Formation Modelling and 6DOF Spacecraft Coordination Control

In this paper we present a 6DOF Euler-Lagrange model formulation of relative translation and rotation in a leader-follower spacecraft formation. To show the applicability of the model, we also present a solution to the problem of relative translational and rotational tracking, using the concept of vectorial integrator backstepping. The controller solution utilizes the quaternion representation to achieve a shorter rotation path on commanded attitude changes, and the equilibrium points in the closed-loop system are proved to be uniformly asymptotically stable. Finally, simulation results are presented to show the performance of the derived control law, together with the impact of orbital perturbations when these are left uncompensated.

[1]  W. H. Clohessy,et al.  Terminal Guidance System for Satellite Rendezvous , 2012 .

[2]  P. Wang,et al.  Synchronized Formation Rotation and Attitude Control of Multiple Free-Flying Spacecraft , 1997 .

[3]  Oliver Montenbruck,et al.  Satellite Orbits: Models, Methods and Applications , 2000 .

[4]  Thor I. Fossen,et al.  Marine Control Systems Guidance, Navigation, and Control of Ships, Rigs and Underwater Vehicles , 2002 .

[5]  Antonio Loria,et al.  Output Feedback Control of Relative Translation in a Leader-Follower Spacecraft Formation , 2006 .

[6]  J. Wen,et al.  The attitude control problem , 1991 .

[7]  R. Battin.  An introduction to the mathematics and methods of astrodynamics , 1987 .

[8]  R. Kristiansen,et al.  Quaternion-Based Backstepping Control of Relative Attitude in a Spacecraft Formation , 2006, Proceedings of the 45th IEEE Conference on Decision and Control.

[9]  F. Y. Hadaegh,et al.  A model predictive control-based approach for spacecraft formation keeping and attitude control , 1999, Proceedings of the 1999 American Control Conference (Cat. No. 99CH36251).

[10]  P. Wang,et al.  Coordination and control of multiple microspacecraft moving in formation , 1996 .

[11]  V. Kapila,et al.  Output feedback control for spacecraft formation flying with coupled translation and attitude dynamics , 2005, Proceedings of the 2005, American Control Conference, 2005..

[12]  J. Junkins,et al.  Analytical Mechanics of Space Systems , 2003 .

[13]  Marcel J. Sidi,et al.  Spacecraft Dynamics and Control: Contents , 1997 .

[14]  Christopher D. Hall,et al.  Spacecraft Dynamics and Control , 2002 .

[15]  Jan Tommy Gravdahl,et al.  A model of relative translation and rotation in leader-follower spacecraft formations , 2007 .

[16]  Jan Tommy Gravdahl,et al.  Modeling and simulation for automatic control , 2002 .

[17]  Hassan K. Khalil,et al.  Nonlinear Systems Third Edition , 2008 .

[18]  S. Bhat,et al.  A topological obstruction to continuous global stabilization of rotational motion and the unwinding phenomenon , 2000 .

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

[20]  Romeo Ortega,et al.  Passivity-based Control of Euler-Lagrange Systems , 1998 .

[21]  G. Hill.  Researches in the Lunar Theory , 1878 .

[22]  James R. Wertz,et al.  Spacecraft attitude determination and control , 1978 .

[23]  Vikram Kapila,et al.  Adaptive nonlinear control for spacecraft formation flying with coupled translational and attitude dynamics , 2001, Proceedings of the 40th IEEE Conference on Decision and Control (Cat. No.01CH37228).

[24]  Guang Yang,et al.  Nonlinear dynamics, trajectory generation, and adaptive control of multiple spacecraft in periodic relative orbits , 2000 .