A Geometrical, Reachable Set Approach for Constrained Pursuit–Evasion Games with Multiple Pursuers and Evaders
Abstract
:1. Introduction
2. Reachable Sets
2.1. Algorithm for Reachable Set Calculation
2.1.1. Initial Simplex
2.1.2. Growing Simplices
3. Game Theory
3.1. Single Pursuer and Single Evader
3.2. Multiple Pursuers and Single Evader
Algorithm 1 Line Search for Capture Time in Multiple Pursuer and Single Evader Game |
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3.3. Single Pursuer and Multiple Evaders
Algorithm 2 Termination Time in Single Pursuer and Multiple Evader Game |
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4. Dynamics
5. Numerical Simulations
5.1. Single Pursuer and Single Evader
5.2. Multiple Pursuers and Single Evader
5.3. Single Pursuer and Multiple Evaders
5.4. Computational Performance
6. Conclusions
Author Contributions
Funding
Data Availability Statement
Conflicts of Interest
Appendix A
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Average | Average | Average | Average | |
---|---|---|---|---|
Case | SDP Time (s) | SOCP Time (s) | SOCP Number | Total Time (s) |
Section 5.1 | 0.59 | 0.0068 | 40 | 0.86 |
Section 5.2 | 0.49 | 0.0064 | 44 | 0.77 |
Section 5.3 | 0.34 | 0.0059 | 59 | 0.69 |
Total Time (s) | Total Time (s) | Total Time (s) | Total Time (s) | |
---|---|---|---|---|
Case | for 5 itr | for 10 itr | for 25 itr | for 100 itr |
Section 5.1 | 8.6 | 17.2 | 43.0 | 172 |
Section 5.2 | 19.3 | 38.5 | 96.3 | 385 |
Section 5.3 | 13.8 | 27.6 | 69.0 | 276 |
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Jansson, O.; Harris, M.W. A Geometrical, Reachable Set Approach for Constrained Pursuit–Evasion Games with Multiple Pursuers and Evaders. Aerospace 2023, 10, 477. https://doi.org/10.3390/aerospace10050477
Jansson O, Harris MW. A Geometrical, Reachable Set Approach for Constrained Pursuit–Evasion Games with Multiple Pursuers and Evaders. Aerospace. 2023; 10(5):477. https://doi.org/10.3390/aerospace10050477
Chicago/Turabian StyleJansson, Olli, and Matthew W. Harris. 2023. "A Geometrical, Reachable Set Approach for Constrained Pursuit–Evasion Games with Multiple Pursuers and Evaders" Aerospace 10, no. 5: 477. https://doi.org/10.3390/aerospace10050477
APA StyleJansson, O., & Harris, M. W. (2023). A Geometrical, Reachable Set Approach for Constrained Pursuit–Evasion Games with Multiple Pursuers and Evaders. Aerospace, 10(5), 477. https://doi.org/10.3390/aerospace10050477