This paper studies a vertical powered descent problem in the context of planetary landing, considering glide-slope and thrust pointing constraints and minimizing any final cost. In a first time, it proves the Max-Min-Max or Max-Singular-Max form of the optimal control using the Pontryagin Maximum Principle, and it extends this result to a problem formulation considering the effect of an atmosphere. It also shows that the singular structure does not appear in generic cases. In a second time, it theoretically analyzes the optimal trajectory for a more specific problem formulation to show that there can be at most one contact or boundary interval with the state constraint on each Max or Min arc.
Accepté le :
Première publication :
Publié le :
DOI : 10.1051/cocv/2022065
Keywords: Optimal Control, Aerospace, Planetary Landing
@article{COCV_2022__28_1_A67_0,
author = {Leparoux, Clara and H\'eriss\'e, Bruno and Jean, Fr\'ed\'eric},
title = {Structure of optimal control for planetary landing with control and state constraints},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
year = {2022},
publisher = {EDP-Sciences},
volume = {28},
doi = {10.1051/cocv/2022065},
mrnumber = {4504128},
zbl = {1503.49007},
language = {en},
url = {https://www.numdam.org/articles/10.1051/cocv/2022065/}
}
TY - JOUR AU - Leparoux, Clara AU - Hérissé, Bruno AU - Jean, Frédéric TI - Structure of optimal control for planetary landing with control and state constraints JO - ESAIM: Control, Optimisation and Calculus of Variations PY - 2022 VL - 28 PB - EDP-Sciences UR - https://www.numdam.org/articles/10.1051/cocv/2022065/ DO - 10.1051/cocv/2022065 LA - en ID - COCV_2022__28_1_A67_0 ER -
%0 Journal Article %A Leparoux, Clara %A Hérissé, Bruno %A Jean, Frédéric %T Structure of optimal control for planetary landing with control and state constraints %J ESAIM: Control, Optimisation and Calculus of Variations %D 2022 %V 28 %I EDP-Sciences %U https://www.numdam.org/articles/10.1051/cocv/2022065/ %R 10.1051/cocv/2022065 %G en %F COCV_2022__28_1_A67_0
Leparoux, Clara; Hérissé, Bruno; Jean, Frédéric. Structure of optimal control for planetary landing with control and state constraints. ESAIM: Control, Optimisation and Calculus of Variations, Tome 28 (2022), article no. 67. doi: 10.1051/cocv/2022065
[1] , and . Lossless convexifìcation of the soft landing optimal control problem with non-convex control bound and pointing constraints. IEEE Trans. Control Syst. Technol. 21 (2013) 2104–2113. | DOI
[2] and Convex programming approach to powered descent guidance for mars landing. J. Guidance Control Dyn. 30 (2007) 1353–1366. | DOI
[3] , , , and CasADi — a software framework for nonlinear optimization and optimal control. Math. Programm. Comput. 11 (2019) 1–36. | MR | Zbl | DOI
[4] Autonomous precision landing of space rockets. The Bridge 46 (2016) 15–20.
[5] , and Minimum-landing-error powered-descent guidance for mars landing using convex optimization. J. Guidance Control Dyn. 33 (2010) 1161–1171. | DOI
[6] , and , L1-minimization for mechanical systems. SIAM J. Control Optim. 54 (2016) 1245–1265. | MR | Zbl | DOI
[7] , and Genericity results for singular curves. J. Differ. Geom. 73 (2006) 45–73. | MR | Zbl
[8] and , A minimal time optimal control for a drone landing problem. ESAIM: COCV 27 (2021) 99. | MR | Zbl
[9] On a class of variational problems in rocket flight. J. Aerospace Sci. 26 (1959) 586–591. | MR | Zbl | DOI
[10] , and Optimal planetary landing with pointing and glide-slope constraints. 2022 61th IEEE Conference on Decision and Control (CDC), 2022. | DOI
[11] Propellant-optimal powered descent guidance. J. Guidance Control Dyn. 41 (2018) 813–826. | DOI
[12] , , , , and Multi-point powered descent guidance based on optimal sensitivity. Aerospace Sci. Technol. 86 (2019) 465–477. | DOI
[13] On the problem of optimal thrust programming for a lunar soft landing. IEEE Trans. Automatic Control 9 (1964) 477–484. | MR | DOI
[14] , and , Fuel-optimal program for atmospheric vertical powered landing. in 2021 60th IEEE Conference on Decision and Control (CDC), 2021, 6312–6319. | DOI
[15] The calculus of variations in applied aerodynamics and flight mechanics. Math. Sci. Eng. 5 (1962) 99–170. | MR | DOI
[16] , and , A comparison of powered descent guidance laws for mars pinpoint landing. In AIAA/AAS Astrodynamics Specialist Conference and Exhibit, August 2006. | DOI
[17] Optimality of intermediate-thrust arcs of rocket trajectories. AIAA J. 3 (1965) 1094–1098. | MR | Zbl | DOI
[18] The local structure of time-optimal trajectories in dimension three under generic conditions. SIAM J. Control Optim. 26 (1988) 899–918. | MR | Zbl | DOI
[19] and , Powered descent guidance methods for the moon and mars. in AIAA Guidance, Navigation, and Control Conference and Exhibit, June 2005. | DOI
[20] The structure of time-optimal trajectories for single-input systems in the plane: the general real analytic case. SIAM J. Control Optim. 25 (1967) 868–904. | MR | Zbl | DOI
[21] , and , Fuel efficient powered descent guidance for mars landing. in AIAA Guidance, Navigation, and Control Conference and Exhibit, 2005. | DOI
[22] , and Minimum-fuel powered descent for mars pinpoint landing. J. Spacecraft Rockets 44 (2007) 324–331. | DOI
[23] Optimal control and applications to aerospace: Some results and challenges. J. Optim. Theory Appl. 154 (2012) 713–758. | MR | Zbl | DOI
[24] , Optimal Control. Modern Birkhauser Classics. Springer, 2010. | MR
[25] , , , , and , Toward improved landing precision on mars. in 2011 Aerospace Conference, March 2011. | DOI
[26] , Modern real analysis, Vol. 278 of Graduate Texts in Mathematics, 2nd edn. Springer, Cham, 2017. With contributions by Monica Torres. | MR | Zbl
Cité par Sources :
