scholarly journals Optimal Space Trajectories with Multiple Coast Arcs Using Modified Equinoctial Elements

2021 ◽  
Author(s):  
Mauro Pontani
Keyword(s):  
Optimization Problem ◽  
Space Mission ◽  
Low Thrust ◽  
Optimal Space Trajectories ◽  
Sequential Solution ◽  
Necessary Conditions For Optimality ◽  
Single Arc ◽  
Finite Thrust ◽  
Solution Methodology ◽  
Optimal Space

AbstractThe detection of optimal trajectories with multiple coast arcs represents a significant and challenging problem of practical relevance in space mission analysis. Two such types of optimal paths are analyzed in this study: (a) minimum-time low-thrust trajectories with eclipse intervals and (b) minimum-fuel finite-thrust paths. Modified equinoctial elements are used to describe the orbit dynamics. Problem (a) is formulated as a multiple-arc optimization problem, and additional, specific multipoint necessary conditions for optimality are derived. These yield the jump conditions for the costate variables at the transitions from light to shadow (and vice versa). A sequential solution methodology capable of enforcing all the multipoint conditions is proposed and successfully applied in an illustrative numerical example. Unlike several preceding researches, no regularization or averaging is required to make tractable and solve the problem. Moreover, this work revisits problem (b), formulated as a single-arc optimization problem, while emphasizing the substantial analytical differences between minimum-fuel paths and problem (a). This study also proves the existence and provides the derivation of the closed-form expressions for the costate variables (associated with equinoctial elements) along optimal coast arcs.

An Efficient and Accurate Solution Methodology for Bilevel Multi-Objective Programming Problems Using a Hybrid Evolutionary-Local-Search Algorithm

2010 ◽  
Vol 18 (3) ◽  
pp. 403-449 ◽  
Author(s):  
Kalyanmoy Deb ◽  
Ankur Sinha
Keyword(s):  
Problem Solving ◽  
Local Search ◽  
Bilevel Programming ◽  
Optimization Problem ◽  
Practical Importance ◽  
Test Problems ◽  
Multi Objective ◽  
Conflicting Objectives ◽  
Bilevel Programming Problems ◽  
Solution Methodology

Bilevel optimization problems involve two optimization tasks (upper and lower level), in which every feasible upper level solution must correspond to an optimal solution to a lower level optimization problem. These problems commonly appear in many practical problem solving tasks including optimal control, process optimization, game-playing strategy developments, transportation problems, and others. However, they are commonly converted into a single level optimization problem by using an approximate solution procedure to replace the lower level optimization task. Although there exist a number of theoretical, numerical, and evolutionary optimization studies involving single-objective bilevel programming problems, not many studies look at the context of multiple conflicting objectives in each level of a bilevel programming problem. In this paper, we address certain intricate issues related to solving multi-objective bilevel programming problems, present challenging test problems, and propose a viable and hybrid evolutionary-cum-local-search based algorithm as a solution methodology. The hybrid approach performs better than a number of existing methodologies and scales well up to 40-variable difficult test problems used in this study. The population sizing and termination criteria are made self-adaptive, so that no additional parameters need to be supplied by the user. The study indicates a clear niche of evolutionary algorithms in solving such difficult problems of practical importance compared to their usual solution by a computationally expensive nested procedure. The study opens up many issues related to multi-objective bilevel programming and hopefully this study will motivate EMO and other researchers to pay more attention to this important and difficult problem solving activity.

An algorithm portfolio based solution methodology to solve a supply chain optimization problem

2009 ◽  
Vol 36 (4) ◽  
pp. 8407-8420 ◽  
Author(s):  
Salik R. Yadav ◽  
Raja Ram M.R. Muddada ◽  
M.K. Tiwari ◽  
Ravi Shankar
Keyword(s):  
Supply Chain ◽  
Optimization Problem ◽  
Supply Chain Optimization ◽  
Algorithm Portfolio ◽  
Solution Methodology

Thermal morphing anisogrid smart space structures part 2: Ranking of geometric parameter importance, trust region optimization, and performance evaluation

2017 ◽  
Vol 24 (13) ◽  
pp. 2873-2893 ◽  
Author(s):  
Austin A Phoenix ◽  
Jeff Borggaard ◽  
Pablo A Tarazaga
Keyword(s):  
Parameter Optimization ◽  
Optimization Problem ◽  
Optimal Allocation ◽  
Search Algorithm ◽  
Thermal Strain ◽  
Computational Cost ◽  
Trust Region ◽  
Minimum Cost ◽  
Space Mission ◽  
Model Parameters

As future space mission structures are required to achieve more with scarcer resources, new structural configurations and modeling capabilities will be needed to meet the next generation space structural challenges. A paradigm shift is required away from the current structures that are static, heavy, and stiff, to innovative lightweight structures that meet requirements by intelligently adapting to the environment. As the complexity of these intelligent structures increases, the computational cost of the modeling and optimization efforts become increasingly demanding. Novel methods that identify and reduce the number of parameters to only those most critical considerably reduce these complex problems, allowing highly iterative evaluations and in-depth optimization efforts to be computationally feasible. This parameter ranking methodology will be demonstrated on the optimization of the thermal morphing anisogrid boom. The proposed novel morphing structure provides high precision morphing through the use of thermal strain as the sole actuation mechanism. The morphing concept uses the helical members in the anisogrid structure to provide complex constrained actuations that can achieve the six degree of freedom morphing capability. This structure provides a unique potential to develop an integrated structural morphing system, where the adaptive morphing capability is integrated directly into the primary structure. To identify parameters of interest, the Q-DEIM model reduction algorithm is implemented to rank the model parameters based on their impact on the morphing performance. This parameter ranking method provides insight into the system and enables the optimal allocation of computational and engineering resources to the most critical areas of the system for optimization. The methodology, in conjunction with a singular value decomposition (SVD), provides a ranking and identifies parameters of relative importance. The SVD is used to truncate the nine parameters problem at two locations, generating a five parameter optimization problem and a three parameter optimization problem. To evaluate the ranking, a parameter sweep in conjunction with a simple minimum cost function search algorithm will compare all 120 five parameter ranking orders to the Q-DEIM ranking. This reduced parameter set significantly reduces the parameter complexity and the computational cost of the model optimization. This paper will present the methodology to define the resulting performance of the optimal thermal morphing anisogrid structure, minimum morphing control, and the systems frequency response capability as a function of available power.

Reduced Transversality Conditions in Optimal Space Trajectories

2013 ◽  
Vol 36 (5) ◽  
pp. 1289-1300 ◽  
Author(s):  
Binfeng Pan ◽  
Zheng Chen ◽  
Ping Lu ◽  
Bo Gao
Keyword(s):  
Space Trajectories ◽  
Transversality Conditions ◽  
Optimal Space Trajectories ◽  
Optimal Space

scholarly journals Optimization of sprint interplanetary trajectories with nuclear bimodal thermal propulsion

2019 ◽  
pp. 74-77
Author(s):  
O. M. Kharytonov ◽  
S. R. Savchenko ◽  
N. Miranda
Keyword(s):  
Optimization Problem ◽  
Electrical Power ◽  
Propulsion System ◽  
Low Thrust ◽  
Small Times ◽  
Limited Power ◽  
Trajectory Method ◽  
Payload Mass ◽  
Interplanetary Missions ◽  
High Thrust

Interplanetary missions require fast and fuel-efficient transfers. Combining small times transfers of high-thrust and efficiency of low-thrust propulsion can provide a good compromise. Saving an amount of fuel from the initial high-thrust burn and using it to correct the trajectory could lead to an economy of fuel. We investigated the optimal way to take advantages of both high and low-thrust propulsion benefits in order to maximize the payload mass of the mission. Using a simple model of ideal engine of limited power and the transporting trajectory method, we determined the analytical expression of final payload mass. The solution of the optimization problem gave us the optimal repartition of fuel between high and low-thrust maneuvers for a given thrust of thermal propulsion and electrical power of low-thrust propulsion system. As the mass of the low-thrust propulsion system depends on the electrical power, we took it into account to determine the optimal electrical power for a sprint trajectory in a given time. As a result, we could obtain the interval of transfer time for which the combination of high and low thrust becomes optimal.

scholarly journals Influence of Steering Angle Profiles on the Orbit Transfer Trajectory

2021 ◽  
Vol 2021 ◽  
pp. 1-12
Author(s):  
Donghun Lee ◽  
Young-Joo Song
Keyword(s):  
Optimization Problem ◽  
Trajectory Design ◽  
Lunar Exploration ◽  
Rotating Frame ◽  
Unknown Parameters ◽  
Steering Angle ◽  
Orbit Transfer ◽  
Transfer Trajectory ◽  
Planar Orbit ◽  
Finite Thrust

This paper considers a planar orbit transfer trajectory design problem using finite thrust modeling. In this problem, the steering angles associated with the thrust direction are calculated from the predetermined profile format, and the unknown parameters in the profile are directly optimized. Three profile formats that were implemented in previous lunar exploration missions are considered. In addition, a steering angle profile defined in the rotating frame and the optimal steering angle profile are newly studied to compare the performances. To this end, the direct parameter optimization problem and the indirect optimization problem are formulated, and the characteristics of the steering angle profile and its influence on the transfer trajectory are analyzed.

Optimal Space Trajectories—A Review of Published Work

1968 ◽  
Vol 72 (686) ◽  
pp. 141-146 ◽  
Author(s):  
D. J. Bell
Keyword(s):  
Gravitational Field ◽  
General Theory ◽  
Optimal Trajectory ◽  
Space Vehicle ◽  
Two Dimensions ◽  
Performance Criteria ◽  
Space Vehicles ◽  
Optimal Space Trajectories ◽  
End Conditions ◽  
Optimal Space

The problem of transferring a space vehicle between two points in a given gravitational field such that the minimum amount of fuel is used has been called the fundamental navigational problem of astronautics. In such a problem it may be required to find the optimum thrust magnitude and thrust direction which yields a minimum fuel trajectory. Furthermore, certain end conditions may be specified which the optimal trajectory must satisfy. In a large number of published papers the velocity of the vehicle is supposed known both at the beginning of the transfer and at the end whereas the time taken to complete the manoeuvre may or may not be given. Also, other performance criteria have been chosen besides minimum fuel. For example, minimum time of transit or maximum orbital altitude at perigee. Papers mentioned in this review deal mainly with flight in two dimensions apart from those sections on general theory. Furthermore, all space vehicles considered are assumed to have a fixed exhaust velocity unless otherwise stated.

scholarly journals Numerical and Analytical Study of Optimal Low-Thrust Limited-Power Transfers between Close Circular Coplanar Orbits

2007 ◽  
Vol 2007 ◽  
pp. 1-23 ◽  
Author(s):  
Sandro da Silva Fernandes ◽  
Wander Almodovar Golfetto
Keyword(s):  
Boundary Value Problem ◽  
Optimization Problem ◽  
Analytical Study ◽  
Numerical Study ◽  
Boundary Value ◽  
Performance Criterion ◽  
Point Boundary ◽  
Low Thrust ◽  
Transformation Theory ◽  
Limited Power

A numerical and analytical study of optimal low-thrust limited-power trajectories for simple transfer (no rendezvous) between close circular coplanar orbits in an inverse-square force field is presented. The numerical study is carried out by means of an indirect approach of the optimization problem in which the two-point boundary value problem, obtained from the set of necessary conditions describing the optimal solutions, is solved through a neighboring extremal algorithm based on the solution of the linearized two-point boundary value problem through Riccati transformation. The analytical study is provided by a linear theory which is expressed in terms of nonsingular elements and is determined through the canonical transformation theory. The fuel consumption is taken as the performance criterion and the analysis is carried out considering various radius ratios and transfer durations. The results are compared to the ones provided by a numerical method based on gradient techniques.

Fabrication and Testing of Applied-Field Magneto Plasma Dynamic Thruster with Argon Propellant

2021 ◽  
Vol 13 (3) ◽  
Author(s):  
C. Akash ◽  
M. Mahavishnc ◽  
E. Manikandan ◽  
M. Manikandan ◽  
K. Vijayaraja
Keyword(s):  
Permanent Magnet ◽  
Discharge Current ◽  
Applied Field ◽  
Specific Impulse ◽  
Space Mission ◽  
Operating Conditions ◽  
Low Thrust ◽  
Plasma Dynamic ◽  
Power Circuit ◽  
High Discharge

The experimental setup of applied-field Magneto Plasma Dynamic Thruster (MPDT) is a form of electrically powered spacecraft propulsion system. The thrusters are used for deep space mission, which consist of long duration, low thrust acceleration and less propellant storage. MPDT uses the force on the charged particle by an electromagnetic field to generate thrust. The technology takes high discharge current for two electrodes and solenoid coil as applied-field. In the present investigation, the high discharge current is replaced by a limited discharge current, it is reduced by the use of capacitors bank to discharge the current for two electrodes. The solenoid coils are replaced by permanent magnet as applied-field to generate the thrust. The basic requirements for MPDT are the power circuit made by capacitors bank of electrolytic type. The electrolytic capacitors are smaller in size and produces limited voltage, which will support limited current flowing between the two electrodes. The material used for anode and cathode are copper and tungsten respectively. A permanent magnet is fixed over the anode coaxially and cathode is placed in center. A propellant will be injected in between the two electrodes. The propellant gas used in this thruster is argon. The performance of the thruster is tested in vacuum condition and the thrust value is measured by a load cell. The prototype of MPDT is tested and measurement of discharge current, thrust, specific impulse and efficiency are carried out. The thrust for various discharge current is measured and the efficient operating conditions of MPDT can be obtained.

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