Rigid-Body Attitude Control

Rigid-body attitude control is motivated by aerospace applications that involve attitude maneuvers or attitude stabilization. The set of attitudes of a rigid body is the set of 3 X 3 orthogonal matrices whose determinant is one. This set is the configuration space of rigid-body attitude motion; however, this configuration space is not Euclidean. Since the set of attitudes is not a Euclidean space, attitude control is typically studied using various attitude parameterizations. Motivated by the desire to represent attitude both globally and uniquely in the analysis of rigid-body rotational motion, this article uses orthogonal matrices exclusively to represent attitude and to develop results on rigid-body attitude control. An advantage of using orthogonal matrices is that these control results, which include open-loop attitude control maneuvers and stabilization using continuous feedback control, do not require reinterpretation on the set of attitudes viewed as orthogonal matrices. The main objec tive of this article is to demonstrate how to characterize properties of attitude control systems for arbitrary attitude maneuvers without using attitude parameterizations.

[1]  J. Stuelpnagel.  On the Parametrization of the Three-Dimensional Rotation Group , 1964 .

[2]  R. Mortensen.  A globally stable linear attitude regulator , 1968 .

[3]  G. Meyer,et al.  DESIGN AND GLOBAL ANALYSIS OF SPACECRAFT ATTITUDE CONTROL SYSTEMS , 1971 .

[4]  P. Holmes,et al.  Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields , 1983, Applied Mathematical Sciences.

[5]  P. Crouch,et al.  Spacecraft attitude control and stabilization: Applications of geometric control theory to rigid body models , 1984 .

[6]  Bong Wie,et al.  Quaternion feedback for spacecraft large angle maneuvers , 1985 .

[7]  J. Junkins,et al.  Optimal Spacecraft Rotational Maneuvers , 1986 .

[8]  P. Hughes.  Spacecraft Attitude Dynamics , 1986 .

[9]  Haim Weiss,et al.  Quarternion feedback regulator for spacecraft eigenaxis rotations , 1989 .

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

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

[12]  M. Shuster.  A survey of attitude representation , 1993 .

[13]  Ralph E. Bach,et al.  Linearization of attitude-control error dynamics , 1993, IEEE Trans. Autom. Control..

[14]  Panagiotis Tsiotras,et al.  Spin-axis stabilization of symmetric spacecraft with two control torques , 1994 .

[15]  Richard M. Murray,et al.  A Mathematical Introduction to Robotic Manipulation , 1994 .

[16]  Augusto Sarti,et al.  Control on the Sphere and Reduced Attitude Stabilization , 1995 .

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

[18]  Panagiotis Tsiotras,et al.  A novel approach to the attitude control of axisymmetric spacecraft , 1995, Autom..

[19]  Wei Kang,et al.  Nonlinear H∞ control and its application to rigid spacecraft , 1995, IEEE Trans. Autom. Control..

[20]  Frank C. Park,et al.  A geometric approach to global attitude stabilization , 1996 .

[21]  Marcel J. Sidi,et al.  Spacecraft Dynamics and Control: A Practical Engineering Approach , 1997 .

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

[23]  F. Park,et al.  Geometry and Inverse Optimality in Global Attitude Stabilization , 1998 .

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

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

[26]  D. Bernstein,et al.  Dynamics and control of a 3D pendulum , 2004, 2004 43rd IEEE Conference on Decision and Control (CDC) (IEEE Cat. No.04CH37601).

[27]  A. D. Lewis,et al.  Geometric Control of Mechanical Systems , 2004, IEEE Transactions on Automatic Control.

[28]  N.H. McClamroch,et al.  Stabilization of a 3D rigid pendulum , 2005, Proceedings of the 2005, American Control Conference, 2005..

[29]  N.A. Chaturvedi,et al.  Global Stabilization of an Inverted 3D Pendulum including Control Saturation Effects , 2006, Proceedings of the 45th IEEE Conference on Decision and Control.

[30]  E. Hairer,et al.  Geometric Numerical Integration , 2022, Oberwolfach Reports.

[31]  N. Harris McClamroch,et al.  Asymptotic stabilization of the hanging equilibrium manifold of the 3D pendulum , 2007 .

[32]  N.A. Chaturvedi,et al.  Stabilization of a Specified Equilibrium in the Inverted Equilibrium Manifold of the 3D Pendulum , 2007, 2007 American Control Conference.

[33]  Dennis S. Bernstein,et al.  Stabilization of a 3D axially symmetric pendulum , 2008, Autom..

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

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

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

[37]  Ricardo G. Sanfelice,et al.  Robust global asymptotic attitude stabilization of a rigid body by quaternion-based hybrid feedback , 2009, Proceedings of the 48h IEEE Conference on Decision and Control (CDC) held jointly with 2009 28th Chinese Control Conference.

[38]  Dennis S. Bernstein,et al.  Asymptotic Smooth Stabilization of the Inverted 3-D Pendulum , 2009, IEEE Transactions on Automatic Control.

[39]  N. Harris McClamroch,et al.  Asymptotic Stabilization of the Inverted Equilibrium Manifold of the 3-D Pendulum Using Non-Smooth Feedback , 2009, IEEE Transactions on Automatic Control.

[40]  Amit K. Sanyal,et al.  A Robust Estimator for Almost Global Attitude Feedback Tracking , 2010 .

[41]  Taeyoung Lee,et al.  Nonlinear Dynamics of the 3D Pendulum , 2011, J. Nonlinear Sci..