-
摘要:
针对具有主动防御能力的飞行器受到攻击导弹的威胁后发射一枚导弹进行防御的制导问题，基于微分对策理论对飞行器和防御弹的制导律进行了设计和分析。首先，对于飞行器、防御弹和攻击弹的侧向控制均有界的情况，基于一种范数型的性能指标推导得出了对策三方的最优制导策略。然后，当攻击弹采用不同制导策略时，对飞行器和防御弹能够对策成功的条件进行了分析，给出了飞行器能够实现逃逸和防御弹能够完成拦截的最小机动条件。最后，进行了非线性仿真，结果表明了所提制导律的有效性，并验证了飞行器若要逃脱攻击弹需满足其最小逃逸机动条件，防御弹若要拦截攻击弹需满足其最小拦截机动条件。
Abstract:For the pursuit-evasion problems between an active defense aircraft which can launch a defending missile from itself and an attacking missile, a guidance law for aircraft and defending missile is derived and analyzed based on the differential game theory. First, Optimal guidance strategies with bounded lateral controls of aircraft, defending missile and attacking missile are derived for the three players by using a norm performance index. Second, the conditions of a successful evasion for the aircraft and a successful interception for the defender are deduced, and the minimal evasion maneuver of the aircraft and the minimal interception maneuver of the defender are obtained. Finally, Nonlinear simulations are carried out to validate the guidance law proposed. It is verified that the aircraft can evade the attacking missile if its maneuver is equal or greater than the minimal evasion maneuver, and the defender can intercept the attacking missile if its maneuver is equal or greater than the minimal interception maneuver.
-
Key words:
- aircraft /
- active defense /
- norm /
- differential game /
- guidance law
-
图 3 防御弹-攻击弹的对策空间(uDmax＜uMmax)
Figure 3. Defender-attacting missile game space (uDmax < uMmax)
图 5 攻击弹首先采用最优逃逸策略时的零控脱靶量
Figure 5. Evolution of ZEM while attacking missile performs optimal evasion first
图 6 攻击弹直接采用最优追踪策略时的零控脱靶量
Figure 6. Evolution of ZEM while attacking missile performs optimal pursuit directly
图 7 攻击弹首先逃逸时的三方运动轨迹(uTmax大于其最小逃逸机动)
Figure 7. Trajectories of three players while attacking missile evades first (uTmaxis larger than minimal evasion maneuver)
图 8 攻击弹首先逃逸时2个剩余对策时间的变化(uTmax大于其最小逃逸机动)
Figure 8. Evolution of two time-to-go while attacking missile evades first (uTmax is larger than minimal evasion maneuver)
图 9 攻击弹首先逃逸时的三方运动轨迹(uTmax小于其最小逃逸机动)
Figure 9. Trajectories of three players while attacking missile evades first (uTmax is smaller than minimal evasion maneuver)
图 10 攻击弹首先逃逸时2个剩余对策时间的变化(uTmax小于其最小逃逸机动)
Figure 10. Evolution of two time-to-go while attacking missile evades first (uTmax is smaller than minimal evasion maneuver)
图 11 攻击弹直接追踪时的三方运动轨迹(uDmax大于其最小拦截机动)
Figure 11. Trajectories of three players while attacking missile pursues directly (uDmax is larger than minimal interception maneuver)
图 12 攻击弹直接追踪时2个剩余对策时间的变化(uDmax大于其最小拦截机动)
Figure 12. Evolution of two time-to-go while attacking missile pursues directly (uDmax is larger than minimal interception maneuver)
图 13 攻击弹直接追踪时的三方运动轨迹(uDmax小于其最小拦截机动)
Figure 13. Trajectories of three players while attacking missile pursues directly (uDmax is smaller than minimal interception maneuver)
图 14 攻击弹直接追踪时2个剩余对策时间的变化(uDmax小于其最小拦截机动)
Figure 14. Evolution of two time-to-go while attacking missile pursues directly (uDmax is smaller than minimal interception maneuver)
表 1 攻击弹首先逃逸时的仿真参数
Table 1. Simulation parameters while attacking missle evades first
仿真参数 飞行器 防御弹 攻击弹 初始位置/m (0, 0) (0, 0) (9 000, -200) 初始航向/(°) 60 20 0 速度/(m·s-1) 300 800 700 
下载: 导出CSV
表 2 攻击弹直接追踪时的仿真参数
Table 2. Simulation parameters for attackingmissile pursues directly
仿真参数 飞行器 防御弹 攻击弹 初始位置/m (0, 0) (0, 0) (3 000, -200) 初始航向/(°) 12 7 0 速度/(m·s-1) 300 800 700
下载: 导出CSV
-
[1] SHAFERMAN V, SHIMA T.Cooperative multiple-model adaptive guidance for an aircraft defending missile[J].Journal of Guidance, Control, and Dynamics, 2010, 33(6):1801-1813. doi: 10.2514/1.49515 [2] SHIMA T.Optimal cooperative pursuit and evasion strategies against a homing missile[J].Journal of Guidance, Control, and Dynamics, 2011, 34(2):414-425. doi: 10.2514/1.51765 [3] PROKOPOV O, SHIMA T.Linear quadratic optimal cooperative strategies for active aircraft protection[J].Journal of Guidance, Control, and Dynamics, 2013, 36(3):753-764. doi: 10.2514/1.58531 [4] RATNOO A, SHIMA T.Line-of-sight interceptor guidance for defending an aircraft[J].Journal of Guidance, Control, and Dynamics, 2011, 34(2):522-532. doi: 10.2514/1.50572 [5] YAMASAKI T, BALAKRISHNAN S N, TAKANO H.Modified command to line-of-sight intercept guidance for aircraft defense[J].Journal of Guidance, Control, and Dynamics, 2013, 36(3):898-902. doi: 10.2514/1.58566 [6] RATNOO A, SHIMA T.Guidance strategies against defended aerial targets[J].Journal of Guidance, Control, and Dynamics, 2012, 35(4):1059-1068. doi: 10.2514/1.56924 [7] BOYELL R L.Defending a moving target against missile or torpedo attack[J].IEEE Transactions on Aerospace and Electronic Systems, 1976, 12(4):522-526. http://d.old.wanfangdata.com.cn/Periodical/bgxb200201019 [8] PERELMAN A, SHIMA T, RUSNAK I.Cooperative differential games strategies for active aircraft protection from a homing missile[J].Journal of Guidance, Control, and Dynamics, 2011, 34(3):761-773. doi: 10.2514/1.51611 [9] GARCIA E, CASBEER D W, PACHTER M.Cooperative strategies for optimal aircraft defense from an attacking missile[J].Journal of Guidance, Control, and Dynamics, 2015, 38(8):1510-1520. doi: 10.2514/1.G001083 [10] GARCIA E, CASBEER D W, PACHTER M.Active target defense differential game:Fast defender case[J].IET Control Theory and Applications, 2017, 11(17):2985-2993. doi: 10.1049/iet-cta.2017.0302 [11] GARCIA E, CASBEER D W, FUCHS C Z, et al.Cooperative missile guidance for active defense of air vehicles[J].IEEE Transactions on Aerospace and Electronic Systems, 2018, 54(2):706-721. doi: 10.1109/TAES.2017.2764269 [12] PACHTER M, GARCIA E, CASBEER D W.Active target defense differential game[C]//52nd Annual Allerton Conference on Communication, Control, and Computing.Piscataway, NJ: IEEE Press, 2014: 46-53. [13] RUSNAK I. The lady, the bandits and the body-guard game[C]//The 44th Israel Annual Conference on Aerospace Sciences.Haifa: Israel Institute of Technology, 2004: 25-26. [14] RUSNAK I.The lady, the bandits and the body guards-A two team dynamic game[C]//Proceedings of the 16th World IFAC Congress.Prague: IFAC, 2005: 441-446. [15] RUSNAK I.Games based guidance in anti-missile defense for high order participants[C]//Proceeding of the 15th IEEE Mediterranean Electrotechnical Conference.Piscataway, NJ: IEEE Press, 2010: 812-817. [16] RUBINSKY S, GUTMAN S.Three body guaranteed pursuit and evasion: AIAA-2012-4910[R].Reston: AIAA, 2012. [17] RUBINSKY S, GUTMAN S.Three-player pursuit and evasion conflict[J].Journal of Guidance, Control, and Dynamics, 2014, 37(1):98-110. doi: 10.2514/1.61832 [18] 孙启龙, 齐乃明, 赵钧, 等.攻击主动防御飞行器的微分对策制导律[J].国防科技大学学报, 2018, 40(3):7-14. http://d.old.wanfangdata.com.cn/Periodical/gfkjdxxb201803002SUN Q L, QI N M, ZHAO J, et al.Differential game guidance laws against active defense aircraft[J].Journal of National University of Defense Technology, 2018, 40(3):7-17(in Chinese). http://d.old.wanfangdata.com.cn/Periodical/gfkjdxxb201803002 [19] SUN Q L, QI N M, XIAO L X, et al.Differential game strategy in three-player evasion and pursuit scenarios[J].Journal of Systems Engineering and Electronics, 2018, 29(2):352-366. doi: 10.21629/JSEE.2018.02.16 [20] TURETSKY V, SHINAR J.Missile guidance laws based on pursuit-evasion game formulations[J].Automatica, 2003, 39(4):607-618. doi: 10.1016/S0005-1098(02)00273-X -
下载:
点击查看大图
计量
- 文章访问数: 788
- HTML全文浏览量: 149
- PDF下载量: 253
- 被引次数: 0
