Fuel-Optimal Low-Thrust Reconfiguration of Formation- Flying Satellites via Homotopic Approach

Li, Jing; Xi, Xiaoning

doi:10.2514/1.57354

Cited by 41 publications

(18 citation statements)

References 15 publications

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“…In 2012, Picot [17] used a simple shooting method and the homotopy method to compute time-minimal and energy-minimal trajectories in the restricted three-body Earth-moon system. Li and Xi [18] proposed a homotopy method to solve a fueloptimal low-thrust formation-flying satellite reconfiguration. Guo et al [19] proposed a hybrid scheme of the homotopy method and the pseudospectral method to the low-thrust trajectory optimization.…”

Section: Introductionmentioning

confidence: 99%

Double-Homotopy Method for Solving Optimal Control Problems

Pan

et al. 2016

Journal of Guidance, Control, and Dynamics

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The homotopy method has long served as a useful tool in solving optimal control problems, particularly highly nonlinear and sensitive ones for which good initial guesses are difficult to obtain, such as some of the well-known problems in aerospace trajectory optimization. However, the traditional homotopy method often fails midway: a fact that occasional practitioners are not aware of, and a topic which is rarely investigated in aerospace engineering. This paper first reviews the main reasons why traditional homotopy fails. A new double-homotopy method is developed to address the common failures of the traditional homotopy method. In this approach, the traditional homotopy is employed until it encounters a difficulty and stops moving forward. Another homotopy originally designed for finding multiple roots of nonlinear equations takes over at this point, and it finds a different solution to allow the traditional homotopy to continue on. This process is repeated whenever necessary. The proposed method overcomes some of the frequent difficulties of the traditional homotopy method. Numerical demonstrations in a nonlinear optimal control problem and a three-dimensional low-thrust orbital transfer problem are presented to illustrate the applications of the method.

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Section: Introductionmentioning

confidence: 99%

Double-Homotopy Method for Solving Optimal Control Problems

Pan

et al. 2016

Journal of Guidance, Control, and Dynamics

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“…The minimum time reorientation maneuver of a rigid spacecraft is a well-known problem; the first related work regarding a numerical approach dates back to the 1990s [1][2][3][4]. These papers have been used as a reference providing some test cases for successive works as in [5][6][7]; the research still focuses on this problem with several approaches, for example, through homotopic approach algorithms [8], pseudospectral optimization analysis [9,10], or with hybrid numerical techniques [11].…”

Section: Introductionmentioning

confidence: 99%

Particle Swarm Optimization for Time-Optimal Spacecraft Reorientation with Keep-Out Cones

Spiller

Ansalone

Curti

2016

Journal of Guidance, Control, and Dynamics

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This paper deals with the problem of spacecraft time-optimal reorientation maneuvers under boundaries and path\ud constraints. The minimum time solution with keep-out constraints is proposed using the particle swarm optimization\ud technique. A novel method based on the evolution of the kinematics and the successive obtainment of the control law is\ud presented and named as inverse dynamics particle swarm optimization. It is established that the computation of the\ud minimum time maneuver with the proposed technique leads to near-optimal solutions, which fully satisfy all the\ud boundaries and path constraints

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“…To cope with the difficulties encountered, the homotopic approach has recently been introduced to solve the TPBVPs . The essence of the method is that, by starting from a trivial related problem, whose solutions are known, or easy to determine, a homotopy scheme is used to continuously deform the problem to approximate the original one and find its solutions.…”

Section: Introductionmentioning

confidence: 99%

“…Homotopic approach can give relatively good results in practice. However, previous work mainly focuses on the fuel‐optimal space trajectory, and seldom published papers apply the homotopy method to the time‐optimal reorientation trajectory optimization. If the homotopic approach is directly applied for the fuel‐optimal control problem to solve the time‐optimal control problem, the quadratic penalty homotopy scheme converges very slow or even cannot obtain the optimal solution.…”

Section: Introductionmentioning

confidence: 99%

Time-optimal reorientation of the rigid spacecraft using a pseudospectral method integrated homotopic approach

2014

Optim. Control Appl. Meth.

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Summary This paper proposes a robust algorithm for time‐optimal rigid spacecraft reorientation trajectory generation. Based on the Pontryagin's maximum principle, the first‐order necessary optimality conditions are derived. These optimality conditions are numerically satisfied by adopting a pseudospectral method integrated homotopic approach to solve the associated shooting functions. First, the energy‐optimal reorientation solution is obtained using the Radau pseudospectral method, which has a spectral convergence speed and can give a precise estimation of the initial costates used to start the homotopic approach. Then, a modified homotopy scheme is given to deform the associated energy‐optimal solution to the desired time‐optimal solution continuously. Finally, for the inertially symmetric spacecraft reorientation problem, the newly found time‐optimal solutions are presented. The performance of the algorithm is illustrated by simulating a general asymmetric rigid spacecraft time‐optimal reorientation problem. Copyright © 2014 John Wiley & Sons, Ltd.

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Fuel-Optimal Low-Thrust Reconfiguration of Formation- Flying Satellites via Homotopic Approach

Cited by 41 publications

References 15 publications

Double-Homotopy Method for Solving Optimal Control Problems

Double-Homotopy Method for Solving Optimal Control Problems

Particle Swarm Optimization for Time-Optimal Spacecraft Reorientation with Keep-Out Cones

Time-optimal reorientation of the rigid spacecraft using a pseudospectral method integrated homotopic approach

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