Thruster failure recovery strategiesfor libration point missions

Maksim ShirobokovKeldysh Institute of Applied Mathematics

Moscow Institute of Physics and Technology

Sergey TrofimovKeldysh Institute of Applied Mathematics

Moscow Institute of Physics and Technology

Contents

• Motivation

• Problem statement

• Theory background

• Test case: Sun-Earth L2, planar periodic orbits

• Conclusion

2/21

Missions to libration points

• Successfully accomplished missions:– ISEE-3, WIND, SOHO, ACE, Genesis

• Promising near-future projects– Deep Space Climate Observatory (NASA)

– LISA Pathfinder (ESA/NASA)

– Spektr-RG (Roscosmos/ESA)

3/21

Features related to periodic motion around collinear libration points

High instability of motion requires the application of station-keeping techniques and their essential components:

• Accurate trajectory determination

• Regular control-law updates

In average, 2-12 m/s per year is required

Thus, any possible thruster (or communication) failure1 threatens a mission and can lead to a significant deviation of the spacecraft from the nominal periodic orbit

1The largest percentage of all fail occurrences relating to the control system falls on thruster failure, see Tafazoli [2009] “A Study of On-Orbit Spacecraft Failures”, Acta Astronautica 4/21

Thsuter failure issue

If a thruster fails, the control is allocated to a redundant set of thrusters:

• attitude control thrusters

• a backup orbital thruster

Most of publications are related only to collision avoidance during rendezvous and docking. The problem of libration point mission recovery has not been deeply studied yet

5/21

Problem statementBasic assumptions:

• the main orbit control thruster failed and produces no thrust• the planned correction maneuver is not performed on time• with some delay, a redundant set of thrusters is used

Transfer to the nominal periodic orbit may appear to be too expensive:• unstable environment leads to fast orbit decay• redundant thruster has usually less fuel than the main one

Therefore, not enough fuel is left to perform station-keeping maneuvers during the planned mission lifetime

6/21

Thruster failure recovery strategies

Two strategies are considered:

• periodic orbit targeting (POT)

• stable manifold targeting (SMT)

In both cases, the aim is the same—to find the “cheapest-to-get” periodic orbit for different values of correction maneuver delay (the time passed since the moment of unsuccessful correction maneuver)

7/21

Circular restricted three-body problem

The planar circular restricted three-body problem (CR3BP) is studied:

• a spacecraft of negligible mass moves under the gravitational influence of two masses and

• the spacecraft is supposed to move in the orbital plane of the primaries

Note: the proposed recovery strategies can be applied to the spatial case (for example, for halo orbits)

1m 2m

8/21

Reference frame Mass parameter

Non-dimensional units:

For the Sun-(Earth+Moon) system

2 1 2m m m

1 1m

2m

0 1

1mx

2 1mx

63.03939 10

9/21

Equations of motionIn rotating frame

where

is the so called effective potential; and are the partial derivatives of with respect to the position variables. The distances between the spacecraft and the primaries equal

2 2

1 2

11, ,2 2

x yU x yr r

2 21r x y 2 2

2 1r x y

2 , 2x yx y U y x U

yUxU

10/21

Libration pointsEquilibrium (libration) points can be found from the equations

Collinear libration points Sun-(Earth+Moon) system

0x yU U

1

2 31 2613 9L H H Hx r r r

2

2 31 2813 9L H H Hx r r r

3

34

5 23 49112 12Lx

10.989987Lx

21.010074Lx

31.000001Lx

1 33Hr 11/21

Richardson’s third-order approximation of periodic orbits

The third-order approximation of periodic orbits in normalized variables and expressed as follows:

where

some constants

Lx x x y y 2 3

22

1 3 32 1 1 11c cos2 cosos 3xx xx a A a Ax a A A 2 3

1 21 1 31 1sin sin 2 sin 3x x xy kA b A b A

222 1 2 0p pk c

22 2 22 9 8 2p c c c 3 3

2 1 1L Lc x x

1 p t 211 xs A

21 23 31 21 31 1, , , , ,a a a b b s

exp ,st expxA u t

exp ,st expyA u t

12/21

Periodic orbit targeting strategy 1 2 minJ y v v

1 2, , ,xy A T T

13/21

Referenceperiodic orbit

Backupperiodic orbit

Gain in delta-v for POT strategy

14/21, reference orbit periodsdt

Change in amplitude for POT strategy

15/21, reference orbit periodsdt

Stable manifold targeting strategy 1 2 minJ y v v

1 2, , , ,xy A T T t

16/21

Referenceperiodic orbit

Stable manifold

Gain in delta-v for SMT strategy

17/21, reference orbit periodsdt

Change in amplitude for SMT strategy

18/21, reference orbit periodsdt

Conclusion

• Two recovery strategies in case of possible thruster failure—periodic orbit targeting and stable manifold targeting—are proposed for collinear libration point missions

• The proposed approach reduces delta-v spent by the redundant set of thrusters and increases the lifetime of the spacecraft

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Future work

• Targeting to periodic orbits with larger amplitudes

requires higher-order approximations of these orbits

• Different positions of the unsuccessful correction

maneuver may bring to different results

20/21

Thank you!