Attitude Tracking Control of a Small Satellite in Low Earth Orbit

In this paper, we modify and apply a robust almost global attitude tracking control scheme to the model of a small satellite. The control scheme, which has been reported in prior literature, is modified to take into account the actuator constraints and actuator configuration of this satellite, which are based on a small satellite currently being developed at the University of Hawaii. The actuators consist of three magnetic torquers and one small reaction wheel. The mass and inertia properties correspond to the known values for this satellite. The satellite is in circular low earth orbit of altitude 600 km and its dynamics model includes gravity, atmospheric and geomagnetic eects. The control strategy used here achieves almost global asymptotically stable attitude trajectory tracking, which implies that the desired attitude trajectory is tracked from all initial conditions on the state except for those that lie on a zero-volume subset within the state space. The continuous feedback control law is also globally defined. Feedback control gains are continuously varied based on known actuator constraints and tracking errors. The almost global asymptotic tracking property can be shown using a generalized Lyapunov analysis on the nonlinear state space of the attitude dynamics. The control torque obtained from this almost-globally-stabilizing feedback control law is partitioned so that each actuator generates a part of this control torque that is within its saturation limits. The control law for the reaction wheel has a singularity when the reaction wheel axis is perpendicular to the local geomagnetic field. To avoid actuator saturation, the control inputs to the actuators are kept constant whenever any actuator reaches a certain fraction of its saturation value. Numerical simulation results for two de-tumbling maneuvers, one where the control law singularity does not appear and one where it does, confirm that the desired attitude trajectory is tracked almost globally.

[1]  P. Tsiotras.  Stabilization and optimality results for the attitude control problem , 1996 .

[2]  Taeyoung Lee,et al.  Global optimal attitude estimation using uncertainty ellipsoids , 2006, Syst. Control. Lett..

[3]  D. Drob,et al.  Nrlmsise-00 Empirical Model of the Atmosphere: Statistical Comparisons and Scientific Issues , 2002 .

[4]  J. Cortés.  Discontinuous dynamical systems , 2008, IEEE Control Systems.

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

[6]  Rajesh Rajamani,et al.  Vehicle dynamics and control , 2005 .

[7]  Bong Wie,et al.  Space Vehicle Dynamics and Control , 1998 .

[8]  N. McClamroch,et al.  A lie group variational integrator for the attitude dynamics of a rigid body with applications to the 3D pendulum , 2005, Proceedings of 2005 IEEE Conference on Control Applications, 2005. CCA 2005..

[9]  Ashish Tewari,et al.  Optimal nonlinear tracking of spacecraft attitude maneuvers , 2004, IEEE Transactions on Control Systems Technology.

[10]  D. Bernstein,et al.  Inertia-Free Spacecraft Attitude Tracking with Disturbance Rejection and Almost Global Stabilization , 2009 .

[11]  Dennis S. Bernstein,et al.  Adaptive Asymptotic Tracking of Spacecraft Attitude Motion with Inertia Matrix Identification , 1998 .

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

[13]  John L. Crassidis,et al.  Optimal Variable-Structure Control Tracking of Spacecraft Maneuvers , 1999 .

[14]  N. McClamroch,et al.  Almost global attitude stabilization of an orbiting satellite including gravity gradient and control saturation effects , 2006, 2006 American Control Conference.

[15]  D. Koditschek.  The Application of Total Energy as a Lyapunov Function for Mechanical Control Systems , 1989 .

[16]  R. M. Wilson,et al.  Book Reviews: Harold L. Herber, Teaching Reading in Content Areas (Second Edition). Englewood Cliffs, N.J.: Prentice Hall, 1978. , 1979 .

[17]  E. M. Lifshitz,et al.  Mechanics. Second edition. , 1969 .

[18]  A. Sanyal,et al.  Almost Global Robust Attitude Tracking Control of Spacecraft in Gravity , 2008 .

[19]  Warren E. Dixon,et al.  Nonlinear Control of Engineering Systems , 2002 .

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

[21]  N.H. McClamroch,et al.  Nonlinear Control of Engineering Systems: A Lyapunov-Based Approach - [Book Review] , 2005, IEEE Control Systems.

[22]  Warren E. Dixon,et al.  Nonlinear Control of Engineering Systems: A Lyapunov-Based Approach , 2003 .

[23]  Garrett Ito,et al.  Geodynamics, Second Edition , 2003 .

[24]  J. Wen,et al.  Robust attitude stabilization of spacecraft using nonlinear quaternion feedback , 1995, IEEE Trans. Autom. Control..

[25]  A. Bloch,et al.  Nonholonomic Mechanics and Control , 2004, IEEE Transactions on Automatic Control.

[26]  I.I. Hussein,et al.  A Discrete Variational Integrator for Optimal Control Problems on SO(3) , 2006, Proceedings of the 45th IEEE Conference on Decision and Control.