Globally asymptotically stable hybrid observers design on SE (3)

This paper deals with the design of globally asymptotically stable invariant observers on the Special Euclidian group SE(3). First, we propose a generic hybrid estimation scheme (depending on a generic potential function) evolving on SE(3) χ R6 for pose (orientation and position) and velocity-bias estimation. Thereafter, the proposed observer is formulated explicitly in terms of inertial vectors and landmark measurements. Interestingly, the proposed globally asymptotically stable estimator, leads to decoupled translational and rotational error dynamics (in the velocity bias-free case), which is an important feature in practical applications with noisy measurements and disturbances.

[1]  R. Mahony,et al.  Complementary filter design on the Special Euclidean group SE(3) , 2007, 2007 European Control Conference (ECC).

[2]  Taeyoung Lee,et al.  Globally Asymptotically Stable Attitude Observer on SO(3) , 2015, 2015 54th IEEE Conference on Decision and Control (CDC).

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

[4]  Ricardo G. Sanfelice,et al.  Invariance Principles for Hybrid Systems With Connections to Detectability and Asymptotic Stability , 2007, IEEE Transactions on Automatic Control.

[5]  Petros A. Ioannou,et al.  Robust Adaptive Control , 2012 .

[6]  Grant Darren Baldwin,et al.  Inertial vision pose estimation using non-linear observers , 2009 .

[7]  Andrew R. Teel,et al.  Hybrid control of rigid-body attitude with synergistic potential functions , 2011, Proceedings of the 2011 American Control Conference.

[8]  Abdelkader Abdessameud,et al.  A globally exponentially stable hybrid attitude and gyro-bias observer , 2016, 2016 IEEE 55th Conference on Decision and Control (CDC).

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

[10]  Abdelhamid Tayebi,et al.  Construction of Synergistic Potential Functions on SO(3) With Application to Velocity-Free Hybrid Attitude Stabilization , 2015, IEEE Transactions on Automatic Control.

[11]  Bijoy K. Ghosh,et al.  Pose estimation using line-based dynamic vision and inertial sensors , 2003, IEEE Trans. Autom. Control..

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

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

[14]  Robert E. Mahony,et al.  Gradient-like observer design on the Special Euclidean group SE(3) with system outputs on the real projective space , 2015, 2015 54th IEEE Conference on Decision and Control (CDC).

[15]  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.

[16]  Robert E. Mahony,et al.  Observer design on the Special Euclidean group SE(3) , 2011, IEEE Conference on Decision and Control and European Control Conference.

[17]  R. Sanfelice,et al.  Hybrid dynamical systems , 2009, IEEE Control Systems.

[18]  Jorge Dias,et al.  Vision and Inertial Sensor Cooperation Using Gravity as a Vertical Reference , 2003, IEEE Trans. Pattern Anal. Mach. Intell..

[19]  Abdelhamid Tayebi,et al.  Attitude and gyro bias estimation using GPS and IMU measurements , 2017, 2017 IEEE 56th Annual Conference on Decision and Control (CDC).

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

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

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