Post on 24-Feb-2016
description
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
19/21
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!