To plan the path for unmanned aerial vehicles (UAVs) considering the impact angle and acceleration constraints, a novel geometric rule is proposed in this paper. Firstly, under the nonlinear engagement kinematics, the geometric rule is derived from the modified circular curve including two parameters, one for the convergence of the acceleration, the other for extending the flight envelope. Furthermore, the convergence of the nominal guidance law developed from the geometric rule is rigorously proved. Secondly, to eliminate the angle tracking error regardless of the initial error size, a fixed-time convergent controller is adopted to formulate the impact angle control guidance law. Moreover, the implementation of the proposed guidance law only requires angle information, which can be readily obtained by the on-board device. The proposed guidance law is also applicable for varying-speed UAVs and moving targets. The simulation results and the comparative studies demonstrate the validity and superiority of the proposed guidance law.
ZhimingZYaoX. Polynomial guidance law for impact angle control with a seeker look angle limit. Proc Inst Mech Eng G J Aerosp Eng2019; 234: 857–870. DOI: 10.1177/0954410019890808.
2.
MohsanSAHKhanMANoorF, et al.Towards the unmanned aerial vehicles (UAVs): a comprehensive review. Drones2022; 6: 147.
3.
BeckerK. Closed-form solution of pure proportional navigation. IEEE Trans Aero Electron Syst1990; 26: 526–533.
4.
YuanP-JHsuS-C. Exact closed-form solution of generalized proportional navigation. J Guid Control Dynam1993; 16: 963–966.
5.
RatnooA. Analysis of two-stage proportional navigation with heading constraints. J Guid Control Dynam2016; 39: 156–164.
6.
KimBSLeeJGHanHS. Biased PNG law for impact with angular constraint. IEEE Trans Aero Electron Syst1998; 34: 277–288.
7.
KimT-HParkB-GTahkM-J. Bias-shaping method for biased proportional navigation with terminal-angle constraint. J Guid Control Dynam2013; 36: 1810–1816.
8.
LeeC-HKimT-HTahkM-J. Interception angle control guidance using proportional navigation with error feedback. J Guid Control Dynam2013; 36: 1556–1561.
9.
RatnooAGhoseD. Impact angle constrained interception of stationary targets. J Guid Control Dynam2008; 31: 1817–1822. DOI: 10.2514/1.37864.
10.
RatnooAGhoseD. Impact angle constrained guidance against nonstationary nonmaneuvering targets. J Guid Control Dynam2010; 33: 269–275. DOI: 10.2514/1.45026.
11.
ErerKSMerttopçuogluO. Indirect impact-angle-control against stationary targets using biased pure proportional navigation. J Guid Control Dynam2012; 35: 700–704. DOI: 10.2514/1.52105.
12.
TekinRErerKS. Switched-gain guidance for impact angle control under physical constraints. J Guid Control Dynam2015; 38: 205–216.
13.
KimMGriderKV. Terminal guidance for impact attitude angle constrained flight trajectories. IEEE Trans Aero Electron Syst1973; 9: 852–859.
14.
RyooC-KChoHTahkM-J. Optimal guidance laws with terminal impact angle constraint. J Guid Control Dynam2005; 28: 724–732. DOI: 10.2514/1.8392.
15.
Chang-KyungRHangjuCMin-JeaT. Time-to-go weighted optimal guidance with impact angle constraints. IEEE Trans Control Syst Technol2006; 14: 483–492. DOI: 10.1109/tcst.2006.872525.
16.
ParkB-GKimT-HTahkM-J. Range-to-go weighted optimal guidance with impact angle constraint and seeker's look angle limits. IEEE Trans Aero Electron Syst2016; 52: 1241–1256.
17.
LiHWangJHeS, et al.Nonlinear optimal impact-angle-constrained guidance with large initial heading error. J Guid Control Dynam2021; 44: 1663–1676. DOI: 10.2514/1.G005868.
18.
TsalikRShimaT. Optimal guidance around circular trajectories for impact-angle interception. J Guid Control Dynam2016; 39: 1278–1291. DOI: 10.2514/1.G001759.
19.
LevantA. Sliding order and sliding accuracy in sliding mode control. Int J Control1993; 58: 1247–1263.
20.
LaghroucheSPlestanFGlumineauA. Higher order sliding mode control based on integral sliding mode. Automatica2007; 43: 531–537. DOI: 10.1016/j.automatica.2006.09.017.
21.
YanBDaiPLiuR, et al.Adaptive super-twisting sliding mode control of variable sweep morphing aircraft. Aero Sci Technol2019; 92: 198–210. DOI: 10.1016/j.ast.2019.05.063.
22.
UtkinVPoznyakAOrlovY, et al.Conventional and high order sliding mode control. J Franklin Inst2020; 357: 10244–10261. DOI: 10.1016/j.jfranklin.2020.06.018.
23.
ZhangYSunMChenZ. Finite-time convergent guidance law with impact angle constraint based on sliding-mode control. Nonlinear Dyn2012; 70: 619–625.
24.
ZhangZLiSLuoS. Composite guidance laws based on sliding mode control with impact angle constraint and autopilot lag. Trans Inst Meas Control2013; 35: 764–776. DOI: 10.1177/0142331213478327.
25.
WangXZhangYWuH. Sliding mode control based impact angle control guidance considering the seeker’s field-of-view constraint. ISA Trans2016; 61: 49–59. DOI: 10.1016/j.isatra.2015.12.018.
26.
ZhaoYShengYLiuX. Sliding mode control based guidance law with impact angle constraint. Chin J Aeronaut2014; 27: 145–152.
27.
KumarSRRaoSGhoseD. Nonsingular terminal sliding mode guidance with impact angle constraints. J Guid Control Dynam2014; 37: 1114–1130.
MingCWangXSunR. A novel non-singular terminal sliding mode control-based integrated missile guidance and control with impact angle constraint. Aero Sci Technol2019; 94: 105368. DOI: 10.1016/j.ast.2019.105368.
30.
ShengYZhangZXiaL. Fractional-order sliding mode control based guidance law with impact angle constraint. Nonlinear Dyn2021; 106: 425–444. DOI: 10.1007/s11071-021-06820-6.
QinZQiXFuY. Terminal guidance based on bézier curve for climb-and-dive maneuvering trajectory with impact angle constraint. IEEE Access2019; 7: 2969–2977. DOI: 10.1109/access.2018.2883405.
33.
ShiHChengZKuangM, et al. Four-stage guidance law for impact time and angle control based on the bezier curve. IEEE Trans Aero Electron Syst. 2023; 60(4): 3766–3778.
34.
YanXKuangMZhuJ. A geometry-based guidance law to control impact time and angle under variable speeds. Mathematics2020; 8: 1029. DOI: 10.3390/math8061029.
WangZHuQHanT, et al.Two-stage guidance law with constrained impact via circle involute. IEEE Trans Aero Electron Syst2020; 57: 1301–1316.
37.
YanXZhuJKuangM, et al.A computational-geometry-based 3-dimensional guidance law to control impact time and angle. Aero Sci Technol2020; 98: 105672. DOI: 10.1016/j.ast.2019.105672.
38.
YanXTangYXuY, et al.Multi-Constrained geometric guidance law with a data-driven method. Drones2023; 7: 639.
39.
HouLLuoHShiH, et al.An optimal geometrical guidance law for impact time and angle control. IEEE Trans Aero Electron Syst2023; 59: 9821–9830.
40.
ManchesterIRSavkinAV. Circular navigation guidance law for precision missile/target engagements. In: Proceedings of the 41st IEEE Conference on Decision and Control, Las Vegas, NV, USA, 10-13 December 2002. IEEE, 2002, pp. 1287–1292.
41.
ManchesterIRSavkinAV. Circular-navigation-guidance law for precision missile/target engagements. J Guid Control Dynam2006; 29: 314–320. DOI: 10.2514/1.13275.
42.
ManchesterIRSavkinAV. Circular navigation missile guidance with incomplete information and uncertain autopilot model. J Guid Control Dynam2004; 27: 1078–1083. DOI: 10.2514/1.3371.
43.
YoonM-G. Relative circular navigation guidance for the impact angle control problem. IEEE Trans Aero Electron Syst2008; 44: 1449–1463.
44.
YoonM-G. Relative circular navigation guidance for three-dimensional impact angle control problem. J Aero Eng2010; 23: 300–308.
45.
ZengXWangJWangX. Trajectory correcting and tracking based impact angle constrained circular guidance. In: Proceedings of 2014 IEEE Chinese Guidance, Navigation and Control Conference, Yantai, China, 8-10 Aug. 2014, pp. 2729–2733.
TsalikRShimaT. Inscribed-angle guidance against moving targets. J Guid Control Dynam2017; 40: 3211–3225. DOI: 10.2514/1.G002786.
48.
HeSLeeC-HShinH-S, et al.Minimum-effort waypoint-following guidance. J Guid Control Dynam2019; 42: 1551–1561.
49.
KeePDongLSiongC. Near optimal midcourse guidance law for flight vehicle. In: 36th AIAA Aerospace Sciences Meeting and Exhibit, Reno, NV, USA, 12-15 January 1998.
50.
ChoNKimY. Modified pure proportional navigation guidance law for impact time control. J Guid Control Dynam2016; 39: 852–872. DOI: 10.2514/1.G001618.
51.
LiXChenWChenZ, et al.Fixed-time circular impact-time guidance with look angle constraint. Aerospace2022; 9: 356.
