Abstract
This paper presents an analytical zero-effort-miss (ZEM)/zero-effort-velocity (ZEV) feedback guidance algorithm using the Levi-Civita transformation, where the ZEM and ZEV vectors can be determined explicitly instead of numerical integration or any propagators. In each guidance cycle, the states of the spacecraft and target are first transformed into Levi-Civita coordinate, the optimal time-to-go is then computed through the Newton–Raphson method and the ZEM/ZEV vectors are determined explicitly, the optimal control inputs are finally transformed back into cartesian coordinate. The effectiveness of the proposed method is demonstrated using a missile intercept and a head-on collision intercept problem.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Guo, Y., Hawkins, M., Wie, B.: Waypoint-optimized zero-effort-miss/zero-effort-velocity feedback guidance for Mars landing. J. Guid. Control Dyn. 36(3), 689–698 (2013)
Battin, R.H.: An Introduction to the Mathematics and Methods of Astrodynamics. AIAA Education Series, Revised edn. Reston (1999)
Bryson, A.E., Ho, Y.C.: Applied Optimal Control. Hemisphere, New York (1975)
Ebrahimi, B., Bahrami, M., Roshanian, J.: Optimal sliding-mode guidance with terminal velocity constraint for fixed-interval propulsive maneuvers. Acta Astronautica 62(10), 556–562 (2008)
Jalali-Naini, S.H., Pourtakdoust, S.H.: Modern midcourse guidance laws in the endoatmosphere. AIAA Guidance, Navigation, and Control Conference and Exhibit (2005)
Hawkins, M., Guo, Y., Wie, B.: ZEM/ZEV feedback guidance application to fuel-efficient orbital maneuvers around an irregular-shaped asteroid. AIAA Guidance, Navigation, and Control Conference (2012)
Guo, Y., Hawkins, M., Wie, B.: Applications of generalized zero-effort-miss/zero-effort-velocity feedback guidance algorithm. J. Guid. Control Dyn. 36(3), 810–820 (2013)
Zhang, B., Tang, S., Pan, B.F.: Multi-constrained suboptimal powered descent guidance for lunar pinpoint soft landing. Aerosp. Sci. Technol. 48, 203–213 (2016)
Ahn, J., Guo, Y., Wie, B.: Precision ZEM/ZEV feedback guidance algorithm utilizing Vinti’s analytical solution of perturbed Kepler problem. AAS 16–345 (2016)
Ann, S., Lee, S., Kim, Y., Ahn, J.: Midcourse guidance for exo-atmospheric interception using response surface based trajectory shaping. IEEE Trans. Aerosp. Electron. Syst. (2020)
Thorne, J.D., Hall, C.D.: Minimum-thrust orbit transfers using the Kustaanheimo-Stiefel transformation. J. Guid. Control Dyn. 20(4), 836–838 (1997)
Hernandez, S., Akella, M.R.: Lyapunov-based guidance for orbit transfers and rendezvous in Levi-Civita coordinates. J. Guid. Control Dyn. 37(4), 1170–1181 (2014)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2022 The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd.
About this paper
Cite this paper
Ma, Y. et al. (2022). Analytical ZEM/ZEV Feedback Guidance Algorithm Using Levi-Civita Transformation. In: Yan, L., Duan, H., Yu, X. (eds) Advances in Guidance, Navigation and Control . Lecture Notes in Electrical Engineering, vol 644. Springer, Singapore. https://doi.org/10.1007/978-981-15-8155-7_342
Download citation
DOI: https://doi.org/10.1007/978-981-15-8155-7_342
Published:
Publisher Name: Springer, Singapore
Print ISBN: 978-981-15-8154-0
Online ISBN: 978-981-15-8155-7
eBook Packages: Intelligent Technologies and RoboticsIntelligent Technologies and Robotics (R0)