scholarly journals Survey of Direct Transcription for Low-Thrust Space Trajectory Optimization with Applications

2014 ◽  
Vol 2014 ◽  
pp. 1-15 ◽  
Author(s):  
F. Topputo ◽  
C. Zhang
Keyword(s):  
Optimal Control ◽  
Trajectory Optimization ◽  
Ad Hoc ◽  
Direct Methods ◽  
Trajectory Design ◽  
Low Thrust ◽  
Direct Transcription ◽  
Classic Theory ◽  
Theory Of Optimal Control ◽  
Space Trajectory Design

Space trajectory design is usually addressed as an optimal control problem. Although it relies on the classic theory of optimal control, this branch possesses some peculiarities that led to the development of ad hoc techniques, which can be grouped into two categories: direct and indirect methods. This paper gives an overview of the principal techniques belonging to the direct methods. The technique known as “direct transcription and collocation” is illustrated by considering Hermite-Simpson, high-order Gauss-Lobatto, and pseudospectral methods. Practical examples are given, and several hints to improve efficiency and robustness are implemented.

scholarly journals Minimum-Fuel Planar Earth-to-Mars Low-Thrust Trajectories Using Bang-Bang Control

2021 ◽  
Author(s):  
Daero Lee
Keyword(s):  
Optimal Control ◽  
Boundary Value Problems ◽  
Electric Propulsion ◽  
Direct Method ◽  
Boundary Value ◽  
Specific Impulse ◽  
Direct Methods ◽  
Optimization Methods ◽  
Low Thrust ◽  
Primer Vector Theory

Recent advance in electric propulsion systems have demonstrated that these engines can be used for for long-duration interplanetary voyages. Constant specific impulse engine described as a thrust-limited engine is an example of this type of engine, processing the ability to operate at a constant level of impulse. The determination of minimum-fuel, planar heliocentric Earth-to-Mars low-thrust trajectories of spacecraft using a constant specific impulse is discussed considering the first-order necessary conditions derived from Lawden’s primer vector theory. The minimum-fuel low-thrust Earth-to-Mars optimization problem is then solved in two-dimensional, heliocentric frame using both indirect and direct methods. In the indirect method, two-point-boundary-value problems are derived to solve boundary value problems for ordinary differential equations. In the direct method, a general-purpose optimal control software called GPOPS-II is adopted to solve these optimal control problems. Numerical examples using two different optimization methods are presented to demonstrate the characteristics of minimum-fuel planar low-thrust trajectories with on-off-on thrust sequences at three chosen flight times and available maximum powers. The results are useful for broad trajectory search in the preliminary phase of mission designs.

scholarly journals A Survey on Low-Thrust Trajectory Optimization Approaches

Aerospace ◽  
2021 ◽  
Vol 8 (3) ◽  
pp. 88
Author(s):  
David Morante ◽  
Manuel Sanjurjo Rivo ◽  
Manuel Soler
Keyword(s):  
Optimal Control ◽  
Objective Function ◽  
Trajectory Optimization ◽  
Optimal Control Problems ◽  
Optimization Problems ◽  
Control Problems ◽  
Mathematical Framework ◽  
Low Thrust ◽  
Discrete State ◽  
Hybrid Optimal Control

In this paper, we provide a survey on available numerical approaches for solving low-thrust trajectory optimization problems. First, a general mathematical framework based on hybrid optimal control will be presented. This formulation and their elements, namely objective function, continuous and discrete state and controls, and discrete and continuous dynamics, will serve as a basis for discussion throughout the whole manuscript. Thereafter, solution approaches for classical continuous optimal control problems will be briefly introduced and their application to low-thrust trajectory optimization will be discussed. A special emphasis will be placed on the extension of the classical techniques to solve hybrid optimal control problems. Finally, an extensive review of traditional and state-of-the art methodologies and tools will be presented. They will be categorized regarding their solution approach, the objective function, the state variables, the dynamical model, and their application to planetocentric or interplanetary transfers.

scholarly journals A Shape-Based Method for Continuous Low-Thrust Trajectory Design between Circular Coplanar Orbits

2017 ◽  
Vol 2017 ◽  
pp. 1-10 ◽  
Author(s):  
Qun Fang ◽  
Xuefeng Wang ◽  
Chong Sun ◽  
Jianping Yuan
Keyword(s):  
Fourier Series ◽  
Trajectory Optimization ◽  
Lower Cost ◽  
Necessary Conditions ◽  
Trajectory Design ◽  
Low Thrust ◽  
First Order ◽  
The Earth ◽  
Free Case ◽  
Preliminary Phase

The shape-based method can provide suitable initial guesses for trajectory optimization, which are useful for quickly converging a more accurate trajectory. Combined with the optimal control theory, an optimized shape-based method using the finite Fourier series is proposed in this paper. Taking the flight time-fixed case and the time-free case into account, respectively, the optimized shape-based method, which considers the first-order optimal necessary conditions, can guarantee that not only an orbit designed during the preliminary phase is optimal, but also the thrust direction is not constrained to be tangential. Besides, the traditional shape-based method using the finite Fourier series, in which the thrust direction is constrained to be tangential, is developed for the time-free case in this paper. The Earth-Mars case and the LEO-GEO case are used to verify the optimized shape-based method’s feasibility for time-fixed and time-free continuous low-thrust trajectory design between circular coplanar orbits, respectively. The optimized shaped-based method can design a lower cost trajectory.

scholarly journals An existence theorem for optimal stochastic programming

1968 ◽  
Vol 8 (1) ◽  
pp. 114-118 ◽  
Author(s):  
A. W. J. Stoddart
Keyword(s):  
Optimal Control ◽  
Stochastic Programming ◽  
Existence Theorem ◽  
Stochastic Systems ◽  
Necessary Conditions ◽  
Sufficient Conditions ◽  
Direct Methods ◽  
Optimal Program ◽  
Sufficient Conditions For Optimality ◽  
Theory Of Optimal Control

In [4], Hanson has obtained necessary conditions and sufficient conditions for optimality of a program in stochastic systems. However, in many cases, especially in a general treatment, a program satisfying these conditions cannot be determined explicitly, so that the question of existence of an optimal program in such systems is significant. In this paper, we obtain conditions sufficient for existence of an optimal program by applying the direct methods of the calculus of variations [9], [6] and the theory of optimal control [7], [5].

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