Analytic Approach to Impact Time Guidance with Look Angle Constraint Using Exact Time-to-Go Solution
Publication: Journal of Aerospace Engineering
Volume 37, Issue 2
Abstract
This paper proposes an analytic approach for impact time control guidance laws against stationary targets using biased proportional navigation. The proposed guidance scheme realizes the impact time control in two different ways: the first approach directly uses the exact time-to-go error to satisfy both the impact time control and the field-of-view constraint, while the second approach adopts a look angle tracking law to indirectly control the impact time, with the reference profile of the look angle generated using the exact time-to-go solution. The stability properties of the proposed guidance laws are discussed, and numerical simulations are carried out to evaluate their performance in terms of accuracy and efficiency.
Get full access to this article
View all available purchase options and get full access to this article.
Data Availability Statement
Some or all data, models, or code that support the findings of this study are available from the corresponding author upon reasonable request.
Acknowledgments
This work was supported by Chung-Ang University Research Grants in 2023 and the National Research Foundation of Korea (NRF) grant funded by the Korean government (MSIT) (No. RS-2023-00251551).
References
Chen, X., and J. Wang. 2018. “Nonsingular sliding-mode control for field-of-view constrained impact time guidance.” J. Guid. Control Dyn. 41 (5): 1214–1222. https://doi.org/10.2514/1.G003146.
Cho, D., H. J. Kim, and M. J. Tahk. 2016. “Nonsingular sliding mode guidance for impact time control.” J. Guid. Control Dyn. 39 (1): 61–68. https://doi.org/10.2514/1.G001167.
Cho, N., and Y. Kim. 2016. “Modified Pure proportional navigation guidance law for impact time control.” J. Guid. Control Dyn. 39 (4): 852–872. https://doi.org/10.2514/1.G001618.
Cho, N., and S. Lee. 2021. “Look-angle-constrained control of arrival time with exact knowledge of time-to-go.” J. Guid. Control Dyn. 44 (10): 1902–1908. https://doi.org/10.2514/1.G006000.
Dhananjay, N., and D. Ghose. 2014. “Accurate time-to-go estimation for proportional navigation guidance.” J. Guid. Control Dyn. 37 (4): 1378–1383. https://doi.org/10.2514/1.G000082.
Dong, W., C. Wang, J. Wang, H. Son, and M. Xin. 2022. “Unified method for field-of-view-limited homing guidance.” J. Guid. Control Dyn. 45 (8): 1415–1434. https://doi.org/10.2514/1.G006710.
Dong, W., C. Wang, J. Wang, and M. Xin. 2023. “Varying-gain proportional navigation guidance for precise impact time control.” J. Guid. Control Dyn. 46 (3): 535–552. https://doi.org/10.2514/1.G007174.
Erer, K. S., and R. Tekin. 2016. “Impact time and angle control based on constrained optimal solutions.” J. Guid. Control Dyn. 39 (10): 2448–2454. https://doi.org/10.2514/1.G000414.
Gasper, G., M. Rahman, and G. George. 2004. Vol. 96 of Basic hypergeometric series. Cambridge, UK: Cambridge University Press.
Harl, N., and S. N. Balakrishnan. 2012. “Impact Time and Angle Guidance with Sliding Mode Control.” IEEE Trans. Control Syst. Technol. 20 (6): 1436–1449. https://doi.org/10.1109/TCST.2011.2169795.
Harrison, G. A. 2012. “Hybrid guidance law for approach angle and time-of-arrival control.” J. Guid. Control Dyn. 35 (4): 1104–1114. https://doi.org/10.2514/1.56131.
He, S., C.-H. Lee, H.-S. Shin, and A. Tsourdos. 2020. Optimal guidance and its applications in missiles and UAVs. Cham, Switzerland: Springer.
Hu, Q., T. Han, and M. Xin. 2018. “New impact time and angle guidance strategy via virtual target approach.” J. Guid. Control Dyn. 41 (8): 1755–1765. https://doi.org/10.2514/1.G003436.
Hu, Q., T. Han, and M. Xin. 2019. “Sliding-mode impact time guidance law design for various target motions.” J. Guid. Control Dyn. 42 (1): 136–148. https://doi.org/10.2514/1.G003620.
Jeon, I. S., and J. I. Lee. 2017. “Impact-time-control guidance law with constraints on seeker look angle.” IEEE Trans. Aerosp. Electron. Syst. 53 (5): 2621–2627. https://doi.org/10.1109/TAES.2017.2698837.
Jeon, I. S., J. I. Lee, and M. J. Tahk. 2006. “Impact-time-control guidance law for anti-ship missiles.” IEEE Trans. Control Syst. Technol. 14 (2): 260–266. https://doi.org/10.1109/TCST.2005.863655.
Jeon, I. S., J. I. Lee, and M. J. Tahk. 2010. “Homing guidance law for cooperative attack of multiple missiles.” J. Guid. Control Dyn. 33 (1): 275–280. https://doi.org/10.2514/1.40136.
Kang, H., P. Wang, and S. Song. 2023a. “A generalized three-dimensional cooperative guidance law for various communication topologies with field-of-view constraint.” Proc. Inst. Mech. Eng., Part G: J. Aerosp. Eng. 237 (10): 2353–2369. https://doi.org/10.1177/09544100231153265.
Kang, H., P. Wang, S. Wei, and S. Song. 2023b. “Three-dimensional impact-time-constrained proportional navigation guidance using range-varying gain.” Aerosp. Sci. Technol. 140: 108419. https://doi.org/10.1177/09544100231153265.https://doi.org/10.1016/j.ast.2023.108419.
Khalil, H. K., and J. W. Grizzle. 1996. Vol. 3. Nonlinear systems. Upper Saddle River, NJ: Prentice Hall.
Kim, H. G., D. Cho, and H. J. Kim. 2019a. “Sliding mode guidance law for impact time control without explicit time-to-go estimation.” IEEE Trans. Aerosp. Electron. Syst. 55 (1): 236–250. https://doi.org/10.1109/TAES.2018.2850208.
Kim, H. G., and H. J. Kim. 2019. “Backstepping-based impact time control guidance law for missiles with reduced seeker field-of-view.” IEEE Trans. Aerosp. Electron. Syst. 55 (1): 82–94. https://doi.org/10.1109/TAES.2018.2848319.
Kim, H.-G., J.-Y. Lee, H. J. Kim, H.-H. Kwon, and J.-S. Park. 2020. “Look-angle-shaping guidance law for impact angle and time control with field-of-view constraint.” IEEE Trans. Aerosp. Electron. Syst. 56 (2): 1602–1612. https://doi.org/10.1109/TAES.2019.2924175.
Kim, J., N. Cho, and Y. Kim. 2019b. “Field-of-view constrained impact angle control guidance guaranteeing error convergence before interception.” In Proc., AIAA Scitech 2019 Forum, 1927. Reston, VA: American Institute of Aeronautics and Astronautics.
Kim, J., N. Cho, and Y. Kim. 2021. “Field-of-view-constrained impact angle control guidance with error convergence before interception considering speed changes.” Proc. Inst. Mech. Eng., Part G: J. Aerosp. Eng. 235 (2): 238–256. https://doi.org/10.1177/0954410020942010.
Kim, M., B. Jung, B. Han, S. Lee, and Y. Kim. 2015. “Lyapunov-based impact time control guidance laws against stationary targets.” IEEE Trans. Aerosp. Electron. Syst. 51 (2): 1111–1122. https://doi.org/10.1109/TAES.2014.130717.
Kim, T.-H., C.-H. Lee, I.-S. Jeon, and M.-J. Tahk. 2013. “Augmented polynomial guidance with impact time and angle constraints.” IEEE Trans. Aerosp. Electron. Syst. 49 (4): 2806–2817. https://doi.org/10.1109/TAES.2013.6621856.
Kumar, S. R., and D. Ghose. 2015. “Impact time guidance for large heading errors using sliding mode control.” IEEE Trans. Aerosp. Electron. Syst. 51 (4): 3123–3138. https://doi.org/10.1109/TAES.2015.140137.
Lee, J. I., I. S. Jeon, and M. J. Tahk. 2007. “Guidance law to control impact time and angle.” IEEE Trans. Aerosp. Electron. Syst. 43 (1): 301–310. https://doi.org/10.1109/TAES.2007.357135.
Lee, S., N. Cho, and Y. Kim. 2020. “Impact-time-control guidance strategy with a composite structure considering the seeker’s field-of-view constraint.” J. Guid. Control Dyn. 43 (8): 1566–1574. https://doi.org/10.2514/1.G005063.
Levant, A. 2001. “Universal single-input-single-output (SISO) sliding-mode controllers with finite-time convergence.” IEEE Trans. Autom. Control 46 (9): 1447–1451. https://doi.org/10.1109/9.948475.
Li, Z., and Z. Ding. 2018. “Robust cooperative guidance law for simultaneous arrival.” IEEE Trans. Control Syst. Technol. 27 (3): 1360–1367. https://doi.org/10.1109/TCST.2018.2804348.
Livermore, R., and T. Shima. 2018. “Deviated pure-pursuit-based optimal guidance law for imposing intercept time and angle.” J. Guid. Control Dyn. 41 (8): 1807–1814. https://doi.org/10.2514/1.G003179.
Lozier, D. W. 2003. “NIST digital library of mathematical functions.” Ann. Math. Artif. Intell. 38 (May): 105–119. https://doi.org/10.1023/A:1022915830921.
Pearson, J. W. 2009. “Computation of hypergeometric functions.” Ph.D. thesis, Dept. of Mathematical Institute, Univ. of Oxford.
Ryoo, C.-K., H. Cho, and M.-J. Tahk. 2006. “Time-to-go weighted optimal guidance with impact angle constraints.” IEEE Trans. Control Syst. Technol. 14 (3): 483–492. https://doi.org/10.1109/TCST.2006.872525.
Saleem, A., and A. Ratnoo. 2016. “Lyapunov-based guidance law for impact time control and simultaneous arrival.” J. Guid. Control Dyn. 39 (1): 164–173. https://doi.org/10.2514/1.G001349.
Sang, D. K., and M. J. Tahk. 2009. “Guidance law switching logic considering the seeker’s field-of-view limits.” Proc. Inst. Mech. Eng., Part G: J. Aerosp. Eng. 223 (8): 1049–1058. https://doi.org/10.1243/09544100JAERO614.
Shneydor, N. A. 1998. “Missile guidance and pursuit: Kinematics, dynamics and control. Cambridge, UK: Woodehead.
Shtessel, Y. B., I. A. Shkolnikov, and A. Levant. 2007. “Smooth second-order sliding modes: Missile guidance application.” Automatica 43 (8): 1470–1476. https://doi.org/10.1016/j.automatica.2007.01.008.
Tahk, M. J., S. W. Shim, S. M. Hong, H. L. Choi, and C. H. Lee. 2018. “Impact time control based on time-to-go prediction for sea-skimming antiship missiles.” IEEE Trans. Aerosp. Electron. Syst. 54 (4): 2043–2052. https://doi.org/10.1109/TAES.2018.2803538.
Tekin, R., and K. S. Erer. 2020. “Impact Time and angle control against moving targets with look angle shaping.” J. Guid. Control Dyn. 43 (5): 1020–1025. https://doi.org/10.2514/1.G004762.
Tekin, R., K. S. Erer, and F. Holzapfel. 2016. “Control of impact time with increased robustness via feedback linearization.” J. Guid. Control Dyn. 39 (7): 1682–1689. https://doi.org/10.2514/1.G001719.
Tekin, R., K. S. Erer, and F. Holzapfel. 2017a. “Adaptive impact time control via look-angle shaping under varying velocity.” J. Guid. Control Dyn. 40 (12): 3247–3255. https://doi.org/10.2514/1.G002981.
Tekin, R., K. S. Erer, and F. Holzapfel. 2017b. “Polynomial shaping of the look angle for impact-time control.” J. Guid. Control Dyn. 40 (10): 2668–2673. https://doi.org/10.2514/1.G002751.
Tekin, R., K. S. Erer, and F. Holzapfel. 2018. “Impact time control with generalized-polynomial range formulation.” J. Guid. Control Dyn. 41 (5): 1190–1195. https://doi.org/10.2514/1.G003279.
Tsalik, R., and T. Shima. 2019. “Circular impact-time guidance.” J. Guid. Control Dyn. 42 (8): 1836–1847. https://doi.org/10.2514/1.G004074.
Wang, P., Y. Guo, G. Ma, and B. Wie. 2019. “New differential geometric guidance strategies for impact-time control problem.” J. Guid. Control Dyn. 42 (9): 1982–1992. https://doi.org/10.2514/1.G004229.
Zarchan, P. 2012. Tactical and strategic missile guidance. Reston, VA: American Institute of Aeronautics and Astronautics.
Zhang, S., Y. Guo, Z. Liu, S. Wang, and X. Hu. 2020. “Finite-Time cooperative guidance strategy for impact angle and time control.” IEEE Trans. Aerosp. Electron. Syst. 57 (2): 806–819. https://doi.org/10.1109/TAES.2020.3037958.
Zhang, Y., X. Wang, and H. Wu. 2014. “Impact time control guidance law with field of view constraint.” Aerosp. Sci. Technol. 39 (Dec): 361–369. https://doi.org/10.1016/j.ast.2014.10.002.
Information & Authors
Information
Published In
Copyright
© 2023 American Society of Civil Engineers.
History
Received: May 11, 2023
Accepted: Sep 26, 2023
Published online: Dec 12, 2023
Published in print: Mar 1, 2024
Discussion open until: May 12, 2024
Authors
Metrics & Citations
Metrics
Citations
Download citation
If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download.