Improved analytical solutions for relative motion of Lorentz spacecraft with application to relative navigation in low Earth orbit

Abstract

Electrostatically charged spacecraft accelerates when orbiting a central body with magnetic field due to the induced Lorentz force. This Lorentz force could be used as propellantless propulsion for orbital maneuvers. Such spacecraft is referred to as Lorentz spacecraft. Modeling the Earth’s magnetic field as a tilted magnetic dipole rotating with the Earth, this paper first presents the analytical expressions that characterize the orbital motion of Lorentz spacecraft with respect to inclined low Earth orbit. Using the information from line-of-sight observations and gyro measurements, coupled with the proposed dynamical model, both extended and unscented Kalman filter are designed to perform relative navigation for Lorentz spacecraft. Two scenarios are simulated to illustrate the accuracy of derived analytical solutions and the performance of proposed filters, respectively. Through comparison with previous work, the accuracy of relative motion model has proved to be greatly enhanced. Numerical simulation results also show that unscented Kalman filter presents more accurate relative state estimation for Lorentz spacecraft than extended Kalman filter.

Keywords

Lorentz spacecraft inclined low Earth orbit tilted magnetic dipole relative navigation Kalman filter

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References

Peck MA. Prospects and challenges for Lorentz-augmented orbits. In: AIAA guidance, navigation, and control conference and exhibit, San Francisco, CA, August 15–18, 2005, paper no. AIAA-2005-5995.

Peck

Streetman

Saaj

. Spacecraft formation flying using Lorentz forces. J Br Interplanet Soc 2007; 60: 263–267.

Peng

Gao

. Lorentz-force-perturbed orbits with application to J₂-invariant formation. Acta Astronaut 2012; 77: 12–28.

Tsujii

Bando

Yamakawa

. Spacecraft formation flying dynamics and control using the geomagnetic Lorentz force. J Guid Control Dynam 2013; 36: 136–148.

Pollock

Gangestad

Longuski

. Inclination change in low-earth orbit via the geomagnetic Lorentz force. J Guid Control Dynam 2010; 33: 1387–1395.

Streetman

Peck

. New synchronous orbit using the geomagnetic Lorentz force. J Guid Control Dynam 2007; 30: 1677–1690.

Atchison

Peck

. Lorentz-augmented Jovian orbit insertion. J Guid Control Dynam 2009; 32: 418–423.

Gangetad

Pollock

Longuski

. Propellantless stationkeeping at Enceladus via the electromagnetic Lorentz force. J Guid Control Dynam 2009; 32: 1466–1475.

Streetman

Peck

. Gravity-assisted maneuvers augmented by the Lorentz force. J Guid Control Dynam 2009; 32: 1639–1647.

10.

Atchison

Peck

Streetman

. Lorentz acceleration in the earth flyby anomaly. J Guid Control Dynam 2010; 33: 1115–1122.

11.

Gangetad

Pollock

Longuski

. Analytical expressions that characterize propellantless capture with eletrostatically charged spacecraft. J Guid Control Dynam 2011; 34: 247–258.

12.

Streetman

Peck

. General bang-bang control method for Lorentz augmented orbit. J Spacecraft Rockets 2010; 47: 484–492.

13.

LAI

. An overview of electron and ion beam effects in charging and discharging of spacecraft. IEEE Trans Nucl Sci 1989; 36: 2027–2032.

14.

Garrett

Whittlesey

. Spacecraft charging, an update. IEEE Trans Plasma Sci 2000; 28: 2017–2028.

15.

Vokrouhlicky

. The geomagnetic effects on the motion of an electrically charged artificial satellite. Celest Mech Dyn Astr 1989; 46: 85–104.

16.

Clohessy

Wiltshire

. Terminal guidance system for satellite rendezvous. J Aerospace Eng 1960; 27: 653–658.

17.

Tschauner

Hempel

. Optimal beschleunigeungs programme fur das rendezvous-manoeuvre. Astronaut Acta 1964; 10: 296–307.

18.

Pollock GE, Gangestad JW and Longuski JM. Analysis of Lorentz spacecraft motion about earth using the Hill-Clohessy-Wiltshire equations. In: AIAA/AAS astrodynamics specialist conference and exhibit, Honolulu, Hawaii, August 18–21, 2008, paper no. AIAA-2008-6762.

19.

Pollock

Gangestad

Longuski

. Analytical solutions for the relative motion of spacecraft subject to Lorentz-force perturbations. Acta Astronaut 2011; 68: 204–217.

20.

Yamakawa H, Bando M, Yano K, et al. Spacecraft relative dynamics under the influence of geomagnetic Lorentz force. In: AIAA/ASS astrodynamics specialist conference, Toronto, Ontario Canada, August 2–5, 2010, paper no. AIAA-2010-8128.

21.

Kim

Crassidis

Cheng

. Kalman filtering for relative spacecraft attitude and position estimation. J Guid Control Dynam 2007; 30: 133–143.

22.

Sun

Crassidis

. Observability analysis of six-degree-of-freedom configuration determination using vector observations. J Guid Control Dynam 2002; 25: 1149–1157.

23.

Gunnam

Hughes

Junkins

. A vision-based DSP embedded navigation sensor. IEEE Sens J 2002; 2: 428–442.

24.

Xing

Cao

Zhang

. Relative position and attitude estimation for satellite formation with coupled translational and rotational dynamics. Acta Astronaut 2010; 67: 455–467.

25.

Dang

Zhang

. Relative position and attitude estimation for inner-formation gravity measurement satellite system. Acta Astronaut 2011; 69: 514–525.

26.

Tang

Yan

Zhong

. Square-root sigma-point Kalman filtering for spacecraft relative navigation. Acta Astronaut 2010; 66: 704–713.

27.

Crassidis

Markley

. Unscented filtering for spacecraft attitude estimation. J Guid Control Dynam 2003; 26: 536–542.

28.

Julier

Uhlmann

. Unscented filtering and nonlinear estimation. Proc IEEE 2004; 92: 401–422.

29.

Wan

Merwe

. The unscented Kalman filter. Haykin S. Kalman filtering and neural networks, New York: Wiley, 2001, pp. 221–280.