The TT&C Task Planning Algorithm Based on Multi-satellite

Jing Li , Jian Bai , Jian-ping Liu State Key Laboratory of Astronautic Dynamics

Xi’an Satellite Control Center Xi’an, China

Carol_lee_0727@sina.com

Pei-jun Yu Northwestern Polytechnical University

Xi’an, China

yupeijun@sina.com

Abstract—The TT&C (Tracking Telemetering and Command) task planning algorithm for multi-satellite based on SDMA-CDMA(Space Division Multiple Access — Code Division Multiple Access) system is proposed in this paper. A kind of ‘one ground station for multi-satellite’ TT&C mode is realized. The proposed algorithm is simulated and validated, at the same time. And the proposed algorithm is compared with traditional algorithm. The results are shown: the reference merit is provided for using TT&C resource reasonably and planning TT&C task scientifically.

Keywords-task planning; multi-satellite; SDMA; CDMA

I. INTRODUCTION With the development of astronautics, the denser and

more complex the spaceflight task is. Thereby, flight task planning is become a research hotpot recently.

Multi-satellite carry out cooperating task is a basic feature of modern spaceflight application. It can be helped by the task planning system. Generally, some features are possessed as[1] : 1) complexity — the tasks to be planned are coupled each other. 2) veracity — the high priority task can be guaranteed to assign first during task planning. 3) characteristic of real time — a task can be planned dynamically.

The problem of TT&C task planning can be defined as: under the presupposition of giving the number of satellite and TT&C station, one task or a group of sequenced tasks are assigned for every ground station based on the task requirement and diagnosis knowledge. So that, at the same time of finishing the task maximumly, the whole TT&C efficiency is optimization.

The traditional TT&C task planning is finished based on ‘one ground station for one satellite’ mode. It is not reasonable for SDMA-CDMA TT&C system. The TT&C task algorithm for multi-satellite based on SDMA-CDMA system is proposed in this paper. The characteristic of the algorithm is to achieve the ‘one ground station for multi-satellite’ mode. The reference merit is provided for using TT&C resource reasonably and planning TT&C task scientifically. This paper is arranged as follow: Firstly, the problem of TT&C task planning is described. Secondly, the constraint conditions of TT&C task planning based on multi-satellite are discussed. Thirdly, the multi-satellite TT&C task planning mode is established. And the concerned algorithm is proposed. Finally, the algorithm is simulated and validated.

II. PROBLEM DESCRIPTION OF TT&C TASK PLANNING Assumption: A set of aerospace U is given. And it

includes finite amount ( ｜ U ｜ =NU) aerospace Ui∈U(i=1,…,NU);A set of TT&C equipment V is given. And it includes finite amount (｜V ｜ =MV) equipment Vi∈V(i=1，…，MV). At any time, the aerospace position can be expressed as (xi

U(t),yiU(t) ,zi

U(t)). At the same time, the finite amount waiting carried out

tasks are included in the task area. So that, the task set T(｜T｜=NT) is composed. Every task Ti∈T(i=1，…，NT) in the set T has a unique ID ((identification), which possess of space position (xi

T,yiT ,zi

T). The result of TT&C task planning is to assign 1～ j

satellites to the equipment during the visible window. Here, j is satellite number which can be tracked simultaneously by a equipment. The task routing Pi can be expressed as:

( ) ( ){ }Tin

Tin

Tin

Ti

Ti

Tii zyxzyxP ,,,,,, 111= (1)

Formula (1) shows the space position when the tasks are carried out in turn. That means, a sequential task set Θi={Ti1,Ti2,…,Tin}should be specified to a equipment Vi.

III. CONSTRAINT CONDITIONS OF TASK PLANNING The aerospace task planning is a constraint optimization

problem. The following constraint conditions should be considered.

a) Maximal executing capacity That is the maximal targets number in the antenna lobe-

width which can be tracked by the equipments. If the task routing is Pk for the equipment Vk and Pk consumes capacity Q(Pk). The maximal executing capacity of Vk is qVk. The constraint is expressed as below.

)()( VVqPQ kVkk ∈∀≤ (2) b) Maximum operating range

It depends on the specification of the equipment. If the task routing is Pk for the equipment Vk and the maximum TT&C distance related Pk is D(Pk). The maximum operating range of Vk is DVk. The constraint is expressed as below.

)()( VVDPD kVkik ∈∀≤ (3) c) The lowest elevation

It depends on the shielding angle of TT&C station. It limits the beginning time of tracking target. If the task routing is Pk for the equipment Vk and the lowest elevation related Pk is E(Pk). The lowest elevation of Vk is EVk. The constraint is expressed as below.

2010 International Conference on Artificial Intelligence and Computational Intelligence

978-0-7695-4225-6/10 $26.00 © 2010 IEEE

DOI 10.1109/AICI.2010.355

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2010 International Conference on Artificial Intelligence and Computational Intelligence

978-0-7695-4225-6/10 $26.00 © 2010 IEEE

DOI 10.1109/AICI.2010.355

556

)()( VVEPE kVkik ∈∀≤ (4) d) Maximum antenna beam width

It depends on the specification of the equipment. It limits the satellites number which can be track simultaneously and the tracking period. If the task routing is Pk for the equipment Vk and the maximum antenna beam width related Pk is θ(Pk). The constraint is expressed as below.

)()( VVP kVkik ∈∀≤ θθ (5) e) Tracking window

The TT&C task can only be carried out during the satellite visible window. If the visible window for task Tk∈Θk is (BVij, EVij), and the position of aerospace Ui is (xT

k, yTk,

zTk) at the moment Sik. The constraint is expressed as below.

),,2,1;,2,1( UTijikij NkNiEVSBV =∀=∀≤≤ (6)

f) Equipment maintenance time To make sure no assign any task to the equipment Vk

when it is abnormal or maintenance. The start maintenance time is SDTk, the end maintenance time is EDTk, and the minimum maintenance time is ΔTk. The constraint is expressed as below.

kkk TEDTSDT Δ+≥ (7) g) Priority relationship

In the preparing task, the two specify tasks T1 and T2 have the priority relationship. Assume: Task T1 will be executed at St1, and task T2 will be executed at St2.The interval between two tasks is Δk. The constraint is expressed as below.

ktt SS Δ+≥ 12 (8) h) Task scheduling

We should insure every task will be scheduled. Suppose the task number which is not assigned is no_service. The constraint is expressed as below.

0_nor 1 ==Θ∪ = serviceoTiNi

U (9)

i) Waiting time The ‘waiting time’ can described as Figure 1. The ‘waiting time’ can be realized in different form, for

example, the antenna can stay in original position first, then reach to next waiting position; also can reach to next position first, and then waiting for the satellite.

IV. TASK PLANNING FORMULATION OF MULTI-SATELLITE Since this is a highly constrained scheduling problem, we

decided to approach this problem using the mixed integer program (MIP) formulation below[2],[3].

The decision variable Wij denotes the scheduling of satellite support group Ui at TT&C equipment Vj while the maximal executing capacity is qVk (i.e. the maximum aerospace in the group is qVk). The necessary condition using equipment Vj to track aerospace group Ui is that Ui should be observed in the antenna beam width (i.e. all the satellites in the group Ui should be observed by Vi simultaneously). The decision variable STij represents the start time of support Ui at Vj. The objective of this model is to maximize the number

of satellite supports scheduled under the condition of equipment specification (i.e. the overlapping support within its visibility window is permitted). The MIP formulation is presented below.

Objective function:

∑∑= ∈

n

i Vjij

i

WMaximize1

(10)

Subject to:

∑∈

=≤iVj

ij niW 1 ,1 (11)

iijijij VjniWBVST ∈∀=∗≤ , 1 , (12)

iijijijij VjniWREVST ∈∀=∗−≤ , 1 ,)( (13)

jgiveniWMSDTRST ijjijij ,)1( ∀−+≤+ (14) jgiveniWMTOEDTST ijijij ,)1( ∀−−+≥ (15)

j

)1()1(

givenih

WMWMMySTTORST hjijihjhjhijij

∀∀

−+−++≤++

(16)

j

)1()1()1(

givenih

WMWMyMSTTORST hjijihjijihjhj

∀∀

−+−+−+≤++

(17) { }1,0∈ijW (18) { }1,0∈ihjy (19)

iij VjiST ∈∀≥ , ,0 (20) Where Rij = Length of required execute task Ti at Vj. TOi = Turnaround time of execute task Ti. SDTj = Start of downtime at Vj. EDTj = End of downtime at Vj. M = A large positive constant. In addition When task Ti is scheduled to equipment Vj, Wij=1;

Otherwise Wij=0. When SThj < STij (i≠j), yihj=1. When SThj ≥ STij , yihj=0.

V. ALGORITHM SIMULATION Here, we will simulate the TT&C task scheduling to the

fifteen satellites and three antennas. The fifteen satellites are included in five geostationary orbit satellites (GEO), three inclination geostationary orbit satellites (IGSO), four medium altitude satellites (MEO) and two low altitude satellites (LEO). The three TT&C ground station are distributed in northwest of China, northeast of China and south of China. i.e. NU=15 and MV=3. The TT&C equipments are used in SDMA-CDMA mode.

The TT&C task is planned as below. • The orbit should be measured at least three times

during a close TT&C arc for GEO satellite. And it must be two hours orbit measurement for every time. i.e. Rij=2hour.

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• The IGSO satellite should be tracked within its every visibility widow. The orbit should be measured at least one hour, . i.e. Rij=1hour.

• The MEO satellite should be tracked within its every visibility widow. The orbit should be measured at least forty minutes, . i.e. Rij=40 minutes.

• The LEO satellite should be tracked within its every visibility widow. The orbit should be measured at least five minutes, . i.e. Rij=5 minutes.

• Three sets of equipments need to be maintained for 1 hour everyday. And the downtime is fixed. i.e. EDTj-SDTj=1 hour.

• It needs ten minutes to prepare tracking satellite for three sets of equipment. i.e. TOi=10 minutes.

• The lowest elevation tracking satellite is five degrees. i.e. EVk=5°.

• The maximum operating range of TT&C equipment is 45000 kilometres. i.e. DVk=45000km.

• When multi-satellite is tracked by the single antenna, the antenna beam width is fifteen degrees. i.e. θVk=15°.

• The priority relationship from high to low is: LEO satellite→MEO satellite→IGSO satellite→GEO satellite.

We use sequential algorithm scheduling task [4]. Sequential algorithms are algorithms that assign tasks one by one following a sequence based on pre-defined rules. First consider a sequential algorithm in which tasks are assigned in task numeric order and resources are used in resources numeric order.

Real problems have many more tasks, many more possible resources (or combinations of resources) and more complex constraints. There are many versions of such sequential algorithms that are used to solve them. However, in general the strategy is similar: 1) choose an order to try tasks and possible resources, 2) test if a new combination is possible and keep it if is, or 3) use some method to find the cause of block and remove it if possible.

The sequential algorithm was developed specifically for scheduling problems where using the earliest contact is known to give good solutions. Empirically, it has been found to produce very good solutions for problems dominated by ground access constraints. It is very fast but because it has very structured search can perform poorly if the problem is well suited to it such as problems with highly conflicted resources.

We simulate the task scheduling under three situations, i.e. 1) the antenna can track only one satellite, 2) the antenna can track two satellites simultaneously,3) the antenna can track three satellites simultaneously. The scheduling results

for two satellites and three satellites are shown in figure 2 and figure 3. And the simulation results are shown in table 1.

We can know from simulation results: when we use same antenna but change the tracking mode (i.e. change tracking mode from mono-satellite to multi-satellite), the proportion of TT&C task planning can be improved, and the using efficiency for TT&C resources is enhanced.

VI. CONCLUSION The unified TT&C task planning viewpoint combining

GEO, MEO and LEO satellites is proposed in this paper. It is different from the oversea TT&C network [5],[6]. The characteristic of this idea is to make use of function tracking multi-satellite. All kinds of task which are operated in different orbits are scheduled reasonability, and the scheduling conflict is decreased, without increase any antenna.

The simulation results show us: to the 15 satellites operated in different orbits, we use sequential algorithm to schedule 709 tasks. If we use mono-satellite tracking mode to schedule the task, the 78.56 percent of all satellite support requests are scheduled. If we use two satellites tracking mode to schedule the task, the 89.70 percent of all satellite support requests are scheduled. If we use three satellites tracking mode to schedule the task, the 90.60 percent of all satellite support requests are scheduled.

Multi-target TT&C is one of key technology for near space TT&C and operationally responsive space TT&C in future. Therefore, the results provided in this paper are valuable to them.

REFERENCES [1] [1] Pachter M，Chandler P. R. Challenges of autonomous control.

IEEE Control Systems Magazine,1998,18(4): 91-97. [2] Zheng Chang-wen, Yan Ping, Ding Ming-yue, Sun Fu-chun. Route

Planning For Air Vehicles. National Defense Industry Press, 2008. [3] T.D.Gooley，J.J.Borsi，J.T.Moore. Automating Air Force Satellite

Control Network (AFSCN) Scheduling. Mathl. Comput. Modelling Vol.24,No 2, 1996, 91-101.

[4] William Fisher. The Optwise Corporation Deconfliction Scheduler Algorithms. Copyright Optwise Corporation 2002-2004

[5] Barbulescu L，H owe A ，W hitley D．AFSCN Scheduling：H ow the Problem and Solution Have Evolved[J]．Mathematic and Computer M odelling，2006，43：1023—1037

[6] Barbulescu L，Watson J P，Whitley D．Scheduling Space— G round Communications for the Air Force Satellite Control Network[J]．Journal of Scheduling，2004，1(7)：7-34

.

TABLE I. SIMULATION RESULTS

No. Tacking Mode Task Request Task scheduled Task scheduled（%） 1 Mono-satellite 709 557 78.56 2 Two satellites 709 636 89.70 3 Three satellites 709 642 90.55

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Figure 1. Time relationship between tasks

Figure 2. Task planning result for mono-satellite tacking mode

Figure 3. Task planning result forthree satellites tacking mode

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