Abstract
This paper summarizes the autonomous guidance methods (AGMs) for pinpoint soft landing on celestial surfaces. We first review the development of powered descent guidance methods, focusing on their contributions for dealing with constraints and enhancing computational efficiency. With the increasing demand for reusable launchers and more scientific returns from space exploration, pinpoint soft landing has become a basic requirement. Unlike the kilometer-level precision for previous activities, the position accuracy of future planetary landers is within tens of meters of a target respecting all constraints of velocity and attitude, which is a very difficult task and arouses renewed interest in AGMs. This paper states the generalized three- and six-degree-of-freedom optimization problems in the powered descent phase and compares the features of three typical scenarios, i.e., the lunar, Mars, and Earth landing. On this basis, the paper details the characteristics and adaptability of AGMs by comparing aspects of analytical guidance methods, numerical optimization algorithms, and learning-based methods, and discusses the convexification treatment and solution strategies for non-convex problems. Three key issues related to AGM application, including physical feasibility, model accuracy, and real-time performance, are presented afterward for discussion. Many space organizations, such as those in the United States, China, France, Germany, and Japan, have also developed free-flying demonstrators to carry out related research. The guidance methods which have been tested on these demonstrators are briefly introduced at the end of the paper.
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References
Açıkmeşe B, Blackmore L, 2011. Lossless convexification of a class of optimal control problems with non-convex control constraints. Automation, 47(2):341–347. https://doi.org/10.1016/j.automatica.2010.10.037
Açıkmeşe B, Ploen SR, 2005. A powered descent guidance algorithm for Mars pinpoint landing. AIAA Guidance, Navigation, and Control Conf and Exhibit, Article 6288. https://doi.org/10.2514/6.2005-6288
Açıkmeşe B, Ploen SR, 2007. Convex programming approach to powered descent guidance for Mars landing. J Guid Contr Dynam, 30(5):1353–1366. https://doi.org/10.2514/1.27553
Açıkmeşe B, Aung M, Casoliva J, et al., 2013a. Flight testing of trajectories computed by G-FOLD: fuel optimal large divert guidance algorithm for planetary landing. 23rd AAS/AIAA Spaceflight Mechanics Meeting, Article 386.
Açıkmeşe B, Carson JM, Blackmore L, 2013b. Lossless convexification of nonconvex control bound and pointing constraints of the soft landing optimal control problem. IEEE Trans Contr Syst Technol, 21(6):2104–2113. https://doi.org/10.1109/TCST.2012.2237346
Akametalu AK, Tomlin CJ, Chen M, 2018. Reachability-based forced landing system. J Guid Contr Dynam, 41(12):2529–2542. https://doi.org/10.2514/1.G003490
Benito J, Mease KD, 2010. Reachable and controllable sets for planetary entry and landing. J Guid Contr Dynam, 33(3):641–654. https://doi.org/10.2514/1.47577
Biegler LT, Zavala VM, 2009. Large-scale nonlinear programming using IPOPT: an integrating framework for enterprise-wide dynamic optimization. Comput Chem Eng, 33(3):575–582. https://doi.org/10.1016/j.compchemeng.2008.08.006
Blackmore L, 2016. Autonomous precision landing of space rockets. Bridge, 46(4):15–20.
Blackmore L, Açıkmeşe B, Scharf DP, 2010. Minimum-landing-error powered-descent guidance for Mars landing using convex optimization. J Guid Contr Dynam, 33(4):1161–1171. https://doi.org/10.2514/1.47202
Blackmore L, Açıkmeşe B, Carson JM III, 2012. Lossless convexification of control constraints for a class of nonlinear optimal control problems. Syst Contr Lett, 61(8):863–870. https://doi.org/10.1016/j.sysconle.2012.04.010
Boggs PT, Tolle JW, 1995. Sequential quadratic programming. Acta Numer, 4(4):1–51. https://doi.org/10.1017/S0962492900002518
Bomze IM, Demyanov VF, Fletcher R, et al., 2007. Nonlinear Optimization. Springer, Berlin, Germany. https://doi.org/10.1007/978-3-642-11339-0
Boyd S, Vandenberghe L, 2004. Convex Optimization. Cambridge University Press, New York, USA.
Boyd S, Parikh N, Chu E, et al., 2011. Distributed optimization and statistical learning via the alternating direction method of multipliers. Found Trends Mach Learn, 3(1):1–122. https://doi.org/10.1561/2200000016
Brent RP, 2013. Algorithms for Minimization without Derivatives. Courier Corporation, New York, USA.
Casoliva J, 2013. Spacecraft Trajectory Generation by Successive Approximation for Powered Descent and Cyclers. PhD Thesis, University of California, Irvine, USA.
Chen SZ, Chu LF, Yang XM, et al., 2019. Application of state prediction neural network control algorithm in small reusable rocket. Acta Aeron Astron Sin, 40(3):149–163 (in Chinese).
Chen WF, Shao ZJ, Wang KX, et al., 2010. Convergence depth control for interior point methods. AIChE J, 56(12):3146–3161. https://doi.org/10.1002/aic.12225
Domahidi A, Zgraggen AU, Zeilinger MN, et al., 2012. Efficient interior point methods for multistage problems arising in receding horizon control. 51st IEEE Conf on Decision and Control, p.668–674. https://doi.org/10.1109/CDC.2012.6426855
Domahidi A, Chu E, Boyd S, 2013. ECOS: an SOCP solver for embedded systems. European Control Conf, p.3071–3076. https://doi.org/10.23919/ECC.2013.6669541
Dueri D, Jing Z, Açıkmeşe B, 2014. Automated custom code generation for embedded, real-time second order cone programming. 19th Int Federation of Automatic Control World Congress, p.1605–1612. https://doi.org/10.3182/20140824-6-ZA-1003.02736
Dueri D, Açıkmeşe B, Scharf DP, et al., 2017. Customized real-time interior-point methods for onboard powered-descent guidance. J Guid Contr Dynam, 40(2):197–212. https://doi.org/10.2514/1.G001480
Dumke M, Sagliano M, Saranrittichai P, et al., 2017. EAGLE — environment for autonomous GNC landing experiments. 10th Int ESA Conf on Guidance, Navigation and Control Systems, p.1–25.
Dumont E, Ecker T, Chavagnac C, et al., 2018. CALLISTO — reusable VTVL launcher first stage demonstrator. Space Propulsion Conf, Article 406.
Ebrahimi B, Bahrami M, Roshanian J, 2008. Optimal sliding-mode guidance with terminal velocity constraint for fixed-interval propulsive maneuvers. Acta Astron, 62(10-11):556–562. https://doi.org/10.1016/j.actaastro.2008.02.002
Eren U, Dueri D, Açıkmeşe B, 2015. Constrained reachability and controllability sets for planetary precision landing via convex optimization. J Guid Contr Dynam, 38(11):2067–2083. https://doi.org/10.2514/1.G000882
Fahroo F, Ross IM, 2008. Pseudospectral methods for infinite-horizon nonlinear optimal control problems. J Guid Contr Dynam, 31(4):927–936. https://doi.org/10.2514/1.33117
Furfaro R, Linares R, 2017. Waypoint-based generalized ZEM/ZEV feedback guidance for planetary landing via a reinforcement learning approach. 3rd IAA Conf on Dynamics and Control of Space Systems, p.401–416.
Furfaro R, Selnick S, Cupples ML, et al., 2011. Nonlinear sliding guidance algorithms for precision lunar landing. 21st AAS/AIAA Space Flight Mechanics Meeting, p.945–964.
García CE, Prett DM, Morari M, 1989. Model predictive control: theory and practice—a survey. Automatica, 25(3):335–348. https://doi.org/10.1016/0005-1098(89)90002-2
Gaudet B, Linares R, Furfaro R, 2018. Integrated guidance and control for pinpoint Mars landing using reinforcement learning. Adv Astron Sci, 167:3135–3154.
Ge DT, Cui PY, Zhu SY, 2019. Recent development of autonomous GNC technologies for small celestial body descent and landing. Progr Aerosp Sci, 110:100551. https://doi.org/10.1016/j.paerosci.2019.06.002
Gill PE, Murray W, Saunders MA, 2005. SNOPT: an SQP algorithm for large-scale constrained optimization. SIAM Rev, 47(1):99–131. https://doi.org/10.1137/S0036144504446096
Giselsson P, Boyd S, 2017. Linear convergence and metric selection for Douglas-Rachford splitting and ADMM. IEEE Trans Autom Contr, 62(2):532–544. https://doi.org/10.1109/TAC.2016.2564160
Grant M, Boyd S, Ye Y, 2008. CVX: MATLAB Software for Disciplined Convex Programming. https://cvxr.com/cvx/ [Accessed on Mar. 1, 2020].
Guo YM, Hawkins M, Wie B, 2013. Waypoint-optimized zero-effort-miss/zero-effort-velocity feedback guidance for Mars landing. J Guid Contr Dynam, 36(3):799–809. https://doi.org/10.2514/1.58098
Harris MW, Açıkmeş B, 2014. Lossless convexification of non-convex optimal control problems for state constrained linear systems. Automatica, 50(9):2304–2311. https://doi.org/10.1016/j.automatica.2014.06.008
Jerez J, Merkli S, Bennani S, et al., 2017. Forces-RTTO: a tool for on-board real-time autonomous trajectory planning. 10th Int ESA Conf on Guidance, Navigation and Control Systems, p.1–22.
Jiang XQ, Furfaro R, Li S, 2018. Integrated guidance for Mars entry and powered descent using reinforcement learning and Gauss pseudospectral method. 4th IAA Conf on Dynamics and Control of Space Systems, p.761–774.
Jouffe L, 1998. Fuzzy inference system learning by reinforcement methods. IEEE Trans Syst Man Cybern Part C Appl Rev, 28(3):338–355. https://doi.org/10.1109/5326.704563
Klumpp AR, 1974. Apollo lunar descent guidance. Automatica, 10(2):133–146. https://doi.org/10.1016/0005-1098(74)90019-3
Lee U, Mesbahi M, 2015. Optimal power descent guidance with 6-DoF line of sight constraints via unit dual quaternions. AIAA Guidance, Navigation, and Control Conf, p.1–25.
Lee U, Mesbahi M, 2017. Constrained autonomous precision landing via dual quaternions and model predictive control. J Guid Contr Dynam, 40(2):292–308. https://doi.org/10.2514/1.G001879
Liu XF, 2019. Fuel-optimal rocket landing with aerodynamic controls. J Guid Contr Dynam, 42(1):65–77. https://doi.org/10.2514/1.G003537
Liu XF, Lu P, 2014. Solving nonconvex optimal control problems by convex optimization. J Guid Contr Dynam, 37(3):750–765. https://doi.org/10.2514/1.62110
Lu P, 2017. Introducing computational guidance and control. J Guid Contr Dynam, 40(2):193. https://doi.org/10.2514/1.G002745
Lu P, 2018. Propellant-optimal powered descent guidance. J Guid Contr Dynam, 41(4):813–826. https://doi.org/10.2514/1.G003243
Lu P, Liu XF, 2013. Autonomous trajectory planning for rendezvous and proximity operations by conic optimization. J Guid Contr Dynam, 36(2):375–389. https://doi.org/10.2514/1.58436
Luenberger DG, Ye YY, 1984. Linear and Nonlinear Programming. Springer, New York, USA
Ma L, Shao ZJ, Chen WF, et al., 2016. Trajectory optimization for lunar soft landing with a Hamiltonian-based adaptive mesh refinement strategy. Adv Eng Softw, 100:266–276. https://doi.org/10.1016/j.advengsoft.2016.08.002
Ma L, Wang KX, Shao ZJ, et al., 2017. Trajectory optimization for planetary multi-point powered landing. IFAC-PapersOnLine, 50(1):8291–8296. https://doi.org/10.1016/j.ifacol.2017.08.1404
Ma L, Wang KX, Xu ZH, et al., 2018a. Trajectory optimization for lunar rover performing vertical takeoff vertical landing maneuvers in the presence of terrain. Acta Astron, 146:289–299. https://doi.org/10.1016/j.actaastro.2018.03.013
Ma L, Wang KX, Xu ZH, et al., 2018b. Trajectory optimization for powered descent and landing of reusable rockets with restartable engines. 69th Int Astronautical Congress, Article 44 659.
Ma L, Wang KX, Xu ZH, et al., 2019. Multi-point powered descent guidance based on optimal sensitivity. Aerosp Sci Technol, 86:465–477. https://doi.org/10.1016/j.ast.2019.01.028
Malyuta D, Reynolds TP, Szmuk M, et al., 2019. Discretization performance and accuracy analysis for the rocket powered descent guidance problem. AIAA Scitech 2019 Forum, Article 925. https://doi.org/10.2514/6.2019-0925
Mao YQ, Szmuk M, Açıkmeşe B, 2016. Successive convexification of non-convex optimal control problems and its convergence properties. 55th Conf on Decision and Control, p.3636–3641. https://doi.org/10.1109/CDC.2016.7798816
Mao YQ, Dueri D, Szmuk M, et al., 2017. Successive convexification of non-convex optimal control problems with state constraints. IFAC-PapersOnLine, 50(1):4063–4069. https://doi.org/10.1016/j.ifacol.2017.08.789
Mao YQ, Szmuk M, Açıkmeşe B, 2018. Successive convexification: a superlinearly convergent algorithm for non-convex optimal control problems. https://arxiv.org/abs/1804.06539v1
Mattingley J, Boyd S, 2012. CVXGEN: a code generator for embedded convex optimization. Opt Eng, 13(1):1–27. https://doi.org/10.1007/s11081-011-9176-9
Mayne DQ, Rawlings JB, Rao CV, et al., 2000. Constrained model predictive control: stability and optimality. Automatica, 36(6):789–814. https://doi.org/10.1016/S0005-1098(99)00214-9
McHenry RL, de Long AJ, Cockrell BF, et al., 1979. Space shuttle ascent guidance, navigation, and control. J Astron Sci, 27:1–38.
Meditch J, 1964. On the problem of optimal thrust programming for a lunar soft landing. IEEE Trans Autom Contr, 9(4):477–484. https://doi.org/10.1109/TAC.1964.1105758
Monchaux D, Rmili B, Hassin J, et al., 2018. FROG, a rocket for GNC demonstrations. 69th Int Astronautical Congress, Article 43 308.
Najson F, Mease KD, 2006. Computationally inexpensive guidance algorithm for fuel-efficient terminal descent. J Guid Contr Dynam, 29(4):955–964. https://doi.org/10.2514/1.17715
Nonaka S, 2018. Flight demonstration by reusable rocket vehicle RV-X. 28th Workshop on JAXA Astrodynamics and Flight Mechanics, SA6000135029.
Pascucci CA, Bennani S, Bemporad A, 2015. Model predictive control for powered descent guidance and control. European Control Conf, p.1388–1393.
Ploen S, Açıkmeşe B, Wolf A, 2006. A comparison of powered descent guidance laws for Mars pinpoint landing. AIAA/AAS Astrodynamics Specialist Conf and Exhibit, Article 6676. https://doi.org/10.2514/6.2006-6676
Prakash R, Burkhart PD, Chen A, et al., 2008. Mars science laboratory entry, descent, and landing system overview. IEEE Aerospace Conf, p.1–18. https://doi.org/10.1109/AERO.2008.4526283
Sagliano M, 2018a. Pseudospectral convex optimization for powered descent and landing. J Guid Contr Dynam, 41(2):320–334. https://doi.org/10.2514/1.G002818
Sagliano M, 2018b. Generalized hp pseudospectral convex programming for powered descent and landing. AIAA Guidance, Navigation, and Control Conf, Article 1870. https://doi.org/10.2514/6.2018-1870
Sagliano M, Mooij E, 2018. Optimal drag-energy entry guidance via pseudospectral convex optimization. AIAA Guidance, Navigation, and Control Conf, Article 1315. https://doi.org/10.2514/6.2018-1315
Sagliano M, Dumke M, Theil S, 2019a. Simulations and flight tests of a new nonlinear controller for the EAGLE lander. J Spacecr Rock, 56(1):259–272. https://doi.org/10.2514/1.A34161
Sagliano M, Tsukamoto T, Hernandez J, et al., 2019b. Guidance and control strategy for the CALLISTO flight experiment. 8th EUCASS Conf for Aeronautics and Aerospace Sciences, Article 284. https://doi.org/10.13009/EUCASS2019-284
Sánchez-Sánchez C, Izzo D, 2018. Real-time optimal control via deep neural networks: study on landing problems. J Guid Contr Dynam, 41(5):1122–1135. https://doi.org/10.2514/1.G002357
Sato S, Tsukamoto T, Yamamoto T, et al., 2018. The study of navigation, guidance, and control system of reusable vehicle experiment (RV-X). 28th Workshop on JAXA Astrodynamics and Flight Mechanics, SA6000135030.
Scharf DP, Regehr MW, Vaughan GM, et al., 2014. ADAPT demonstrations of onboard large-divert guidance with a VTVL rocket. IEEE Aerospace Conf, p.1–18. https://doi.org/10.1109/AERO.2014.6836462
Scharf DP, Açıkmeşe B, Dueri D, et al., 2017. Implementation and experimental demonstration of onboard powered-descent guidance. J Guid Contr Dynam, 40(2):213–229. https://doi.org/10.2514/1.G000399
Schulman J, Wolski F, Dhariwal P, et al., 2017. Proximal policy optimization algorithms. https://arxiv.org/abs/1707.06347
Seelbinder D, 2017. On-board Trajectory Computation for Mars Atmospheric Entry based on Parametric Sensitivity Analysis of Optimal Control Problems. PhD Thesis, Universitat Bremen, Bremen, Germany.
Song ZY, Zhao DJ, Lv XG, 2015 Terminal attitude-constrained guidance and control for lunar soft landing. Adv Astron Sci, 153:137–147.
Sostaric R, Rea J, 2005. Powered descent guidance methods for the Moon and Mars. AIAA Guidance, Navigation, and Control Conf and Exhibit, Article 6287. https://doi.org/10.2514/6.2005-6287
Stellato B, Banjac G, Goulart P, et al., 2018. OSQP: an operator splitting solver for quadratic programs. https://arxiv.org/abs/1711.08013v2
Szmuk M, Açıkmeşe B, 2016. Successive convexification for fuel-optimal powered landing with aerodynamic drag and non-convex constraints. AIAA Guidance, Navigation, and Control Conf, Article 378. https://doi.org/10.2514/6.2016-0378
Szmuk M, Açıkmeşe B, 2018. Successive convexification for 6-DoF Mars rocket powered landing with free-final-time. AIAA Guidance, Navigation, and Control Conf, Article 617. https://doi.org/10.2514/6.2018-0617
Szmuk M, Eren U, Açıkmeşe B, 2017. Successive convexification for Mars 6-DoF powered descent landing guidance. AIAA Guidance, Navigation, and Control Conf, Article 1500. https://doi.org/10.2514/6.2017-1500
Szmuk M, Reynolds T, Açıkmeşe B, et al., 2019. Successive convexification for 6-DoF powered descent guidance with compound state-triggered constraints. AIAA Scitech 2019 Forum, Article 926. https://doi.org/10.2514/6.2019-0926
Toh KC, Tutuncu RH, Todd MJ, 2004. On the implementation of SDPT3 (version 3.1) — a MATLAB software package for semidefinite-quadratic-linear programming. IEEE Int Conf on Robotics and Automation, p.290–296. https://doi.org/10.1109/CACSD.2004.1393891
Topcu U, Casoliva J, Mease KD, 2005. Fuel efficient powered descent guidance for Mars landing. AIAA Guidance, Navigation, and Control Conf and Exhibit, Article 6286. https://doi.org/10.2514/6.2005-6286
Topcu U, Casoliva J, Mease KD, 2007. Minimum-fuel powered descent for Mars pinpoint landing. J Spacecr Rock, 44(2):324–331. https://doi.org/10.2514/1.25023
Tsiotras P, Mesbahi M, 2017. Toward an algorithmic control theory. J Guid Contr Dynam, 40(2):194–196. https://doi.org/10.2514/1.G002754
Wang C, Song ZY, 2018a. Convex model predictive control for rocket vertical landing. 37th Chinese Control Conf, p.9837–9842. https://doi.org/10.23919/ChiCC.2018.8483147
Wang C, Song ZY, 2018b. Rapid trajectory optimization for lunar soft landing with hazard avoidance. Adv Astron Sci, 161:885–900.
Wang JB, Cui NG, 2018. A pseudospectral-convex optimization algorithm for rocket landing guidance. AIAA Guidance, Navigation, and Control Conf, Article 1871. https://doi.org/10.2514/6.2018-1871
Wang KX, Shao ZJ, Zhang ZJ, et al., 2007. Convergence depth control for process system optimization. Ind Eng Chem Res, 46(23):7729–7738. https://doi.org/10.1021/ie070073s
Wenzel A, 2017. On-board Convex Optimization for Powered Descent Landing of EAGLE. PhD Theis, Lulea University of Technology, Lulea, Sweden.
Wenzel A, Sagliano M, Seelbinder D, 2018. Performance analysis of real-time optimal guidance methods for vertical take-off, vertical landing vehicles. 69th Int Astronautical Congress, Article 44 498.
Wright SJ, 1997. Primal-Dual Interior-Point Methods. Society for Industrial and Applied Mathematics, Philadelphia, USA.
Yang RQ, Liu XF, 2019. Comparison of convex optimization-based approaches to solve nonconvex optimal control problems. AIAA Scitech 2019 Forum, Article 1666. https://doi.org/10.2514/6.2019-1666
Zeilinger MN, Raimondo DM, Domahidi A, et al., 2014. On real-time robust model predictive control. Automatica, 50(3):683–694. https://doi.org/10.1016/j.automatica.2013.11.019
Zhang B, Tang S, Pan BF, 2016. Multi-constrained suboptimal powered descent guidance for lunar pinpoint soft landing. Aerosp Sci Technol, 48:203–213. https://doi.org/10.1016/j.ast.2015.11.018
Zhang HH, Guan YF, Huang XY, et al., 2014a. Guidance navigation and control for Chang’E-3 powered descent. Sci Sin Technol, 44(4):377–384. https://doi.org/10.1360/092014-43
Zhang HH, Liang J, Huang XY, et al., 2014b. Autonomous hazard avoidance control for Chang’E-3 soft landing. Sci Sin Technol, 44(6):559–568. https://doi.org/10.1360/092014-51
Zhang Y, Guo YN, Ma GF, et al., 2017. Collision avoidance ZEM/ZEV optimal feedback guidance for powered descent phase of landing on Mars. Adv Space Res, 59(6):1514–1525. https://doi.org/10.1016/j.asr.2016.12.040
Zhao DJ, Song ZY, 2017. Reentry trajectory optimization with waypoint and no-fly zone constraints using multi-phase convex programming. Acta Astron, 137:60–69. https://doi.org/10.1016/j.actaastro.2017.04.013
Zhao DJ, Jiang BY, Lv XG, 2015. Terminal attitude-constrained optimal feedback guidance for pinpoint planetary landing. Adv Astron Sci, 153:1689–1696.
Zhou LY, Xia YQ, 2014. Improved ZEM/ZEV feedback guidance for Mars powered descent phase. Adv Space Res, 54(11):2446–2455. https://doi.org/10.1016/j.asr.2014.08.011
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Zheng-yu SONG guided the AGM research for LM rockets, and organized and revised the manuscript. Cong WANG completed the demonstration algorithm of Peacock, carried out the simulations, and drafted the manuscript. Stephan THEIL, David SEELBINDER, and Marco SAGLIANO provided their first-hand experience on EAGLE and CALLISTO projects, and helped revise the manuscript. Xin-fu LIU revised parts of the manuscript. Zhi-jiang SHAO provided his experience on OCFE and made suggestions to the manuscript.
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Project supported by the National Natural Science Foundation of China (No. 61773341) and the International Academy of Astronautics Study Group SG 3.32
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Song, Zy., Wang, C., Theil, S. et al. Survey of autonomous guidance methods for powered planetary landing. Front Inform Technol Electron Eng 21, 652–674 (2020). https://doi.org/10.1631/FITEE.1900458
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DOI: https://doi.org/10.1631/FITEE.1900458