Geometric interpretation of the Tschauner–Hempel solutions for satellite relative motion

Sinclair, Andrew J.; Sherrill, Ryan E.; Lovell, T. Alan

doi:10.1016/j.asr.2015.01.032

Cited by 21 publications

(10 citation statements)

References 42 publications

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“…Event triggered MPC [61] could be an applicable tool. Also, recent modelling developments (e.g., [62], [63]) could be applied to simplify handling of elliptical orbits. Many of the studies cited in this tutorial assume good quality state estimates with idealised uncertainty models and rigid-body models of the spacecraft.…”

Section: Discussionmentioning

confidence: 99%

A tutorial on model predictive control for spacecraft rendezvous

Hartley

2015

2015 European Control Conference (ECC)

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This tutorial paper provides a review of recent advances in the field of spacecraft rendezvous using model predictive control (MPC), an advanced optimal control strategy based on on-line constrained optimisation of control inputs based on predictions of future trajectories. Firstly, the rendezvous objectives, and the generic constrained MPC problem formulation are summarised. This is followed by a discussion of how to select the three key ingredients used in an MPC design: the prediction model, the constraints and the cost function. Since MPC implementation relies on finding the solution to constrained optimisation problems in real-time, computational aspects are also briefly examined. The paper concludes with conjecture on ways the use of MPC in this application could be further advanced.

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Section: Discussionmentioning

confidence: 99%

A tutorial on model predictive control for spacecraft rendezvous

Hartley

2015

2015 European Control Conference (ECC)

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“…We note that the determinant of Φ(r, v, ν) is equal to (e 2 − 1), so that the matrix is nonsingular for any e ∈ [0, 1). It follows that the values of K can be inferred from rectangular coordinates through the inverse transformation [34]…”

Section: General Solution Of the Keplerian Relative Motion Problemmentioning

confidence: 99%

Long-term evolution of mid-altitude quasi-satellite orbits

et al. 2020

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Quasi-satellite orbits are of great interest for the exploration of planetary moons because of their dynamical features and close proximity with respect to the surface of scientifically relevant objects like Phobos and Deimos. This paper explores the equations of the elliptical Hill problem, offering a new analytical insight into the long-term evolution of mid-altitude quasi-satellite orbits. Our developments are based on the Yamanaka-Ankersen solution of the Tschauner-Hempel equations and capture the effects of the secondary's gravity and orbital eccentricity on the shape and orientation of near-equatorial retrograde relative trajectories. The analytical solution of the in-plane and out-of-plane components of the secular motion is achieved by averaging over the relative longitude of a spacecraft as seen from the co-rotating frame of the two primaries. Developments are validated against the numerical integration of quasi-periodic trajectories that N. Baresi (B)

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“…In this solution, the position and velocity of the chaser depend on an initial true anomaly of the target. Therefore the geometry of the solutions have been extensively studied by some authors [7][8][9]. In [7], the fundamental solutions of the TH equations are interpreted geometrically as generalizations of the well-known solutions of the Hill's equations.…”

Section: Introductionmentioning

confidence: 99%