Co-state initialization for the minimum-time low-thrust trajectory optimization

Taheri, Ehsan; Li, Nan I.; Kolmanovsky, Ilya

doi:10.1016/j.asr.2017.02.010

Cited by 56 publications

(13 citation statements)

References 30 publications

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“…However, deriving the first-order optimal necessary conditions is challenging in this case [137]. For some special low-thrust orbits, Lawden [138] described the first-order optimal necessary conditions based on the primer vector theory.…”

Section: Figure 15: Optimal Design Approaches Of Low-thrust Trajectorymentioning

confidence: 99%

Overview of Earth-Moon Transfer Trajectory Modeling and Design

Zhang¹,

Yu²,

Dai³

2023

Computer Modeling in Engineering &Amp; Sciences

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The Moon is the only celestial body that human beings have visited. The design of the Earth-Moon transfer orbits is a critical issue in lunar exploration missions. In the 21st century, new lunar missions including the construction of the lunar space station, the permanent lunar base, and the Earth-Moon transportation network have been proposed, requiring low-cost, expansive launch windows and a fixed arrival epoch for any launch date within the launch window. The low-energy and low-thrust transfers are promising strategies to satisfy the demands. This review provides a detailed landscape of Earth-Moon transfer trajectory design processes, from the traditional patched conic to the state-of-the-art low-energy and low-thrust methods. Essential mechanisms of the various utilized dynamic models and the characteristics of the different design methods are discussed in hopes of helping readers grasp the basic overview of the current Earth-Moon transfer orbit design methods and a deep academic background is unnecessary for the context understanding.

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Section: Figure 15: Optimal Design Approaches Of Low-thrust Trajectorymentioning

confidence: 99%

Overview of Earth-Moon Transfer Trajectory Modeling and Design

Zhang¹,

Yu²,

Dai³

2023

Computer Modeling in Engineering &Amp; Sciences

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“…Traditionally, the problem has been solved using optimal control theory from Section 2.1, and for this we can cite the books (Longuski et al, 2014;Lawden, 1963;Bryson Jr. and Ho, 1975;Kirk, 1970;Conway, 2014). Numerous solution methods have been studied, including methods based on primer vector theory (Russell, 2007;Petropoulos and Russell, 2008;Restrepo and Russell, 2017), direct methods based on solving an NLP (Betts, 2000;Arrieta-Camacho and Biegler, 2005;Ross et al, 2007;Starek and Kolmanovsky, 2012;Rao, 2015, 2016), and indirect methods (Alfano and Thorne, 1994;Fernandes, 1995;Kechichian, 1995;Haberkorn et al, 2004;Gong et al, 2008;Gil-Fernandez and Gomez-Tierno, 2010;Zimmer et al, 2010;Pan et al, 2012;Pontani and Conway, 2013;Cerf, 2016;Taheri et al, 2016Taheri et al, , 2017Rasotto et al, 2015;Lizia et al, 2014). Some recent advances for indirect methods include homotopy methods (Pan et al, 2019;Pan and Pan, 2020;Cerf et al, 2011), optimal switching surfaces (Taheri and Junkins, 2019), the RASHS and CSC approaches from Section 2.5.2 (Saranathan and Grant, 2018;Taheri et al, 2020a,b), and simultaneous optimization (also known as co-optimization) of the trajectory and the spacecraft design parameters (Arya et al, 2020).…”

Section: Orbit Transfer and Injectionmentioning

confidence: 99%

Advances in Trajectory Optimization for Space Vehicle Control

Malyuta¹,

Yu²,

Elango³

et al. 2021

Preprint

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Space mission design places a premium on cost and operational efficiency. The search for new science and life beyond Earth calls for spacecraft that can deliver scientific payloads to geologically rich yet hazardous landing sites. At the same time, the last four decades of optimization research have put a suite of powerful optimization tools at the fingertips of the controls engineer. As we enter the new decade, optimization theory, algorithms, and software tooling have reached a critical mass to start seeing serious application in space vehicle guidance and control systems. This survey paper provides a detailed overview of recent advances, successes, and promising directions for optimization-based space vehicle control. The considered applications include planetary landing, rendezvous and proximity operations, small body landing, constrained attitude reorientation, endo-atmospheric flight including ascent and reentry, and orbit transfer and injection. The primary focus is on the last ten years of progress, which have seen a veritable rise in the number of applications using three core technologies: lossless convexification, sequential convex programming, and model predictive control. The reader will come away with a well-rounded understanding of the state-of-the-art in each space vehicle control application, and will be well positioned to tackle important current open problems using convex optimization as a core technology.

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“…As the final mass is free, the transversality conditions in (16) tell that the final mass costate should be zero…”

Section: Statement Of the Problem A Minimum-fuel Problemmentioning

confidence: 99%

“…Since only the first-order necessary conditions are considered, the TPBVP trends to have many local extremums that satisfy all these conditions [15]. Therefore, the main difficulties in using the indirect methods consist of two parts: the sensitivity of the local solutions to the initial guesses for the unknowns caused by the strong nonlinearity and discontinuous integrated functions [16], and finding the best solution among many local solutions [17].…”

Section: Introductionmentioning

confidence: 99%

Practical Homotopy Methods for Finding the Best Minimum-Fuel Transfer in the Circular Restricted Three-Body Problem

Pan

2020

IEEE Access

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Finding a solution to a low-thrust minimum-fuel transfer trajectory optimization problem in the circular restricted three-body problem (CRTBP) is already known to be extremely difficult due to the strong nonlinearity and the discontinuous bang-bang control structure. What is less commonly known is that such a problem can have many local solutions that satisfy all the first-order necessary conditions of optimality. In this paper, the existence of multiple solutions in the CRTBP is fully demonstrated, and a practical technique that involves multiple homotopy procedures is proposed, which can robustly search as many as desired local solutions to determine the best solution with the optimal performance index. Due to the common failure of the general homotopy method in tracking a homotopy path, the parameter bounding fixed-point (PBFB) homotopy is coupled to construct the double-homotopy, which can overcome the difficulties by tracking the discontinuous homotopy path. Furthermore, the PBFB homotopy is capable to achieve multiple solutions that lie on separate homotopy path branches. The minimum-time problem is first solved by the doublehomotopy on the thrust magnitude to infer a reasonable transfer time. Then the auxiliary problem is solved by the double-homotopy and the PBFP homotopy, and multiple local solutions with smooth control profiles are obtained. By tracking homotopy paths starting from these solution points, multiple solutions to the minimum-fuel problem are obtained, and the best solution is eventually identified. Numerical demonstration of the minimum-fuel transfers from a GEO to an Earth-Moon L 1 halo orbit is presented to substantiate the effectiveness of the technique. INDEX TERMS Circular restricted three-body problem, Earth-Moon transfers, homotopy method, trajectory optimization.

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Co-state initialization for the minimum-time low-thrust trajectory optimization

Cited by 56 publications

References 30 publications

Overview of Earth-Moon Transfer Trajectory Modeling and Design

Overview of Earth-Moon Transfer Trajectory Modeling and Design

Advances in Trajectory Optimization for Space Vehicle Control

Practical Homotopy Methods for Finding the Best Minimum-Fuel Transfer in the Circular Restricted Three-Body Problem

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