Distributed situational observer in a displaced orbit: relative dynamics and control

Abstract. We design a distributed situational observer using formation flying in a displaced orbit. The main focus of our investigation is the relative dynamics and control of displaced orbits obtained by low-thrust propulsion. The spatial dynamics in Newtonian form are used to derive the numerical relative motions, and their natural frequencies discovered by eigenvalue decomposition separate from each other at a critical height that differentiates the structural stability, bifurcation, and instability. Using the Jordan decomposition, six fundamental motions are achieved, including the stationary multiequilibria, the periodic oscillations that correspond to the natural frequencies, and the maximum leaving or approaching velocity caused by the different geometric and algebraic multiplicities. Off-axis equilibrium is obtained by a proposed open-loop control, and the motions nearby are proven to be equivalent to the numerical relative motions. The reduced dynamics in Hamiltonian form are used to derive the analytical solutions for linearized relative motions. Bounded relative trajectories with arbitrary initial values are achieved by two extraclosed-loop controls. Using the off-axis equilibrium and resonance of natural frequencies, the applications of a fixed relative baseline vector for interferometric SAR or Fresnel zone lens missions and repeating relative ground tracks for a phased array antenna mission are addressed in terms of the trajectory design.

[1]  Sheng Cheng,et al.  Phased-array antenna system for the MESSENGER deep space mission , 2001, 2001 IEEE Aerospace Conference Proceedings (Cat. No.01TH8542).

[2]  Gerhard Krieger,et al.  Interferometric Synthetic Aperture Radar (SAR) Missions Employing Formation Flying , 2010, Proceedings of the IEEE.

[3]  Ming Xu,et al.  Nonlinear dynamical analysis for displaced orbits above a planet , 2008 .

[4]  A. Srivastava,et al.  Micro-patterned photo-aligned ferroelectric liquid crystal Fresnel zone lens. , 2015, Optics letters.

[5]  Camilla Colombo,et al.  Comparison of Hamiltonian structure-preserving and Floquét mode station-keeping for Libration-point orbits , 2014 .

[6]  Ming Xu,et al.  The J2 invariant relative configuration of spaceborne SAR interferometer for digital elevation measurement , 2010 .

[7]  Wei Wang,et al.  Extreme values of relative distances for spacecraft in elliptic displaced orbits , 2016 .

[8]  Massimiliano Vasile,et al.  Low-Thrust-Enabled Highly-Non-Keplerian Orbits in Support of Future Mars Exploration , 2011 .

[9]  Gerhard Krieger,et al.  TanDEM-X: A Satellite Formation for High-Resolution SAR Interferometry , 2006, IEEE Transactions on Geoscience and Remote Sensing.

[10]  Shuang Li,et al.  Optimal slew path planning for the Sino-French Space-based multiband astronomical Variable Objects Monitor mission , 2018 .

[11]  Hexi Baoyin,et al.  Solar sail formation flying around displaced solar orbits , 2007 .

[12]  Harry Dankowicz,et al.  Some special orbits in the two-body problem with radiation pressure , 1994 .

[13]  Colin R. McInnes,et al.  Dynamics, Stability, and Control of Displaced Non-Keplerian Orbits , 1998 .

[14]  Jonathan P. How,et al.  Spacecraft Formation Flying: Dynamics, Control and Navigation , 2009 .

[15]  Zhigang Zhang,et al.  Deployment research of multi-tethered InSAR system for GMTI mission , 2016, 2016 IEEE International Geoscience and Remote Sensing Symposium (IGARSS).

[16]  Sheng-ping Gong,et al.  Formation around planetary displaced orbit , 2007 .

[17]  Zhaohui Dang,et al.  Linearized relative motion equations through orbital element differences for general Keplerian orbits , 2018, Astrodynamics.

[18]  Ming Xu,et al.  Structure-Preserving Stabilization for Hamiltonian System and its Applications in Solar Sail , 2009 .

[19]  Colin R. McInnes,et al.  Survey of Highly Non-Keplerian Orbits with Low-Thrust Propulsion , 2011 .

[20]  Alessandro Antonio Quarta,et al.  Electric sail elliptic displaced orbits with advanced thrust model , 2017 .

[21]  Wei Wang,et al.  Invariant Manifold and Bounds of Relative Motion Between Heliocentric Displaced Orbits , 2016 .

[22]  D. Scheeres,et al.  Control of Hovering Spacecraft Near Small Bodies: Application to Asteroid 25143 Itokawa , 2005 .

[23]  C. McInnes,et al.  The Existence and Stability of Families of Displacement Two-Body Orbits , 1997 .

[24]  Wei Wang,et al.  Analysis of relative motion in non-Keplerian orbits via modified equinoctial elements , 2016 .

[25]  Daniel J. Scheeres,et al.  Stabilizing Motion Relative to an Unstable Orbit: Applications to Spacecraft Formation Flight , 2003 .

[26]  Colin R. McInnes,et al.  Dynamics and control of displaced periodic orbits using solar sail propulsion , 2006 .

[27]  Colin R. McInnes,et al.  Displaced geostationary orbit design using hybrid sail propulsion , 2011 .

[28]  C. McInnes,et al.  Displaced non-Keplerian orbits using impulsive thrust , 2011 .

[29]  Colin R. McInnes,et al.  Solar Sail Formation Flying for Deep-Space Remote Sensing , 2009 .