Journal of Systems Engineering and Electronics ›› 2018, Vol. 29 ›› Issue (2): 352-366.doi: 10.21629/JSEE.2018.02.16
• Control Theory and Application • Previous Articles Next Articles
Qilong SUN1(
), Naiming QI1,*(), Longxu XIAO2(), Haiqi LIN1()
Received:2017-02-23
Online:2018-04-26
Published:2018-04-27
Contact:
Naiming QI
E-mail:sunqilong27@163.com;qinaimingok_hit@163.com;xlxx@sina.com;linhaiqi_hit@163.com
About author:SUN Qilong was born in 1989. He is a Ph.D. candidate at Harbin Institute of Technology. He received his B.S. and M.S. degrees in Harbin Institute of Technology in 2012 and 2014, respectively. His research interests are vehicle guidance and control and the dynamics and control of motorized momentum exchange tether systems. E-mail: Supported by:Qilong SUN, Naiming QI, Longxu XIAO, Haiqi LIN. Differential game strategy in three-player evasion and pursuit scenarios[J]. Journal of Systems Engineering and Electronics, 2018, 29(2): 352-366.
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Fig 1
Engagement geometry"
Fig 2
Optimal trajectories of ${Z_{AD}}$"
Fig 3
Optimal trajectories of${Z_{AT}}$"
Fig 4
ZEM distance for case 1 as a function of time"
Fig 5
ZEM distance for case 2 as a function of time"
Fig 6
ZEM distance for the first condition as a function of time"
Fig 7
ZEM distance for the second condition as a function of time"
Fig 8
ZEM distance for the derived guidance law as a function of time"
Table 1
Initial parameters"
| Parameter | T | A | D |
| Initial position | (5, 0.2) | (0, 0) | (5, 0.2) |
| Initial speed | 300 | 600 | 700 |
Table 2
Initial parameters for Case 1"
| Parameter | T | A | D |
| Initial course | 14 | 0 | – 5.4 |
| Maximal acceleration | 50 | 80 | 75 |
Fig 9
Trajectories with parameters shown in Table 2"
Fig 10
Time-to-go with parameters shown in Table 2"
Fig 11
Trajectories with parameters shown in Table 2 except$||u{'_D}|{|^{max}} = 80{\rm{m/}}{{\rm{s}}^{\rm{2}}}$"
Fig 12
Trajectories with parameters shown in Table 2 except$||u{'_D}|{|^{max}} = 80{\rm{m/}}{{\rm{s}}^{\rm{2}}}$and$||u{'_D}|{|^{max}} = 100{\rm{m/}}{{\rm{s}}^{\rm{2}}}$"
Fig 13
Time-to-go with parameters shown in Table 2 except$||u{'_D}|{|^{max}} = 80{\rm{m/}}{{\rm{s}}^{\rm{2}}}$and$||u{'_D}|{|^{max}} = 100{\rm{m/}}{{\rm{s}}^{\rm{2}}}$"
Table 3
Initial parameters for Example 1"
| Parameter | T | A | D |
| Initial course | 14 | 0 | 23 |
| Maximal acceleration | 50 | 80 | 75 |
Fig 14
Trajectories with parameters shown in Table 3"
Fig 15
Time-to-go with parameters shown in Table 3"
Fig 16
Trajectories with parameters shown in Table 3 except$||u{'_D}|{|^{max}} = 80{\rm{m/}}{{\rm{s}}^{\rm{2}}}$"
Fig 17
Trajectories with parameters shown in Table 3 except$||u{'_D}|{|^{max}} = 80{\rm{m/}}{{\rm{s}}^{\rm{2}}}$and$||u{'_D}|{|^{max}} = 73{\rm{m/}}{{\rm{s}}^{\rm{2}}}$"
Fig 18
Time-to-go with parameters shown in Table 3 except$||u{'_D}|{|^{max}} = 80{\rm{m/}}{{\rm{s}}^{\rm{2}}}$and$||u{'_D}|{|^{max}} = 73{\rm{m/}}{{\rm{s}}^{\rm{2}}}$"
Table 4
Initial parameters for Example 2"
| Parameter | T | A | D |
| Initial course | 14 | 0 | 8 |
| Maximal acceleration | 50 | 80 | 50 |
Fig 19
Trajectories with parameters shown in Table 4"
Fig 20
Time-to-go with parameters shown in Table 4"
Fig 21
Trajectories with parameters shown in Table 4 except$||u{'_D}|{|^{max}} = 65{\rm{m/}}{{\rm{s}}^{\rm{2}}}$"
Fig 22
Trajectories with parameters shown in Table 4 except$||u{'_D}|{|^{max}} = 65{\rm{m/}}{{\rm{s}}^{\rm{2}}}$and$||u{'_D}|{|^{max}} = 100{\rm{m/}}{{\rm{s}}^{\rm{2}}}$"
Fig 23
Trajectories with parameters shown in Table 4 except$||u{'_D}|{|^{max}} = 65{\rm{m/}}{{\rm{s}}^{\rm{2}}}$, $||u{'_D}|{|^{max}} = 100{\rm{m/}}{{\rm{s}}^{\rm{2}}}$and${\gamma _{{\rm{A0}}}} = - 2{\rm{^\circ }}$"
Fig 24
Time-to-go with parameters shown in Table 4 except$||u{'_D}|{|^{max}} = 65{\rm{m/}}{{\rm{s}}^{\rm{2}}}$, $||u{'_D}|{|^{max}} = 100{\rm{m/}}{{\rm{s}}^{\rm{2}}}$and${\gamma _{{\rm{A0}}}} = - 2{\rm{^\circ }}$"
Table 5
Initial parameters for Example 3"
| Parameter | T | A | D |
| Initial course | 60 | 0 | 15 |
| Maximal acceleration | 40 | 150 | 80 |
| Initial position | (9, 0.2) | (9, 0.2) | (9, 0.2) |
| Initial speed | 300 | 600 | 800 |
Fig 25
Trajectories with parameters shown in Table 5"
Fig 26
Time-to-go with parameters shown in Table 5"
Fig 27
Trajectories with parameters shown in Table 5 except$||u{'_D}|{|^{max}} = 100{\rm{m/}}{{\rm{s}}^{\rm{2}}}$"
Fig 28
Trajectories with parameters shown in Table 5 except$||u{'_D}|{|^{max}} = 100{\rm{m/}}{{\rm{s}}^{\rm{2}}}$and$||u{'_D}|{|^{max}} = 180{\rm{m/}}{{\rm{s}}^{\rm{2}}}$"
Fig 29
Time-to-go with parameters shown in Table 5 except$||u{'_D}|{|^{max}} = 100{\rm{m/}}{{\rm{s}}^{\rm{2}}}$and$||u{'_D}|{|^{max}} = 180{\rm{m/}}{{\rm{s}}^{\rm{2}}}$"
Table 6
Initial parameters for Example 4"
| Parameter | T | A | D |
| Initial course | 70 | 0 | 7 |
| Maximal acceleration | 40 | 180 | 50 |
| Initial position | (9, 0.2) | (0, 0) | (9, 0.2) |
| Initial speed | 300 | 600 | 800 |
Fig 30
Trajectories by using the optimal pursuit guidance law"
Fig 31
Trajectories by using (46)"
Fig 32
Trajectories by using the optimal pursuit guidance law with parameters given in Table 6 except$||u{'_D}|{|^{max}} = 80{\rm{m/}}{{\rm{s}}^{\rm{2}}}$"
Fig 33
rajectories by using (46) with parameters given in Table 6 except$||u{'_D}|{|^{max}} = 80{\rm{m/}}{{\rm{s}}^{\rm{2}}}$"
Fig 34
Trajectories by using the optimal pursuit guidance law with parameters given in Table 5"
Fig 35
Trajectories by using the optimal pursuit guidance law with parameters given in Table 5 except$||u{'_D}|{|^{max}} = 180{\rm{m/}}{{\rm{s}}^{\rm{2}}}$"
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