1. Distributed Control and Autonomous Systems Lab. Sang-Hyuk Yun and Hyo-Sung Ahn Distributed Control and Autonomous Systems Laboratory (DCASL ) Department of the mechatronics Gwangju Institute of Science and Technology (GIST)

2. Gwangju Institute of Science and Technology Distributed Control and Autonomous Systems Lab. 2 Contents Introduction Main Points of Multi-Antenna Scheduling (MAS) Algorithms 1 and 2 Multi-Antenna Scheduling (MAS) Algorithm 1 Multi-Antenna Scheduling (MAS) Algorithm 2 Simulation Conclusion

3. Gwangju Institute of Science and Technology Distributed Control and Autonomous Systems Lab. 3 Introduction: Motivation Multi-antenna scheduling (MAS) problem is to resolve visibility conflicts between multiple satellites and multiple antennas at a ground station. Multiple satellites must be mapped to multiple antennas with the hard constraint of visibility conflicts. Our purpose is to find an optimal schedule for multi-antenna and multi-satellite when there are multiple satellites with visibility conflicts and multiple antennas at a ground station.

4. Gwangju Institute of Science and Technology Distributed Control and Autonomous Systems Lab. 4 Introduction: Background Time Window –When a satellite is visible to a ground station during an interval, the satellite is available for the interval. The interval is called “time window”. –It is possible for satellites to be supported from a ground station during the time window. Reconfiguration Time –An antenna at a ground station switches support from one satellite to another satellite, a finite amount of time is required.

5. Gwangju Institute of Science and Technology Distributed Control and Autonomous Systems Lab. 5 Introduction: Background Visibility Conflict –Visibility conflicts occur when Multiple satellites pass over and are visible to a ground station simultaneously The difference between the time of loss of signal (LOS) of one satellite and the time of acquisition of signal (AOS) of another satellite is less than the reconfiguration time.

6. Gwangju Institute of Science and Technology Distributed Control and Autonomous Systems Lab. 6 Introduction: Background Priority Value, –Support time –Visibility conflict at a previous ground station –Operation priority –Number of missions –User priority –Path over a ground station –Storage capacity Objective function,

7. Gwangju Institute of Science and Technology Distributed Control and Autonomous Systems Lab. 7 Main Points of MAS Algorithms: Basic Assumption In order of time of AOS, there exist satellites from to All satellites have visibility conflicts The support time of is equal to the time window of, There exist multiple antennas at a ground station, It is possible for all antennas to support all satellites The reconfiguration time of all antennas is constant

8. Gwangju Institute of Science and Technology Distributed Control and Autonomous Systems Lab. 8 Main Points of MAS Algorithms: Characteristics of MAS Algorithms In order of time of AOS, M satellites are assigned one to one to antennas. We define the satellites as the initially assigned satellites (IASs). We search all feasible schedules by using backtracking. We choose the path that maximizes the summation of priority values in the tree. We apply the child node condition for the efficiency of the algorithms.

9. Gwangju Institute of Science and Technology Distributed Control and Autonomous Systems Lab. 9 Main Points of MAS Algorithms: All Schedules Search

10. Gwangju Institute of Science and Technology Distributed Control and Autonomous Systems Lab. 10 Main Points of MAS Algorithms: Child Node Condition Child node condition is the criterion that limits the number of child nodes during backtracking. Child nodes are limited by the node of the satellite in the level when the node of the satellite is the first node for time of AOS in the level. We lose a chance in which K satellites are assigned to an antenna when we form a path including one among several nodes of satellites of the level in the level.

11. Gwangju Institute of Science and Technology Distributed Control and Autonomous Systems Lab. 11 Multi-Antenna Scheduling (MAS) Algorithm 1 Select the initially assigned satellites (IASs) in order of time of AOS. Assign one of IASs to A1 as the first satellite of all feasible schedules for A1. Search all feasible schedules by using backtracking and find an optimal schedule for A1. Assign another satellite of IASs to A2 as the first satellite of all feasible schedules for A2. Search all feasible schedules and find an optimal schedule for A2. Repeat the above process for all antennas. The critical point is that we determine what order of IASs is the best as the first satellite assigned to each antenna in order to find an optimal schedule for multiple antennas.

12. Gwangju Institute of Science and Technology Distributed Control and Autonomous Systems Lab. 12 MAS algorithm 1 (Cont.) MAS algorithm 1 is local approach. MAS algorithm 1 provides an optimal schedule for each antenna. MAS algorithm 1 dose not guarantee that the schedule for multi-antenna is optimal.

13. Gwangju Institute of Science and Technology Distributed Control and Autonomous Systems Lab. 13 Multi-Antenna Scheduling (MAS) Algorithm 2 Select the initially assigned satellites (IASs) in order of time of AOS. Assign the first IAS to A1 as the first satellite of all feasible schedules for A1. Find one feasible schedule for A1. Assign the second IAS to A2 as the first satellite of all feasible schedules for A2 except for satellites included in the schedules for A1. Repeat the process and form schedules for all antennas. Search all feasible schedules for all antennas by using backtracking and applying the child node condition. Find an optimal schedule for multi-antenna system.

14. Gwangju Institute of Science and Technology Distributed Control and Autonomous Systems Lab. 14 MAS Algorithm 2 (Cont.) is a root. is located in the next level of all the last nodes of the tree with as a root. Form trees with as a root. Trees with as a root are subtrees of a tree with as a root. Find an optimal schedule for multi-antenna in a great tree consisting of a number of subtrees. 1 56 78 4 8 2 9 99 2222 56 657 57 56 9 7

15. Gwangju Institute of Science and Technology Distributed Control and Autonomous Systems Lab. 15 MAS Algorithms 2 (Cont.) MAS algorithm 2 is global approach. MAS algorithm 2 finds an optimal schedule for multi- antenna at once by considering the condition of all antennas.

16. Gwangju Institute of Science and Technology Distributed Control and Autonomous Systems Lab. 16 Greedy Algorithm Greedy algorithm makes the choice that looks best at the moment. The most significant difference between the MAS algorithms and the greedy algorithm is that the MAS algorithms search all feasible schedules to find an optimal schedule but the greedy algorithm does not.

17. Gwangju Institute of Science and Technology Distributed Control and Autonomous Systems Lab. 17 Greedy Algorithm (Cont.) Select IASs in order of time of AOS. Assign one of IASs to A1 as the first satellite (the first input, in ) Find all child nodes in subject to the child node condition. In all the values of, select one that has the maximum priority value and take it to the parent node (input ). Repeat this process until there are no more child nodes satisfying 8 5 78 64 1 798 9 P1=12 P5=12 P8=5 P6=10P4=3 P7=10 P10=6 P9=7 P12=11 P11=15

18. Gwangju Institute of Science and Technology Distributed Control and Autonomous Systems Lab. 18 Greedy Algorithm (Cont.) Find an optimal schedule for A1. Assign another satellite of the IASs to A2 as the first satellite (the first input in ). Repeat the process until there are no more child nodes (outputs) satisfying. Find an optimal schedule for A2. Repeat the process for all antennas. Determine what order of IASs is the best as the first satellite assigned to each antenna to find an optimal schedule for multi-antenna.

19. Gwangju Institute of Science and Technology Distributed Control and Autonomous Systems Lab. 19 Simulation [The Satellite Information] Set up 30 satellites, 3 ground-station antennas and 100 second reconfiguration time for the simulation. The programs for the simulation were developed in the C programming language and were run on a 2.93 GHz Pentium 4 computer

20. Gwangju Institute of Science and Technology Distributed Control and Autonomous Systems Lab. 20 Simulation: Comparison between MAS Algorithms and Greedy Algorithm [The Result of MAS Algorithm 1] [The Result of MAS Algorithm 2][The Result of Greedy Algorithm]

21. Gwangju Institute of Science and Technology Distributed Control and Autonomous Systems Lab. 21 Simulation: Comparison between MAS Algorithms 1 and 2 There exists a trade-off between optimality and efficiency in finding an optimal solution for multi-antenna in MAS algorithms 1 and 2. MAS algorithm 2 is better than MAS algorithm 1 in terms of optimality. MAS algorithm 1 is better than MAS algorithm 2 in terms of efficiency.

22. Gwangju Institute of Science and Technology Distributed Control and Autonomous Systems Lab. 22 Comparison between MAS Algorithms (Cont.) [Comparison with the optimality of MAS algorithms 1 and 2]

23. Gwangju Institute of Science and Technology Distributed Control and Autonomous Systems Lab. 23 Comparison between MAS Algorithms (Cont.) [Comparison with the optimality of MAS algorithms 1 and 2]

24. Gwangju Institute of Science and Technology Distributed Control and Autonomous Systems Lab. 24 Conclusion MAS algorithm 1 locally finds an optimal solution for the MAS problem. MAS algorithm 2 globally finds an optimal solution for the MAS problem. There exists a trade-off between optimality and efficiency in finding an optimal solution for multi-antenna in MAS algorithms. Depending on the characteristics of satellite information or the situation such as time to spare, MAS algorithms can be used properly.

25. Gwangju Institute of Science and Technology Distributed Control and Autonomous Systems Lab. 25 Thanks!! Q & A