Optimal Steering for North-South Stationkeeping of Geostationary Spacecraft

Kechichian, Jean Albert

doi:10.2514/2.4094

Cited by 15 publications

(2 citation statements)

References 6 publications

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“…The formulation of a "Zermelo TCM" problem may not be satisfactory due to linearizations. Rather than linearize equations and limit its scope to two-dimensions, the dynamics for a generic Zermelo problem can be posed as,ẋ = f 0 (x) + u (23) where f 0 is the drift vector field. Equation (16) fits this description directly when we let x = (r, v).…”

Section: Finally the Quantity B(t) In (20) Denotes The Remainder Of Tmentioning

confidence: 99%

Unscented Optimal Control for Orbital and Proximity Operations in an Uncertain Environment: A New Zermelo Problem

Ross

Proulx

Karpenko

2014

AIAA/AAS Astrodynamics Specialist Conference

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Orbital and proximity operations in an uncertain environment are critical technology requirements for NASA's asteroid retrieval mission and the OSIRIS-REx program. One approach for establishing orbits around a body with an uncertain gravity field is to use the concept of operations employed in the NEAR-Shoemaker mission. Such operations may not be easily or cost-effectively portable to highly irregularly-shaped asteroids that may be in a tumbling state. In this paper, we propose the concept of unscented optimal control to design safe guidance commands that can produce orbits with guaranteed safety margins. Unscented optimal control is based on combining the concept of the unscented transform with standard optimal control to produce a new approach for enabling an open-loop management of navigational, gravitational and other uncertainties. Many space operations problems in an uncertain environment can be conceptualized as Zermelo-type problems with uncertain currents. Under this backdrop, a collection of uncertain Zermelo problems is discussed using unscented optimal control. Results show dramatic improvements in performance including the case of near-zero targeting errors under uncertainty.

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Section: Finally the Quantity B(t) In (20) Denotes The Remainder Of Tmentioning

confidence: 99%

Unscented Optimal Control for Orbital and Proximity Operations in an Uncertain Environment: A New Zermelo Problem

Ross

Proulx

Karpenko

2014

AIAA/AAS Astrodynamics Specialist Conference

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“…According to the historical and technical review by Serres [57], E. Zermelo formulated his famous problem in 1931 in connection with the steering of a ship in a wind vector field. Since then, the problem has been connected to other problems in disparate fields including many in aerospace engineering: North-South stationkeeping of a spacecraft [58,59], control of an electrodynamic tether [60], and proximity operations for relative motion [14]. The differential equations for Zermelo's problem can be written as,…”

Section: A Step 1: a Baseline Deterministic Zermelo Problem Formulati...mentioning

confidence: 99%

Monte Rey Methods for Unscented Optimization

Ross

Proulx

Karpenko

2016

AIAA Guidance, Navigation, and Control Conference

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In a nutshell, unscented trajectory optimization is the generation of optimal trajectories through the use of an unscented transform. Although unscented trajectory optimization was introduced by the authors about a decade ago, it is reintroduced in this paper as a special instantiation of tychastic optimal control theory. Tychastic optimal control theory (from Tyche, the Greek goddess of chance) avoids the use of a Brownian motion and the resulting Itô calculus even though it uses random variables across the entire spectrum of a problem formulation. This approach circumvents the enormous technical and numerical challenges associated with stochastic trajectory optimization. Furthermore, it is shown how a tychastic optimal control problem that involves nonlinear transformations of the expectation operator can be quickly instantiated using an unscented transform. These nonlinear transformations are particularly useful in managing trajectory dispersions be it associated with path constraints or targeted values of final-time conditions. This paper also presents a systematic and rapid process for formulating and computing the most desirable tychastic trajectory using an unscented transform. Numerical examples are used to illustrate how unscented trajectory optimization may be used for risk reduction and mission recovery caused by uncertainties and failures.

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Semianalytical Study of Geosynchronous Orbits About a Precessing Oblate Earth Under Lunisolar Gravitation and Tesseral Resonance

Belyanin

Gurfil

2009

J of Astronaut Sci

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Previous studies of geosynchronous orbits indicated that the equinoctial precession (EP) of the Earth affects the long-term behavior of geosynchronous satellites for missions exceeding ten years. However, these studies did not include the lunisolar gravitation and tesseral resonance. In the present study, a model that includes the latter effects is developed. In particular. it is shown that the EP affects motion in the vicinity of the stable and unstable geostationary points. This effect is pronounced in the vicinity of the unstable points, shifting the satellite away from the geosynchronous altitude. Moreover, it is shown that secular inclination growth on lime scales of 10-20 years is induced by the EP. This requires additional stationkeeping maneuvers that may increase the overall fuel usage by about 1%, An additional contribution of the present study is an analysis of EP-perturbed orbits with free inclination drift. An optimal initial node location, minimizing the incl ination drift, is calculated while ta king into account the effect of the EP. It is shown that the classical optimal initial node locations are changed due to the effect of the EP. A maneuvering program in the presence of EP is developed. It is shown that the timing and number of station keeping maneuvers is affected by the EP. The models developed herein utilize non-singular orbital elements.

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Optimal Steering for North-South Stationkeeping of Geostationary Spacecraft

Cited by 15 publications

References 6 publications

Unscented Optimal Control for Orbital and Proximity Operations in an Uncertain Environment: A New Zermelo Problem

Unscented Optimal Control for Orbital and Proximity Operations in an Uncertain Environment: A New Zermelo Problem

Monte Rey Methods for Unscented Optimization

Semianalytical Study of Geosynchronous Orbits About a Precessing Oblate Earth Under Lunisolar Gravitation and Tesseral Resonance

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