. 131, 2008, AAS 08-068. 18 Whitley, R. J., Ocampo, C. A., and Williams, J., “Performance of an Autonomous Multi-Maneuver Algorithm for Lunar Trans-Earth Injection,” Journal of Spacecraft and Rockets, Vol. 49, January-February 2012, pp. 165–174. 19 Gill, P. E., Murray, W., and Saunders, M. A., “SNOPT: An SQP Algorithm for Large-Scale Constrained Optimization,” SIAM Review , Vol. 47, No. 1, 2005, pp. 99–131. 20 Ocampo, C., “Finite Burn Maneuver Modeling for a Generalized Spacecraft Trajectory Design and Optimization System,” Annals of the New York Academy of Science, Vol. 1017, May 2004, pp. 210–233. 21 Gooding, R. H., “On Universal Elements, and Conversion Procedures to and from Position and Velocity,” Celestial Mechanics, Vol. 44, 1988.


Figure 11. Failed DRO Departure Abort. A failed DRO departure abort requires two AUX maneuvers, resulting in a total mission duration of 23.6 days.


Figure 12. Failed Return LGA Abort. A single AUX maneuver can be used to recover from a failed return LGA maneuver. This is the only case where all the Orion propellant is not used.


mi No

na

lR

eturn

Figure 13. Early/Late DRO Returns. AUX abort return trajectories are shown here for stays at the ARV from 0 to 8 days (the nominal stay time is 5 days).

26 24 22 20

[days]

18 Total Mission Duration Return Time

16 14 12 10 8 6

0

1

2

3

4 5 DRO Stay T im e [days]

6

7

8

Figure 14. Early and Late Returns from the DRO. The nominal DRO stay time is 5 days, with a total mission duration of 25.6 days. When departing earlier or later using a two-maneuver AUX sequence, the total mission duration can only be reduced by 1-2 days.
