Low-Thrust Many-Revolution Trajectory Optimization via Differential Dynamic Programming and a Sundman Transformation

Aziz, Jonathan; Parker, Jeffrey S.; Scheeres, Daniel J.; Englander, Jacob A.

doi:10.1007/s40295-017-0122-8

Cited by 28 publications

(9 citation statements)

References 24 publications

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“…The sunlight fraction is then a step function between one and zero, and relies only on Eqs. (7) to (9) for the necessary geometry. With the Heaviside definition of a step function, the sunlight fraction is half-valued at the eclipse transition.…”

Section: Smoothed Sunlight Fractionmentioning

confidence: 99%

“…Advancements in the application of the second-order gradient-based method, differential dynamic programming [6][7][8][9] (DDP), towards spacecraft trajectory optimization have motivated the development of a twice-differentiable power model. This work proposes a model based on the geometry of overlapping discs 10) that smooths the eclipse transition with a logistic function in the same manner that has seen previous success when applied to the discontinuity in discrete number of thrusters available.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

A Smoothed Eclipse Model for Solar Electric Propulsion Trajectory Optimization

Aziz

Scheeres

Parker

et al. 2019

AEROSPACE TECHNOLOGY JAPAN

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Solar electric propulsion (SEP) is the dominant design option for employing low-thrust propulsion on a space mission. Spacecraft solar arrays power the SEP system but are subject to blackout periods during solar eclipse conditions. Discontinuity in power available to the spacecraft must be accounted for in trajectory optimization, but gradient-based methods require a differentiable power model. This work presents a power model that smooths the eclipse transition from total eclipse to total sunlight with a logistic function. Example trajectories are computed with differential dynamic programming, a second-order gradient-based method.

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Section: Smoothed Sunlight Fractionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

A Smoothed Eclipse Model for Solar Electric Propulsion Trajectory Optimization

Aziz

Scheeres

Parker

et al. 2019

AEROSPACE TECHNOLOGY JAPAN

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“…The results indicated that these newly-proposed optimization strategies are effective and can provide feasible solutions for solving the constrained space vehicle trajectory design problems. Interior point method (IP) [41] Interior point sequential quadratic programming (IPSQP) [42] Linear programming (LP) [43] Second order cone programming (SOCP) [44] Semidefinite programming (SDP) [45] Dynamic programming (DP) [46] Differential dynamic programming (DDP) [47] Stochastic differential dynamic programming (SDDP) [48]…”

Section: Optimization Algorithmsmentioning

confidence: 99%

A review of optimization techniques in spacecraft flight trajectory design

Chai

Tsourdos

Chai

et al. 2019

Progress in Aerospace Sciences

105

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For most atmospheric or exo-atmospheric spacecraft flight scenarios, a welldesigned trajectory is usually a key for stable flight and for improved guidance and control of the vehicle. Although extensive research work has been carried out on the design of spacecraft trajectories for different mission profiles and many effective tools were successfully developed for optimizing the flight path, it is only in the recent five years that there has been a growing interest in planning the flight trajectories with the consideration of multiple mission objectives and various model errors/uncertainties. It is worth noting that in many practical spacecraft guidance, navigation and control systems, multiple performance indices and different types of uncertainties must frequently be considered during the path planning phase. As a result, these requirements bring the development of multi-objective spacecraft trajectory optimization methods as well as stochastic spacecraft trajectory optimization algorithms. This paper aims to broadly review the state-of-the-art development in numerical multi-objective trajectory optimization algorithms and stochastic trajectory planning techniques for spacecraft flight operations. A brief description of the mathematical formulation of the problem is firstly introduced. Following that, various optimization methods that can be effective for solving spacecraft trajectory planning problems are reviewed, including the gradient-based methods, the convexification-based methods, and the evolutionary/metaheuristic methods. The multi-objective

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“…In many cases, however, finding an adequate set of tuning parameters for such guidance laws can be as time consuming as the optimization process itself. Along a different line, some efforts have been made to study the impact of different parameterizations of the orbital motion on the computational efficiency of the optimization process, see, e.g., [19,20]. In particular, it is found in [19] that regularizing the orbital dynamics provides an effective way to speed-up the computation.…”

Section: Introductionmentioning

confidence: 99%

“…Along a different line, some efforts have been made to study the impact of different parameterizations of the orbital motion on the computational efficiency of the optimization process, see, e.g., [19,20]. In particular, it is found in [19] that regularizing the orbital dynamics provides an effective way to speed-up the computation. In this paper, we will show that large computational gains are possible by working on the parametrization, while retaining the ability to solve the control problem to full optimality.…”

Section: Introductionmentioning

confidence: 99%

Optimal Low-Thrust Orbit Transfers Made Easy: A Direct Approach

Leomanni,

Bianchini,

Garulli

et al. 2021

Preprint

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The optimization of low-thrust, multi-revolution orbit transfer trajectories is often regarded as a difficult problem in modern astrodynamics. In this paper, a flexible and computationally efficient approach is presented for the optimization of low-thrust orbit transfers under eclipse constraints. The proposed approach leverages a new dynamic model of the orbital motion and a Lyapunov-based initial guess generation scheme that is very easy to tune. A multi-objective, single-phase formulation of the optimal control problem is devised, which provides a convenient way to trade off fuel consumption and time of flight. A distinctive feature of such a formulation is that it requires no prior information about the structure of the optimal solution. Simulation results for two benchmark orbit transfer scenarios indicate that minimum-time, minimum-fuel and mixed time/fuel-optimal instances of the control problem can be readily solved via direct collocation, while incurring a significantly lower computational demand with respect to existing techniques.

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Low-Thrust Many-Revolution Trajectory Optimization via Differential Dynamic Programming and a Sundman Transformation

Cited by 28 publications

References 24 publications

A Smoothed Eclipse Model for Solar Electric Propulsion Trajectory Optimization

A Smoothed Eclipse Model for Solar Electric Propulsion Trajectory Optimization

A review of optimization techniques in spacecraft flight trajectory design

Optimal Low-Thrust Orbit Transfers Made Easy: A Direct Approach

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