spacecraft support in remote sensing task scheduling

SPACECRAFT SUPPORT IN REMOTE SENSING TASK SCHEDULING Tapan P Bagchi Study completed at Industrial & Management Engineering IIT Kanpur

Ref. Near Optimal Scheduling of Spacecraft Task Support TAES IEEE 2009

1

The World of LEO Spacecraft


2

Remote Sensing may have many objectives…

Telecommunication

Flood control Crop yield estimation Rescue Infrastructure development Space missions Ref. Near Optimal Scheduling of Spacecraft Task Support TAES IEEE 2009

3

Summary 



Remote sensing is worth $5000/minute. Visibility clashes reduce communication network utilization

Talk presents new methods for the optimal allotment of ground station support time to low earth orbiting (LEO) spacecraft experiencing clashing visibilities  Method is a generalization of the classical product mix problem in which "production quantities" to maximize total profit  The problem is non-linear and NP-complete.  System implemented at ISRO, Bangalore in 2002; 9% LEO utilization improvement achieved 


4

$5000 per minute! The LEO Spacecraft The Terrain The Orbit


5

Remote Sensing Spacecraft Missions


6

Station, Chain and Visibility Clash —its resolution lies not in electronics, but in math

Station clash Chain clash


Visibilit y clash

7

Previous Work 

 

  



Hubble telescope observations (1995): Heuristic logic, hill-climbing and schedule repair schemes used to determine a hierarchical ordering of activities to schedule the most constrained activities first. NASA's Terriers satellite (1992): Dispatching rules implemented without the explicit consideration of optimality Agnese and Brousse (1995, 1998): A search by depth first and branch and bound methods; greedy search used to determine task allocations A commercial scheduling system called ILOG (1998) satisfies critical constraints only and produces a support/don’t support task lineup Pemberton and Galiber (1998) A constraint-based Approach to Satellite Scheduling Wolfe and Sorensen (2000): Priority dispatch rule, look ahead heuristic and GA compared for task allocation on yes/no basis, no visibility clashes resolved GREAS (2001): A scheduling and mission planning tool does task mapping-to-resource using a constraint satisfaction approach


8

NASA’s Solution to Visibility Clash


9

NASA: “In visibility conflict support one or the other”


10

What is a Visibility Clash? 



Incidents when two or more spacecraft passing over a ground station have overlapping visibilities (acquisition/loss of signal AOS/LOS) Ground station resources must be apportioned equitably among the spacecraft so as to generate maximum value in the mission.


11

Total visibility V of all three spacecraft Visibility of spacecraft 1

Clash

b1 of Satellite 2 2 Visibility Visibility of spacecraft

a1

2

Clash

b2

a2

s1 = Start of support of spacecraft 1 x1

e1 = End of support

Visibility of spacecraft 3

s2 = Start of support of spacecraft 2

a3

b3 s3 = Start of support

x2 e2 = End of support

x3 e3 = End of support

Station reconfiguration time

IIT Kanpur Model: Clashing Spacecraft Visibilities over an ISRO Ground Station Ref. Near Optimal Scheduling of Spacecraft Task Support TAES IEEE 2009

12

Variants of Visibility Clash Topologies Linked clash

Simple clash S/C1

Nested clashes S/C1

S/C1

S/C2

S/C2

S/C2

S/C3

S/C3

S/C3

S/C4

S/C4

S/C4 S/C5

Jumped Clashes

Complicated nests

S/C1

S/C1 S/C2

S/C2 S/C3 S/C3 S/C4 S/C4 S/C5 S/C5 S/C6 Ref. Near Optimal Scheduling of Spacecraft Task Support TAES IEEE 2009

13

Mathematical Formulation V = Difference of first clashing AOS and last LOS. i = Total number of spacecraft visibilities clashing over a station (i = 0……I). P = The Utility or Value Function (= f(x1, x2, x3,…, xn)) to be maximized ai = Start of visibility (AOS) of spacecraft i. bi = End of visibility (LOS) of spacecraft i. si = Start of support of spacecraft i. ei = End of support of spacecraft i. xi (= si – ei) = Support given to spacecraft i when it passes over a station. min = Minimum time required for support once support is commenced. max = Maximum time required for support. r = Station reconfiguration time reconfiguration time is added to end support of previous supported spacecraft. Ci = Utility or profit contributed to P per unit time when spacecraft i is supported. ti+1 is a binary variable that indicates whether spacecraft i is supported or not. Thus if xi = 0, ti+1 = 0 and if xI > 0, ti+1 = 1 for i = 1, 2, 3, …, I; t1 = 0.


14

The Optimization Model Maximize P = f(x1, x2, x3,… xn) In general, the objective or evaluation function f(x1, x2, x3,… xn) may be nonlinear, discontinuous, and have multiple peaks. In the special case when f(x1, x2, x3,… xn) is linear, I

P =

C x i 1

I

V =

x i 1

= total value generated

(1)

 ( t i ) * r = total visibility at the ground station

(2)

i i

I

i

i 1

Subject to: (i) Start of support (si) of spacecraft ‘i’ must be at AOSi or later and it should be equal to or less then LOSi. bi  si  ai (ii)

(3)

End of support (ei) of spacecraft i must be at LOSi and it should be equal to or greater than AOSi. Maximum ai  ei  bi (4) k  ( i 1).....1

(iii)

Station Reconfiguration allowance. si  {(ek  tk+1)} + r Ref. Near Optimal Scheduling of Spacecraft Task Support TAES IEEE 2009

(5)

15

The Optimization Model (contd.) (iv)

Duration of support of spacecraft i. x i = ei - s i

(6)

(v)

Constraint for minimum time of support. This may be either 0 or greater than the quantity min. Therefore, xi = 0 or xi  min (7)

(vi)

Maximum time of support should be less than the quantity max, as specified by the decision maker. xi  max

(8)

Nonnegativity constraint si, ei  0;

(9)

(vii)

xi  0 ;

Note: The real life objective function is nonlinear and proprietary:

Maximize P = over all i {i + ((1- e-iti)/i)}

Optimization is subject to constraints identical to (3) to (9).


16

A Numerical Example ● ● ● ● ●

The maximum support required is uniformly 1800 seconds The minimum support required, once support is decided to be given, is 480 seconds. The visible time windows are as follows, expressed in seconds from a reference point: a1 = 0, b1 = 840, a2 = 900, b2 = 1800. Station reconfiguration time is 600 seconds. The profit function involves a discontinuous exponentially decaying objective function

Profit = 0 for t < 480 , i + (1 – e-iti)/ i for t  480 where i = 480*i, i = 0.00958/i and t = (Duration of total support - 480). ●

GA search was used, parameterized by DOE at population size = 20, probability of crossover = 0.95 and probability of mutation = 0.1, number of generations to run = 100. Ref. Near Optimal Scheduling of Spacecraft Task Support TAES IEEE 2009

17

Numerical Solutions

Random Seed

1

2

3

4

5

Spacecraft 1 Start of support

0

0

0

0

0

Spacecraft 1 End of support

601

600

601

602

605

Spacecraft 2 Start of support

1201

1200

1202

1202

1205

Spacecraft 2 End of support

1800

1800

1800

1800

1800

Total profit generated

1103

1103

1103

1103

1103

 GA Solution methodology is robust  Tabu search and simulated annealing solutions comparable Ref. Near Optimal Scheduling of Spacecraft Task Support TAES IEEE 2009

18

Remote Sensing may have many objectives… and Payoffs

Telecommunication

Flood control Crop yield estimation Rescue Infrastructure development Space missions Ref. Near Optimal Scheduling of Spacecraft Task Support TAES IEEE 2009

19

A Real Life Objective Function

Marginal rate of return  /100

0

min (8 minutes)

max (16 minutes)


Total support time t

20

Factors Constituting  PRIORITY PENALTY Maximum elevation

2

Spacecraft priority

10

Exclusive pass (orbit over a single station)

8

Critically dependent operations Special TTC operations (must be done in that pass)

10 10

Service (visibility gap)

5

Minimum operations on the spacecraft

6

Exactly ‘n’ ascending operations per spacecraft

2

Exactly ‘m’ descending operations per spacecraft

2

Operator constraint

2

Ground station constraint


2

21

Evaluation of : An Illustration

For illustration assume that  consists of two dominant but separable parts:  = Max (FactorExclusive, FactorCyclic, FactorPrecedent, FactorSupportGap) + FactorSpacecraft + FactorElevation FactorExclusive, FactorCyclic, and FactorPrecedent are expressions of the character of the task to be performed. FactorSpacecraft is also an expression of importance or priority. In practice these factors may each be subjectively quantified in consultation with mission specialists as weights, each set on a scale of 1 to 10. The other factors in the table depend on dynamically developing conditions.


22

The Search Space and GA Solution for Two Clashing Spacecraft Visibilities Total Visibility Constraint: S1 + reconfig time + S2 = 1800

1800 1500

Total Return as function of Support Times S1 and S2

1200 Total

Return 900 600 300

540

Support to Satellite 1

0

0 0

200


400

600

800

Support to Sat ellite 2

23

Concluding Remarks—Part 1 









The going rate for providing an extra minute of remote sensing services now is worth about $5000.00 US. So, every extra support minute a good schedule can squeeze out of the communication network would be worth the effort of spending a few minutes of computation but perhaps not more. 300 clashes may be resolved by GA in about 5 minutes on a Pentium III 500 Mhz system. No known analytical method can optimally resolve these clashes. GA may also help produce Pareto-optimal solutions to resolve complex, multi-objective visibility clash problems Part 2 of this paper describes more complex satellite support scenarios and their possible resolution Ref. Near Optimal Scheduling of Spacecraft Task Support TAES IEEE 2009

24

Pareto-optimal Solutions by GA THE “EFFICIENT FRONT” CONTAINING THE NONDOMINATED SOLUTIONS

 g(x)

x*

SUBOPTIMAL DOMINATED SOLUTIONS

f(x)  Nondominated Multi-objective Maximizing Solutions Ref. Near Optimal Scheduling of Spacecraft Task Support TAES IEEE 2009

25

OPTIMAL SPACECRAFT SUPPORT IN REMOTE SENSING—Part 2


26

Summary of this part of the talk ●

Optimal allotment of simultaneous support to LEO spacecraft with clashing visibilities at 

multiple ground stations with



multiple antennas (chains)



Linear priority system

●

The problem is NP-complete.

●

Exact, time-indexed integer programming method is proposed to resolve

●



visibility clash, chain clash, and station clash, and



with or without pre-emption of support

Numerical results are presented Ref. Near Optimal Scheduling of Spacecraft Task Support TAES IEEE 2009

27

$5000 per minute! That’s just the civilian market


28

Station, Chain and Visibility Clash

Station clash Chain clash

Visibilit y clash


29

What is a Support Clash ?   









(LEO) spacecraft now form a critical infrastructure To accomplish their mission, LEOs must remain in pre-planned contact with ground stations that upload commands and download data. A support clash is an incident when multiple ground stations, multiple antennas (chains), or even a single chain may attempt to engage several passing spacecraft simultaneously . Visibility clashes are particular incidents of support clash when two or more spacecraft passing over a single ground station have overlapping visibilities. A station clash is the incident when two or more ground stations view the same assortment of spacecraft with or without visibility clash occurring. A chain clash occurs at a ground station when the same spacecraft is simultaneously visible to two or more chains and the support to be provided must be apportioned among them. We address the optimal resolution of support clashes  at a single chain,  among several chains, and  among stations. Ref. Near Optimal Scheduling of Spacecraft Task Support TAES IEEE 2009

30

A Taxonomy of Spacecraft Support ●

A taxonomy of spacecraft support clash resolution problems may be given as:  

Nature of clash Station clash 

Chain clash  Visibility clash

Preemption-resumption policy  Objective function Once support is switched, a station or chain reconfiguration time is in effect. 

●


31

Stages of a Spacecraft Launch

Each stage requires specific and critical communication (health, position, command, data upload/download) with ground stations over which the spacecraft is visible Ref. Near Optimal Scheduling of Spacecraft Task Support TAES IEEE 2009

32

A Generalized Framework for Analysis  

 

 



acs denotes Acquisition of signal (AOS)

bcs: denotes the time when loss of signal (LOS) of the spacecraft s at chain c occurs. Reconfiguration time = rcsu Visibility windows of spacecraft may overlap (visibility clash), acu< bcs + rcsu. cs Minimum d min If xcst=1, chain c supports spacecraft s during time interval t cs and maximum d max A simpler version of this problem resembles parallel machine scheduling and it is NP-complete (Agnese et al, 1995, 1998).


33

Operational Constraints… Operation No.

1

Operation Name

TM

Satellites Affected All eight

Minimum Duration

Specified by satellite

When Performed

Other constraints

Independent/ Dependent (I/D)

I1A: once every day

Minimum elevation, specified by ground station

I

IP2:

twice day

every

Others: AELGP 2

TC

All except IP2

No minimum

AELGP

3

TR

All eight

No minimum

I1A: thrice every day IP2:

twice day

D TMTC Only from one sister station;

D TCTR

not with DW or RawSS or SPS_RT *

D TCPB

every

Others: AELGP 4

PB

All except IP2 and SC2

Specified by spacecraft

I1A: once every day Others: once every orbit

5

PYS

I1B, I1C, I1D, IP3, IP4

No minimum

Twice every day, DNFELGP

D TCPYS

6

DTG1TST

1B

10 minutes

Once a cycle, night pass

Along with DW

7

DW

All except SC2, I1B

No minimum

On request

Not with PB

Ref. Near Optimal SC2:once Scheduling of day Spacecraft every Not with RPA or GRB or PB Task Support TAES IEEE 2012 I1B:

with

Not with RawSS or PB

D TCDTG1TST D TCDW TCDW

34

A Time-Indexed Formulation Time is discretised into a contiguous sequence of intervals indexed by discrete time indices, 1, 2, 3, etc.

The Optimization Model: Maximize P = f({xcst})

(1)

Subject to constraints:

Start and end of support are restricted by visibility: (i)

(ii)

Start of support (scs) of spacecraft s may begin at AOSs or later and it must end no later than LOSs: bcs  scs  acs

(2)

End of support (ecs) of spacecraft s must end at LOSs or earlier and begin at AOSs or later acs  scs  ecs  bcs

(3)

When support is switched, support begins after chain reconfiguration: (iii)

Chain reconfiguration is performed each time support is switched from spacecraft s to the next spacecraft, u, being supported. Hence scu  ecs + rcsu Ref. Near Optimal Scheduling of Spacecraft Task Support TAES IEEE 2009

(4) 35

The Optimization Model (contd.) Support provided is limited by max and min durations: (iv)

cs

If spacecraft s is supported by chain c, it is supported for a minimum period of d min time units. This constraint is implemented by defining a time-indexed binary (0, 1) variable ycst for each (c, s) pair such that

xcsk 

k

y

csw cs w  max( a cs , k  d min 1)

0

and cs k  d min 1

x

w k

csw

c, s

(5)

cs  d min  M ( ycsk  1)

when and M is a very large, positive quantity (Winston, 1994). (v)

cs

Total support provided to spacecraft s at chain c is constrained by d max : bcs

cs x  d  cst max

c, s

(6)

t  a cs


36

The Optimization Model (contd.) (vi) At one time index t, only one spacecraft may be supported by a chain: S

x s 1

cst

 1, t

c

(7)

(vii) At one time index t, only one chain may support a given spacecraft: C

x c 1

(viii)

cst

 1, t , s

(8)

Reconfiguration time rcsu when support at a chain c is switched from spacecraft s to a following spacecraft u is enforced by the following constraint: ycsw + ycuz  1, c (9) cs

when u = s +1, s + 2, …, S, z = w,…, (w + d min + rcsu – 1), w = acs,…, bcs Ref. Near Optimal Scheduling of Spacecraft Task Support TAES IEEE 2009

37

The Optimization Model (contd.) Overlapping visibilities: (ix)

Two chains c1 and c2 with overlapping visibilities cannot support the same spacecraft s in the period during which their visibilities overlap. This constraint is imposed by min(bc1 s , bc 2 s )

s x  Mp  c1st c1c 2 , s, c1

and

t  max( a c1 s , a c 2 s )

(10)

min(bc1 s , bc 2 s )

s x  M ( 1  p  c 2st c1c 2 ), s, c 2

(11)

t  max( a c1 s , a c 2 s ) s

when c1 ≠ c2; pc1c 2 is a 0-1 variable and M a very large positive quantity (Winston, 1994). Ref. Near Optimal Scheduling of Spacecraft Task Support TAES IEEE 2009

38

Station-specific Constraints… Lucknow

LUCKNOW 1

IRS-1B, SROSS

TM

2

TC

3

00:00 TO 24:00

DW

LUCKNOW 2

All eight

TM

2

TC

3

TR

7.5

PB

5.5

DW

RPA

PYS

CS_RST

VHF_TC

Mauritius

MAURTIOUS

All except IRS-1A, IRS-P2

TM

5

TC

5

Ref. Near Optimal Scheduling ofTRSpacecraft Task Support TAES IEEEPB2012

15:00 TO 21:00

7.5 5.5

39

The Optimization Model (contd.) Preemption by higher priority tasks: (x) In the special situation when support of spacecraft s by chain c is preempted to support another higher priority spacecraft but the preempted support is not resumed (i.e., it is curtailed), the following constraint is enforced: L

L

cs x  y  d  cst  cst min  1,  c, s t 1

(12)

t 1

Continuity of support constraint: (xi) Visibility slot availability and continuity of support constraints:

xcst = 0 for t = 0, …, (acs-1) and (bcs+1), …, L; ycst

cs d = 0 for t = 0, …, (acs-1) and (bcs – min + 1), …, L;

c, s.


(13) 40

The Optimization Model (contd) (xii) Non-negativity constraints xcst  0, ycst  0, p s  0, c, c1, c2, s, t

(14)

c1c 2

In general, the objective or evaluation function f(x1, x2, x3,…, xn) involving n supports being simultaneously optimized may be nonlinear, discontinuous, and have multiple peaks. In the special case when f(x1, x2, x3,…, xn) is linear, and cst = cs, independent of t, the objective becomes, C

Maximize P =

S

L

 c1 s 1 t 1

cs xcst

when L = total length of the planning horizon . = max[bcs  rcsu ], c  C , s  S , u  S , c, s ,u

(15)

su

This problem may be solved in integer programming. Ref. Near Optimal Scheduling of Spacecraft Task Support TAES IEEE 2009

41

A Numerical Example The profit per unit support time {cs} and visibility data (acs, bcs) are shown on Table 1. cs = min

cs

d max= 30, and d 4 and In this problem, reconfiguration times {rcuv} are uniformly 2 time units. Input data for Clash Resolution: Space -craft

S1 S2 S3 S4

Station 1 Chain 1 Chain 2  a, b  a, b 3 1, 3 1, 20 20 6 8, 2 8, 15 15 3 18, 8 18, 40 40 5 25, 4 25, 30 30

Station 2 Chain 1 Chain 2  a, b  a, b 1 16, 2 16, 35 35 1 23, 9 23, 30 30 5 33, 6 33, 55 55 3 40, 3 40, 45 45


42

The Solution: Optimal use of Handovers Stn 2 Ch 2 Stn 2 Ch 1 Stn 1 Ch 2 Stn 1 Ch 1

idle

0

10

S1

idle

20 S2

30 idle

40 S3

idle

50

60 sec

S4

Gantt Chart of final Satellite Supports-—all 4 visibilities supported. Conventional scheduling supports only 1 spacecraft. Ref. Near Optimal Scheduling of Spacecraft Task Support TAES IEEE 2009

43

Implementation used SW Engineering


44

Concluding Remarks 

RESULTS SHOW 8 – 10% IMPROVEMENT IN REMOTE SENSING SPACECRAFT UTILIZATION; Paper in IEEE TAES



GA Method took 1 minute to resolve a single occasion of clash by CPLEX running on a SUN Sparc 30 system



In real life, 6 or 8 ground stations, with 2-3 chains each, would develop nearly 500 clashes each week.



Request for new tasks keep coming throughout the week.



Remote sensing is worth about $5000.00 US,  Every extra minute that a good schedule can squeeze out of the network.

 

… We are not on moon yet! Work is currently under way to articulate the broader problem, help reduce computations by shortcuts and hybrid heuristics Ref. Near Optimal Scheduling of Spacecraft Task Support TAES IEEE 2009

45

Many challenges still remain!


46

Open Questions that remain…  



What is the basic complexity of the problem? Must provide due satisfaction of the "hard" constraints (e.g., resource limitations) that cannot be violated in developing a schedule, and Maximize the satisfaction of the "soft" constraints (e.g., giving priority in a conflict situation to certain tasks or the tasks performed on certain satellites in order that the utility generated out of the total weekly support be maximum). Ref. Near Optimal Scheduling of Spacecraft Task Support TAES IEEE 2009

47

Credits 

 





Rao, Santhalakshmi, Venkateswarlu and Soma articulated the problem for ISRO, oriented the project team and evaluated the IIT Kanpur prototype system Garima Shahi documented dispatch rules and the constraints Sagar Kapse compared GA with SA and TS Sanjay Kumar—Formulated four new constraints, coded the GA and IP and optimized the models Bagchi interfaced with the space agency and modeled the nonlinear objective function


48

ISRO’s feedback Date:Tue, 16 Oct 2001 11:01:43 +0530From:"P.Soma" | Block Address | Add to Address BookReplyto:[email protected]:ISTRAC To:[email protected], [email protected], [email protected], [email protected], [email protected], [email protected]:IMPACT project – regarding Dear Professor Bagchi, The project objectives as stated in the project proposal "Development of scheduling algorithm and software for multi satellite operations scheduling by Genetic Algorithm" have all been accomplished and we are glad that we could do it successfully as per schedule. We have certainly achieved what we have intended in the proposal; Congratulations to you and IITK team for the excellent work done. IMPACT software will be used for TTC and Payload scheduling operationally at ISTRAC. Feedback to you will continue for further refinement and fine tuning. Though the project activities as set by us is completed, we will have to keep the project alive until the second year payments are made by ISRO to IITK and subsequently the accounts settled from IITK end by FUC. Dr.Ananth informs me that the payments will be done at the earliest. Therefore, we may have to keep the project alive until say Jan 2002. We may be able to take up extensions to the project as suggested by you in your email by working out a new project only. This can be done only after the formal conclusion of the present project. With best regards P.Soma Ref. Near Optimal Scheduling of Spacecraft Task Support TAES IEEE 2009

49

spacecraft support in remote sensing task scheduling

spacecraft support in remote sensing task scheduling

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