Attitude State Estimation with Multirate Measurements for Almost Global Attitude Feedback Tracking

A state estimation scheme that does not depend on the statistical distribution of bounded measurement noise is presented. This scheme is used to provide state estimates for feedback in an attitude tracking control scheme that exhibits almost global asymptotically stable tracking of a desired attitude trajectory with perfect state measurements. The control and estimation schemes use the global, unique representation of rigid body attitude provided by rotation matrices. Attitude and angular velocity state estimate updates are obtained from discrete multi-rate measurements using a deterministic filtering scheme. Propagation of discrete state estimates is carried out with a Lie group variational integrator, which preserves the orthogonality of rotation matrices during numerical propagation without reprojection. This integrator is also used to numerically simulate the feedback system. The performance of this attitude tracking control scheme is then compared with that of a recently reported quaternion observer-based continuous feedback attitude tracking scheme. This quaternion-based attitude tracking scheme is shown to exhibit unstable, unwinding behavior. Numerical

[1]  F. Markley,et al.  Unscented Filtering for Spacecraft Attitude Estimation , 2003 .

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

[3]  John L. Crassidis,et al.  Minimum Model Error Approach for Attitude Estimation , 1997 .

[4]  J. Norton,et al.  State bounding with ellipsoidal set description of the uncertainty , 1996 .

[5]  A. Sanyal.  Optimal Attitude Estimation and Filtering Without Using Local Coordinates Part I: Uncontrolled and Deterministic Attitude Dynamics , 2005, 2006 American Control Conference.

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

[7]  J. Stuelpnagel,et al.  A Least Squares Estimate of Satellite Attitude (Grace Wahba) , 1966 .

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

[9]  N. McClamroch,et al.  Rigid-Body Attitude Control , 2011, IEEE Control Systems.

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

[11]  Taeyoung Lee,et al.  Attitude maneuvers of a rigid spacecraft in a circular orbit , 2006, 2006 American Control Conference.

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

[13]  Nikolaj Nordkvist,et al.  Attitude feedback tracking with optimal attitude state estimation , 2010, Proceedings of the 2010 American Control Conference.

[14]  Robert E. Mahony,et al.  Nonlinear Complementary Filters on the Special Orthogonal Group , 2008, IEEE Transactions on Automatic Control.

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

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

[17]  I. Bar-Itzhack.  New Method for Extracting the Quaternion from a Rotation Matrix , 2000 .

[18]  Amit K. Sanyal,et al.  An Almost Global Tracking Control Scheme for Maneuverable Autonomous Vehicles and its Discretization , 2011, IEEE Transactions on Automatic Control.

[19]  M. Shuster,et al.  Three-axis attitude determination from vector observations , 1981 .

[20]  G. Wahba.  A Least Squares Estimate of Satellite Attitude , 1965 .

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

[22]  Carlos Silvestre,et al.  A Nonlinear GPS/IMU based observer for rigid body attitude and position estimation , 2008, 2008 47th IEEE Conference on Decision and Control.

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

[24]  Xiaoming Hu,et al.  Drift-free attitude estimation for accelerated rigid bodies , 2004, Autom..

[25]  Jordan M. Berg,et al.  Intrinsic Observer-Based Stabilization for Simple Mechanical Systems on Lie Groups , 2005, SIAM J. Control. Optim..

[26]  Anthony M. Bloch,et al.  Stability and stabilization of relative equilibria of dumbbell bodies in central gravity , 2005 .

[27]  J. Marsden,et al.  Discrete mechanics and variational integrators , 2001, Acta Numerica.

[28]  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..

[29]  M. Innocenti,et al.  Stability considerations in quaternion attitude control using discontinuous Lyapunov functions , 2004 .

[30]  Uri Shaked,et al.  A game theory approach to robust discrete-time H∞-estimation , 1994, IEEE Trans. Signal Process..

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

[32]  Elizabeth Dimmitt Gregory.  A comparison study of state estimators for a spherical pendulum , 2011 .

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

[34]  Abdelhamid Tayebi,et al.  Unit Quaternion-Based Output Feedback for the Attitude Tracking Problem , 2008, IEEE Transactions on Automatic Control.

[35]  J. Marsden,et al.  Introduction to mechanics and symmetry , 1994 .

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

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

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

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

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