Document Type : Scientific extension


Aerospace Research Institute, Ministry of Science, Research and Technology, Tehran, Iran


First, the history of space explorations is reviewed briefly in this paper alongside with current successful and future missions in this field. Then,missions with landing on celestial bodies, especiallyMoon and Mars landings, and their technical problems and mission challenges are reviewed. Then, as one of the requirements for landing missions, the soft landing problem is introduced in details. As a specialcase, the soft landing on the Moon with mission phases and other system requirements is presented. Due to the importance of fuel saving in the space, the soft landing problem on Moon is modeled as a minimum fuel optimal control problem with nonlinear ordinary differential equations. The governing equations, initial and final conditions in various cases and common performance index formulations are also given based on the recentreferences. Finally, the results of a numerical simulation in a test case problem of Moon landing arereviewed.


[1] Liu, X-L., Duan, G.R. andTeo, K. L, “Optimal soft landing control for Moon lander“,Automatica, Vol. 44, No.4, 2008, pp. 1097-1103.
[2] Rijesh, M.P., Sijo, G., Philip, N. K., Natarajan, P., “Geometrical Guidance Algorithm for Soft Landing on Lunar Surface“,Third International Conference onAdvances in Control and Optimization of Dynamical Systems,Indian Institute of Technology Kanpur,2014.
[3] Park, B.G., Ahn, J.S., Tahk, M. J., “Two-Dimensional Trajectory Optimization for Soft Lunar Landing Consideringa Landing Site“,International Journal of Aeronautical & Space Science, Vol. 12, No. 3, 2011, pp. 288-295.
[4] Bennett, F.V., “Apollo Experiment Report - Mission Planning for Lunar Module Descent and Ascent“, NASA Technical Report, NASA TN D-6846, 1972, pp.1-24.
[5] Klumppi, A.R., “Apollo Lunar Descent Guidance“,Automatica, Vol. 10, No. 2, 1974, pp. 133-146.
[6] D'Souza C.N, “An Optimal Guidance law for Planetary Landing“, Guidance, Navigation, and Control Conference, New Orleans, 1997, pp. 1376-1371.
[7] Ch, D.H., Jeong, B., Lee, D. and Ban, H.,“OptimalPeriluneAltitudeofLunarLandingTrajectory“,InternationalJournal of Aeronautical & Space Sciences,Vol. 10, No. 1, 2009, pp. 67-74.
[8] Zhou, J.Y., Teo, K.L., Zhou, D. and Zhao G.H., “Optimal Guidance for Lunar Module Soft Landing“,Nonlinear Dynamics and Systems Theory, Vol. 10, No.2, 2010, pp.189-201.
[9] Mathavaraj, S., Pandiyan, R. andPadhi, R., “Minimum-Landing-Error Powered-Descent Guidancefor Mars Landing Using Convex Optimization“, Journal of Guidance, Control, and Dynamics, Vol.33, No.4, 2010, pp. 1161-1171.
[10] Mathavaraj, S., Pandiyan, R. andPadhi, R., “Optimal trajectory planning for multiple Lunar landing, IFAC-PapersOnLine, Vol.49, No. 1, 2016, pp. 124-129.