Equal distribution of satellite constellations on circular target orbits

This paper addresses the problem of equal distribution of satellite constellations on circular target orbits. The control goal is to make the constellation converge to a circular target orbit, while spatially distributing the satellites at equal inter-satellite distances. The solution is defined in the port-Hamiltonian framework, which gives a clear physical interpretation of the obtained control laws, insight into the energy consumption and complete stability proofs. The controller consists of two parts: the internal control system steers each individual satellite to the target orbit, the external control system equally distributes the satellite constellation. Numerical simulation results are given to illustrate the effectiveness of the approach.

[1]  A. Schaft.  L2-Gain and Passivity Techniques in Nonlinear Control. Lecture Notes in Control and Information Sciences 218 , 1996 .

[2]  C. McInnes.  Autonomous ring formation for a planar constellation of satellites , 1995 .

[3]  Kazunori Sakurama,et al.  Trajectory tracking control of port-controlled Hamiltonian systems via generalized canonical transformations , 2001, Autom..

[4]  A. Schaft,et al.  L2-Gain and Passivity in Nonlinear Control , 1999 .

[5]  Daniele Zonetti,et al.  Port Hamiltonian modeling of power networks , 2012 .

[6]  Jacquelien M.A. Scherpen,et al.  Control for formation flying of satellites: port-Hamiltonian approach , 2013 .

[7]  S. Ploen,et al.  A survey of spacecraft formation flying guidance and control (part 1): guidance , 2003, Proceedings of the 2003 American Control Conference, 2003..

[8]  Arjan van der Schaft,et al.  Port-Hamiltonian Systems on Graphs , 2011, SIAM J. Control. Optim..

[9]  Max Donath,et al.  American Control Conference , 1993 .

[10]  van der Arjan Schaft,et al.  International Symposium on Mathematical Theory of Networks and Systems , 2012 .

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

[12]  Soon-Jo Chung,et al.  Application of Synchronization to Formation Flying Spacecraft: Lagrangian Approach , 2008, 0803.0170.

[13]  Béla Bollobás,et al.  Modern Graph Theory , 2002, Graduate Texts in Mathematics.

[14]  Romeo Ortega,et al.  Putting energy back in control , 2001 .

[15]  F.Y. Hadaegh,et al.  A survey of spacecraft formation flying guidance and control. Part II: control , 2004, Proceedings of the 2004 American Control Conference.

[16]  Stefano Stramigioli,et al.  Modeling and Control of Complex Physical Systems - The Port-Hamiltonian Approach , 2014 .

[17]  T. Sugie,et al.  Canonical transformation and stabilization of generalized Hamiltonian systems , 1998 .

[18]  Jacquelien M.A. Scherpen,et al.  Spatial distribution of satellite constellations on circular orbits , 2013, CDC 2013.

[19]  Per Johan Nicklasson,et al.  Spacecraft formation flying: A review and new results on state feedback control , 2009 .

[20]  Richard G. Cobb,et al.  TechSat 21 - Space Missions using Collaborating Constellations of Satellites , 1998 .

[21]  Yuri Ulybyshev.  Long-Term Formation Keeping of Satellite Constellation Using Linear-Quadratic Controller , 1998 .