Global Search Capabilities of Indirect Methods for Impulsive Transfers

Shen, Hong Xin; Casalino, Lorenzo; Luo, Ya Zhong

doi:10.1007/s40295-015-0073-x

Cited by 13 publications

(5 citation statements)

References 20 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…This curious result is consistent with some planar cases in the literature. 57,59 However, the results in our paper correspond to significantly more difficult multiple-revolution 3D cases and it is shown that same exact ∆v (up to seven significant digits) exist with different number of impulses. Thus, Edelbaum's question "How many impulses?…”

Section: Remarks On N * Rev and Optimal Number Of Impulsesmentioning

confidence: 52%

“…On the other hand, if we seek to minimize for a final thrust, we will find N rev = 8 to be optimal because (Figure 34), this maneuver belongs to the fundamental minimum-fuel surface of Figure 36. In the literature, it is hypothesized that for multiple-revolution non-coplanar cases, a large number of N impulses (with unknown times, impulse magnitudes and directions) may become more convenient for optimal rendezvous [50,59]. However, finding the optimal N impulses by NLP becomes a complex task, for large N , through traditional approaches as discussed in [46].…”

Section: Remarks On N * Rev and Optimal Number Of Impulsesmentioning

confidence: 99%

“…In order to avoid local sub-optimal convergence, a number of studies have focused on the application of evolutionary algorithms [53][54][55][56][57] that compromise between local and global search processes to identify multiple local minima. In addition, indirect-based methods are studied in [58] and a homotopic-based indirect scheme is presented in [59], which improves potential 2-impulse Lambert solutions out of the total 2N rev,max + 1 solutions. Nevertheless, while all of the aforementioned methods have been able to find multi-impulse solutions that improve on the 2-impulse solutions with varying degrees of success, none can claim global optimality, nor can they answer Edelbaum's question with certainty.…”

mentioning

confidence: 99%

See 2 more Smart Citations

How Many Impulses Redux

Taheri

Junkins

2019

J Astronaut Sci

View full text Add to dashboard Cite

A central problem in orbit transfer optimization is to determine the number, time, direction and magnitude of velocity impulses that minimize the total impulse. This problem was posed in 1967 by T. N. Edelbaum, and while notable advances have been made, a rigorous means to answer Edelbaum's question for multiple-revolution maneuvers has remained elusive for over five decades. We revisit Edelbaum's question by taking a bottom-up approach to generate a minimum-fuel switching surface. Sweeping through time profiles of the minimum-fuel switching function for increasing admissible thrust magnitude, and in the high-thrust limit, we find that the continuous thrust switching surface reveals the N -impulse solution. It is also shown that a fundamental minimum-thrust solution plays a pivotal role in our process to determine the optimal minimum-fuel maneuver for all thrust levels. Remarkably, we find the answer to Edelbaum's question is not generally unique, but is frequently a set of equal-∆v extremals. We further find, when Edelbaum's question is refined to seek the number of finite-duration thrust arcs for a specific rocket engine, that a unique extremal is usually found. Numerical results demonstrate the ideas and their utility for several interplanetary and Earth-bound optimal transfers that consist of up to eleven impulses or, for finite thrust, short thrust arcs. Another significant contribution of the paper can be viewed as a unification in astrodynamics where the connection between impulsive and continuous-thrust trajectories are demonstrated through the notion of optimal switching surfaces. NOMENCLATURE f = vector function of unforced dynamics B = control influence matrix c = exhaust velocity, m/s g 0 = Earth gravitational acceleration, m/s 2 h = specific angular momentum vector, km 2 /s H = Hamiltonian I sp = specific impulse, s J = cost functional

show abstract

Section: Remarks On N * Rev and Optimal Number Of Impulsesmentioning

confidence: 52%

Section: Remarks On N * Rev and Optimal Number Of Impulsesmentioning

confidence: 99%

mentioning

confidence: 99%

See 1 more Smart Citation

How Many Impulses Redux

Taheri

Junkins

2019

J Astronaut Sci

View full text Add to dashboard Cite

show abstract

“…Grant and Braun [3] design a fast trajectory optimization method by combining indirect optimization, continuation, and symbolic manipulation theories. Shen et al [4] propose an optimization method combining the indirect method and homotopy approach for solving an impulse trajectory. In the research of dealing with the problem of difficult selection of the initial values of co-state variables in indirect methods, Lee et al [5] propose a non-functional approximation or extrapolation initial guess structure to deal with specific energy targeting problems.…”

Section: Introductionmentioning

confidence: 99%

DDPG-Based Convex Programming Algorithm for the Midcourse Guidance Trajectory of Interceptor

Li,

et al. 2024

Aerospace

View full text Add to dashboard Cite

To address the problem of low accuracy and efficiency in trajectory planning algorithms for interceptors facing multiple constraints during the midcourse guidance phase, an improved trajectory convex programming method based on the lateral distance domain is proposed. This algorithm can achieve fast trajectory planning, reduce the approximation error of the planned trajectory, and improve the accuracy of trajectory guidance. First, the concept of lateral distance domain is proposed, and the motion model of the midcourse guidance segment in the interceptor is converted from the time domain to the lateral distance domain. Second, the motion model and multiple constraints are convexly and discretely transformed, and the discrete trajectory convex model is established in the lateral distance domain. Third, the deep reinforcement learning algorithm is used to learn and train the initial solution of trajectory convex programming, and a high-quality initial solution trajectory is obtained. Finally, a dynamic adjustment method based on the distribution of approximate solution errors is designed to achieve efficient dynamic adjustment of grid points in iterative solving. The simulation experiments show that the improved trajectory convex programming algorithm proposed in this paper not only improves the accuracy and efficiency of the algorithm but also has good optimization performance.

show abstract

“…However, the initial adjoints estimation of the initialization phase for the first trajectory is still required, and this task could be more complex than expected because it may require additional powerful algorithms to obtain convergence, such as multistart techniques, particle swarm optimization, adaptive simulated annealing, and pseudospectral methods . In the authors' previous works,(–) the generic approach consists in solving a simpler problem with analytic results to approximate the optimal initial adjoints in the full problem, but they are only limited to impulsive transfers. The application of this approach is here extended; a new homotopic structure is developed and applied to the optimization of low‐thrust trajectories.…”

Section: Introductionmentioning

confidence: 99%

No‐guess indirect optimization of asteroid mission using electric propulsion

Shen

2018

Optim Control Appl Methods

Self Cite

View full text Add to dashboard Cite

Summary This paper researches the optimal opportunities and trajectories for an asteroid‐Earth return mission and compares different options in terms of time length and reentry velocity. High specific impulse and steering capabilities of solar electric propulsion are exploited to perform deep space maneuvers. An indirect method based on the theory of optimal control is applied to find the trajectory that maximizes the final mass. The boundary value problem that arises from the application of the optimal control theory is solved by means of a shooting procedure based on Newton's method. In particular, the best opportunities to reach the Earth are first analyzed by searching a time‐free transfer that intercepts the Earth's orbit at the most favorable point; suitable launch windows are then determined. This technique shows significant benefit to define the initial solution that is required to start the optimization process so that no initial guess of adjoints is required for the optimization. Mission opportunities returning from asteroid Bennu (101955) are presented.

show abstract

Global Search Capabilities of Indirect Methods for Impulsive Transfers

Cited by 13 publications

References 20 publications

How Many Impulses Redux

How Many Impulses Redux

DDPG-Based Convex Programming Algorithm for the Midcourse Guidance Trajectory of Interceptor

No‐guess indirect optimization of asteroid mission using electric propulsion

Contact Info

Product

Resources

About