Analysis of optimal strategies for soft landing on the Moon from lunar parking orbits

Ramanan, R. V.; Lal, M. J.

doi:10.1007/bf02715967

Cited by 36 publications

(19 citation statements)

References 2 publications

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“…Presenting a novel analytical solution that allows some related studies such as hardware-in-the loop analysis to be performed with high reliability is the main advantage of this work. Ramana proposed a numerical technique of a controlled random search to solve a similar problem [9], but this numerical method may encounter some practical problems. In another study [8], to minimize the control effort expenditure, the commanded acceleration is introduced as the performance measure.…”

Section: Resultsmentioning

confidence: 99%

“…An optimal guidance law that minimized the commanded acceleration in three dimensions was obtained by Souza [8]. Ramana has designed an optimal trajectory for soft landing on the moon by solving the boundary value equations through a numerical approach named controlled random search [9]. Lee investigated on the optimal trajectory and the feedback linearization control of a re-entry vehicle during the terminal-area energy management (TAEM) phase [10].…”

Section: Introductionmentioning

confidence: 99%

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An analytical guidance law of planetary landing mission by minimizing the control effort expenditure

2009

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An optimal trajectory design of a module for the planetary landing problem is achieved by minimizing the control effort expenditure. Using the calculus of variations theorem, the control variable is expressed as a function of costate variables, and the problem is converted into a two-point boundary-value problem. To solve this problem, the performance measure is approximated by employing a trigonometric series and subsequently, the optimal control and state trajectories are determined. To validate the accuracy of the proposed solution, a numerical method of the steepest descent is utilized. The main objective of this paper is to present a novel analytic guidance law of the planetary landing mission by optimizing the control effort expenditure. Finally, an example of a lunar landing mission is demonstrated to examine the results of this solution in practical situations.

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Section: Resultsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

An analytical guidance law of planetary landing mission by minimizing the control effort expenditure

2009

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“…In the previous optimal lunar landing trajectories, the lunar lander frequently increased its altitude to earn enough time to reduce the horizontal velocity as shown in Figure 2 [1,2]. This phenomenon depends on its thrust-mass ratio.…”

Section: Simulationmentioning

confidence: 99%

“…Park et al designed the optimal trajectory for the specific landing site by issuing a pseudospectral method in 2D space, and the solution is generally used for the optimal lunar landing researches [1]. Before this research, Ramanan and Lal suggested the same optimal lunar landing strategies and analyzed the strategies on a case-by-case basis for the various perilune altitudes [2]. In general, the lower perilune altitude saves fuel for the landing in the powered descent phase, but fuel for the deorbit burn is increased.…”

Section: Introductionmentioning

confidence: 99%

Optimal Lunar Landing Trajectory Design for Hybrid Engine

Cho

Kim

Leeghim

2015

Mathematical Problems in Engineering

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The lunar landing stage is usually divided into two parts: deorbit burn and powered descent phases. The optimal lunar landing problem is likely to be transformed to the trajectory design problem on the powered descent phase by using continuous thrusters. The optimal lunar landing trajectories in general have variety in shape, and the lunar lander frequently increases its altitude at the initial time to obtain enough time to reduce the horizontal velocity. Due to the increment in the altitude, the lunar lander requires more fuel for lunar landing missions. In this work, a hybrid engine for the lunar landing mission is introduced, and an optimal lunar landing strategy for the hybrid engine is suggested. For this approach, it is assumed that the lunar lander retrofired the impulsive thruster to reduce the horizontal velocity rapidly at the initiated time on the powered descent phase. Then, the lunar lander reduced the total velocity and altitude for the lunar landing by using the continuous thruster. In contradistinction to other formal optimal lunar landing problems, the initial horizontal velocity and mass are not fixed at the start time. The initial free optimal control theory is applied, and the optimal initial value and lunar landing trajectory are obtained by simulation studies.

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“…Ramanan and Lal [5] presented several strategies for soft landings from the lunar parking orbit. In [6], using a Hermite-Simpson collocation method, the rapid trajectory optimization during the powered descent phase was addressed for soft lunar landings.…”

Section: Introductionmentioning

confidence: 99%

Three-dimensional trajectory optimization of soft lunar landings from the parking orbit with considerations of the landing site

Park

Tahk

2011

Int. J. Control Autom. Syst.

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Minimum fuel, three-dimensional trajectory optimization from a parking orbit considering the desired landing site is addressed for soft lunar landings. The landing site is determined by the final longitude and latitude; therefore, a two-dimensional approach is limited and a three-dimensional approach is required. In addition, the landing site is not usually considered when performing lunar landing trajectory optimizations, but should be considered in order to design more accurate and realistic lunar landing trajectories. A Legendre pseudospectral (PS) method is used to discretize the trajectory optimization problem as a nonlinear programming (NLP) problem. Because the lunar landing consists of three phases including a de-orbit burn, a transfer orbit phase, and a powered descent phase, the lunar landing problem is regarded as a multiphase problem. Thus, a PS knotting method is also used to manage the multiphase problem, and C code for Feasible Sequential Quadratic Programming (CFSQP) using a sequential quadratic programming (SQP) algorithm is employed as a numerical solver after formulating the problem as an NLP problem. The optimal solutions obtained satisfy all constraints as well as the desired landing site, and the solutions are verified through a feasibility check.

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Analysis of optimal strategies for soft landing on the Moon from lunar parking orbits

Cited by 36 publications

References 2 publications

An analytical guidance law of planetary landing mission by minimizing the control effort expenditure

An analytical guidance law of planetary landing mission by minimizing the control effort expenditure

Optimal Lunar Landing Trajectory Design for Hybrid Engine

Three-dimensional trajectory optimization of soft lunar landings from the parking orbit with considerations of the landing site

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