Analysis of Non-Linear Attitude Observers for Time-Varying Reference Measurements

This paper provides a comprehensive stability analysis of a suite of nonlinear attitude observers that have been developed over the last few years. The observers considered are based on vectorial measurements of an a priori known reference direction. By treating the reference direction and the measurement in the same analysis framework, and allowing time-variation of either, we are able to define general persistency of excitation criteria that incorporate and generalize convergence criteria used in prior work. A key outcome is conditions that ensure almost global asymptotic and local exponential stability of attitude observers based on a single vector measurement as long as the excitation conditions are met on the reference and system trajectory. The approach generalizes stability results provided in prior work, based on rank conditions, that required at least two or more vector measurements.

[1]  M. Kreĭn,et al.  Stability of Solutions of Differential Equations in Banach Spaces , 1974 .

[2]  Robert E. Mahony,et al.  A nonlinear observer for 6 DOF pose estimation from inertial and bearing measurements , 2009, 2009 IEEE International Conference on Robotics and Automation.

[3]  Alexander Stanoyevitch,et al.  Introduction to Numerical Ordinary and Partial Differential Equations Using MATLAB (Pure and Applied Mathematics: A Wiley-Interscience Series of Texts, Monographs and Tracts) , 2004 .

[4]  Y. Oshman,et al.  Attitude Estimation from Vector Observations Using a Genetic-Algorithm-Embedded Quaternion Particle Filter , 2006 .

[5]  Philippe Martin,et al.  Non-Linear Symmetry-Preserving Observers on Lie Groups , 2007, IEEE Transactions on Automatic Control.

[6]  P. Rouchon,et al.  A non-linear symmetry-preserving observer for velocity-aided inertial navigation , 2006, 2006 American Control Conference.

[7]  E. J. Lefferts,et al.  Kalman Filtering for Spacecraft Attitude Estimation , 1982 .

[8]  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.

[9]  O. Egeland,et al.  Passivity-based adaptive attitude control of a rigid spacecraft , 1994, IEEE Trans. Autom. Control..

[10]  J. L. Farrell,et al.  Attitude determination by kalman filtering , 1970 .

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

[12]  J. Vasconcelos,et al.  A Nonlinear Observer for Rigid Body Attitude Estimation using Vector Observations , 2008 .

[13]  Héctor J. Sussmann,et al.  Single-input observability of continuous-time systems , 1978, Mathematical systems theory.

[14]  John L. Crassidis,et al.  Survey of nonlinear attitude estimation methods , 2007 .

[15]  Robert M. Sanner,et al.  A coupled nonlinear spacecraft attitude controller and observer with an unknown constant gyro bias and gyro noise , 2003, IEEE Trans. Autom. Control..

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

[17]  K. Narendra,et al.  On the uniform asymptotic stability of certain linear nonautonomous differential equations , 1976 .

[18]  Robert E. Mahony,et al.  Attitude estimation on SO[3] based on direct inertial measurements , 2006, Proceedings 2006 IEEE International Conference on Robotics and Automation, 2006. ICRA 2006..

[19]  Abdelhamid Tayebi,et al.  Attitude stabilization of a VTOL quadrotor aircraft , 2006, IEEE Transactions on Control Systems Technology.

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

[21]  Alireza Khosravian,et al.  Globally exponential estimation of satellite attitude using a single vector measurement and gyro , 2010, 49th IEEE Conference on Decision and Control (CDC).

[22]  Pierre Rouchon,et al.  An intrinsic observer for a class of Lagrangian systems , 2003, IEEE Trans. Autom. Control..

[23]  Philippe Martin,et al.  Symmetry-Preserving Observers , 2006, IEEE Transactions on Automatic Control.

[24]  Robert E. Mahony,et al.  Gradient-Like Observers for Invariant Dynamics on a Lie Group , 2008, IEEE Transactions on Automatic Control.

[25]  Rita Cunha,et al.  A nonlinear position and attitude observer on SE(3) using landmark measurements , 2010, Syst. Control. Lett..

[26]  Robert E. Mahony,et al.  Observers for systems with invariant outputs , 2009, 2009 European Control Conference (ECC).

[27]  Robert E. Mahony,et al.  Nonlinear attitude observers on SO(3) for complementary and compatible measurements: A theoretical study , 2009, Proceedings of the 48h IEEE Conference on Decision and Control (CDC) held jointly with 2009 28th Chinese Control Conference.

[28]  Naomi Ehrich Leonard,et al.  Coordinated patterns of unit speed particles on a closed curve , 2007, Syst. Control. Lett..

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

[30]  Hugh F. Durrant-Whyte,et al.  Inertial navigation systems for mobile robots , 1995, IEEE Trans. Robotics Autom..

[31]  S. Salcudean.  A globally convergent angular velocity observer for rigid body motion , 1991 .

[32]  F. Markley,et al.  Nonlinear Attitude Filtering Methods , 2005 .

[33]  Minh-Duc Hua.  Attitude estimation for accelerated vehicles using GPS/INS measurements , 2010 .

[34]  Thor I. Fossen,et al.  A nonlinear observer for GPS and INS integration , 2001, Proceedings of the 40th IEEE Conference on Decision and Control (Cat. No.01CH37228).

[35]  Philippe Martin,et al.  Invariant observers for attitude and heading estimation from low-cost inertial and magnetic sensors , 2007, 2007 46th IEEE Conference on Decision and Control.

[36]  Domenico Campolo,et al.  Inertial/Magnetic Sensors Based Orientation Tracking on the Group of Rigid Body Rotations with Application to Wearable Devices , 2006, 2006 IEEE/RSJ International Conference on Intelligent Robots and Systems.

[37]  Philippe Martin,et al.  An Invariant Observer for Earth-Velocity-Aided Attitude Heading Reference Systems , 2008 .

[38]  F. Markley.  Attitude Error Representations for Kalman Filtering , 2003 .

[39]  J. Hale,et al.  Ordinary Differential Equations , 2019, Fundamentals of Numerical Mathematics for Physicists and Engineers.

[40]  J. Crassidis,et al.  Particle Filtering for Sequential Spacecraft Attitude Estimation , 2004 .