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Distributed Satellites Dynamic Allocation for Grids with Time Windows: A Potential Game Approach

Weiyi Yang, Yingwu Chen, Xiaolu Liu, Jun Wen, Lei He

TL;DR

This work tackles dynamic grid with time-window allocation for distributed satellites (DGAP) by formulating a single-stage problem (sDGAP) and solving it within time-window stages. A smooth global utility h(x) is used to approximate the non-continuous objective, enabling a potential-game formulation in which a satellite’s local payoff aligns with the global objective. A novel distributed SeTVBRP algorithm, featuring selective action and time-variant parameters, is proposed and proven to converge to a Nash equilibrium; it also enables efficient multi-stage allocations. Extensive simulations demonstrate that SeTVBRP outperforms existing learning algorithms and is robust across regional and global scenarios, with favorable performance in multi-stage allocations and scalability to larger grids and satellite counts. The approach offers a scalable, theoretically grounded method for coordinated task allocation in distributed satellite swarms with time-window constraints, with potential for integration of learning components and more realistic mission constraints in future work.

Abstract

The allocation of tasks to a large number of distributed satellites is a difficult problem owing to dynamic changes in massive tasks and the complex matching of tasks to satellites. To reduce the complexity of the problem, tasks that are geographically close can be divided into a predefined grid with a specific time window and processed together. The problem then becomes a dynamic grid with time-window allocation problem (DGAP). To ensure consistent visibility between satellites and grids, the timeline of the DGAP is partitioned into several decision-making stages that are determined by dynamic changes in the time window. Subsequently, the DGAP can be resolved progressively adopting the potential game approach in the single-stage DGAP (sDGAP). First, to solve the discontinuity in the goal of the sDGAP, we approximate the goal by a smooth exponential sum function that we regard as the global utility function. Second, a potential game theoretic framework is constructed by decomposing this global utility function into the local utility functions of individuals. We prove that each Nash equilibrium of the proposed potential game is the optimal solution of the sDGAP. Third, to solve the potential game, a distributed algorithm, referred to as the selective time-variant better reply process (SeTVBRP) algorithm, is proposed and its convergence is proved. The SeTVBRP algorithm is an improved algorithm based on the better reply process algorithm, where two improvement methods (i.e., the selective action method and time-variant parameter method) are introduced. Through factor analysis, we demonstrate the effectiveness of the two improvement methods for the sDGAP. Last, numerical results show that the proposed algorithm outperforms existing learning algorithms and is effective in solving the DGAP.

Distributed Satellites Dynamic Allocation for Grids with Time Windows: A Potential Game Approach

TL;DR

This work tackles dynamic grid with time-window allocation for distributed satellites (DGAP) by formulating a single-stage problem (sDGAP) and solving it within time-window stages. A smooth global utility h(x) is used to approximate the non-continuous objective, enabling a potential-game formulation in which a satellite’s local payoff aligns with the global objective. A novel distributed SeTVBRP algorithm, featuring selective action and time-variant parameters, is proposed and proven to converge to a Nash equilibrium; it also enables efficient multi-stage allocations. Extensive simulations demonstrate that SeTVBRP outperforms existing learning algorithms and is robust across regional and global scenarios, with favorable performance in multi-stage allocations and scalability to larger grids and satellite counts. The approach offers a scalable, theoretically grounded method for coordinated task allocation in distributed satellite swarms with time-window constraints, with potential for integration of learning components and more realistic mission constraints in future work.

Abstract

The allocation of tasks to a large number of distributed satellites is a difficult problem owing to dynamic changes in massive tasks and the complex matching of tasks to satellites. To reduce the complexity of the problem, tasks that are geographically close can be divided into a predefined grid with a specific time window and processed together. The problem then becomes a dynamic grid with time-window allocation problem (DGAP). To ensure consistent visibility between satellites and grids, the timeline of the DGAP is partitioned into several decision-making stages that are determined by dynamic changes in the time window. Subsequently, the DGAP can be resolved progressively adopting the potential game approach in the single-stage DGAP (sDGAP). First, to solve the discontinuity in the goal of the sDGAP, we approximate the goal by a smooth exponential sum function that we regard as the global utility function. Second, a potential game theoretic framework is constructed by decomposing this global utility function into the local utility functions of individuals. We prove that each Nash equilibrium of the proposed potential game is the optimal solution of the sDGAP. Third, to solve the potential game, a distributed algorithm, referred to as the selective time-variant better reply process (SeTVBRP) algorithm, is proposed and its convergence is proved. The SeTVBRP algorithm is an improved algorithm based on the better reply process algorithm, where two improvement methods (i.e., the selective action method and time-variant parameter method) are introduced. Through factor analysis, we demonstrate the effectiveness of the two improvement methods for the sDGAP. Last, numerical results show that the proposed algorithm outperforms existing learning algorithms and is effective in solving the DGAP.

Paper Structure

This paper contains 18 sections, 65 equations, 12 figures, 6 tables, 1 algorithm.

Table of Contents

  1. Introduction
  2. Related works
  3. Problem Formulation
  4. Problem description
  5. Formulation of DGAP
  6. Formulation of sDGAP
  7. Global utility function
  8. Potential game model
  9. Algorithm design
  10. Selective Time Variant Better Reply Process
  11. Convergence analysis
  12. Multi-stage dynamic allocation
  13. Simulation and comparison results
  14. Simulation settings
  15. Parameter analysis experiments
  16. ...and 3 more sections

Figures (12)

  • Figure 1: Satellites and grids distribution diagram
  • Figure 2: Schematic of the observation capabilities of different satellites for different grids
  • Figure 3: The diagram of transition time
  • Figure 4: Diagram for multi-stage dynamic allocation
  • Figure 5: Schematic diagram of scenario, where the grid represents the observation grid and the curve represents the ground track of the imaging satellite
  • ...and 7 more figures