Nonlinear semi-analytical uncertainty propagation of trajectory under impulsive maneuvers

Yang, Zhen; Luo, Yuling; Jin, Zheming

doi:10.1007/s42064-018-0036-7

Cited by 27 publications

(10 citation statements)

References 29 publications

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“…In a similar way, further reduction in velocity range can construct the orbit transfer by more impulses and increase the difficulty of spacecraft orbit maneuver optimization. Nevertheless, uncertain spacecraft trajectory is more likely with the increasing number of impulses [48].…”

Section: Resultsmentioning

confidence: 99%

Hierarchical Optimization Algorithm and Applications of Spacecraft Trajectory Optimization

Shi

Zhao

2022

Aerospace

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The pursuit of excellent performance in meta-heuristic algorithms has led to a myriad of extensive and profound research and achievements. Notably, many space mission planning problems are solved with the help of meta-heuristic algorithms, and relevant studies continue to appear. This paper introduces a hierarchical optimization frame in which two types of particles—B-particles and S-particles—synergistically search for the optima. Global exploration relies on B-particles, whose motional direction and step length are designed independently. S-particles are for fine local exploitation near the current best B-particle. Two specific algorithms are designed according to this frame. New variants of classical benchmark functions are used to better test the proposed algorithms. Furthermore, two spacecraft trajectory optimization problems, spacecraft multi-impulse orbit transfer and the pursuit-evasion game of two spacecraft, are employed to examine the applicability of the proposed algorithms. The simulation results indicate that the hierarchical optimization algorithms perform well on given trials and have great potential for space mission planning.

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Section: Resultsmentioning

confidence: 99%

Hierarchical Optimization Algorithm and Applications of Spacecraft Trajectory Optimization

Shi

Zhao

2022

Aerospace

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“…When a spacecraft is dominated by one force and the orbital state transition matrix can be derived by the linearization hypothesis in some form as affected by an initial state uncertainty or a small orbital maneuver [26][27][28], can be approximately calculated by the state transition matrix which is…”

Section: Type Imentioning

confidence: 99%

Reachable Set Analysis of Practical Trans-Lunar Orbit via a Retrograde Semi-Analytic Model

Sheng-gang

2022

Preprint

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Different from the Apollo flight mode, a safer trans-lunar flight mode for the crews is preferred. The previous-arrived lunar module rendezvous with the crew exploration vehicle on the low lunar destination orbit, and then the crews ride the lunar module for descending the lunar surface destination. The lunar module, which includes the descent and ascent stages, flies from low Earth orbit to the low lunar destination orbit with two tangential impulses. The low lunar destination orbital reachable-set of its practical trans-lunar orbit limits the crew’s lunar surface reachable area. Therefore, the low lunar destination orbital reachable-set of the practical trans-lunar orbit is analyzed in this paper. A retrograde semi-analytic model is proposed for rapidly computing the practical two-impulse trans-lunar orbit firstly, which refers the ephemeris table twice for more precision perilune orbital elements. Then, the envelope of the reachable-set, which is generated using the multiple-level traversal searching approach with the retrograde semi-analytic model, is re-checked by the continuation theory with the high-precision orbital model. Besides, some factors that affect the reachable-set are also measured. The results show that neither the Earth-Moon distance nor the trans-lunar duration affects the reachable-set. However, if the trans-lunar injection inclination is smaller than the inclination of the moon’s path, the reachable-set becomes smaller or even reduces into an empty set. In brief, the proposed retrograde semi-analytic model for computing the reachable-set provides a helpful and fast tool for selecting an applicable lunar surface landing site for the manned lunar mission overall design.

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“…For the first situation, the final mean and covariance matrix can be computed by independently applying the second terms of Eqs. (36) and 41…”

Section: B Covariance Propagation With Deputy Maneuveringmentioning

confidence: 99%

“…It decouples a large uncertainty propagation problem into many small problems, which is an effective methodology to represent a non-Gaussian distribution and to reduce the effects of nonlinearity in dynamics. Moreover, some hybrid methods had also been developed through integrating the advantages of different uncertainty propagators, such as the combined GMM and STTs method [35,36], and the combined GMM and PC method [37]. Recently, a detailed review of orbital uncertainty propagation was given by Luo and Yang [38].…”

Section: Introductionmentioning

confidence: 99%

Nonlinear Analytical Uncertainty Propagation for Relative Motion near J2-Perturbed Elliptic Orbits

Yang

Luo

Lappas

et al. 2018

Journal of Guidance, Control, and Dynamics

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An analytical uncertainty propagation method based on state transition tensors (STTs) has been developed for satellite relative motion near J2-perturbed, elliptic orbits. The STTs used to propagate the relative state uncertainty are derived by adding a correction into the original STTs for propagating relative state. A new set of transitive STTs is further derived in order to propagate uncertainties for relative motion with abrupt state jumps, e.g. impulsive maneuvers executing on any of the two satellites. The nonlinear analytical solution for propagating the first two moments and the probability density function are formulated by combining the STTs with a Gaussian mixture model. Numerical results show that the proposed method outperforms the linear covariance method and provides good agreement with Monte Carlo simulations on nonlinear, non-Gaussian uncertainty propagation. Moreover, as the STTs can be analytically computed and account for the J2-perturbation, the proposed uncertainty propagator is computationally efficient, which will be potentially useful for onboard conjunction analysis in satellites formulation flying mission.

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Nonlinear semi-analytical uncertainty propagation of trajectory under impulsive maneuvers

Cited by 27 publications

References 29 publications

Hierarchical Optimization Algorithm and Applications of Spacecraft Trajectory Optimization

Hierarchical Optimization Algorithm and Applications of Spacecraft Trajectory Optimization

Reachable Set Analysis of Practical Trans-Lunar Orbit via a Retrograde Semi-Analytic Model

Nonlinear Analytical Uncertainty Propagation for Relative Motion near J2-Perturbed Elliptic Orbits

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