Nonlinear Observers for Stereo-Vision-Aided Inertial Navigation

This paper considers the problem of attitude, position and linear velocity estimation for rigid body systems, relying on an inertial measurement unit (IMU) and a stereo vision system. We provide a generic stability result for a class of nonlinear time-varying systems evolving on SO(3)×Rn, which is used for the development of two nonlinear observers, guaranteeing almost global asymptotic stability and local exponential stability, for autonomous systems evolving in a 3-dimensional space. The first observer considers stereo bearing measurements of a single landmark, while the second one uses stereo bearing measurements of multiple landmarks. Two numerical examples are provided to illustrate the performance of the proposed observers.

[1]  Tarek Hamel,et al.  Position estimation from direction or range measurements , 2017, Autom..

[2]  Axel Barrau,et al.  Invariant particle filtering with application to localization , 2014, 53rd IEEE Conference on Decision and Control.

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

[4]  Miaomiao Wang,et al.  A Globally Exponentially Stable Nonlinear Hybrid Observer for 3D Inertial Navigation , 2018, 2018 IEEE Conference on Decision and Control (CDC).

[5]  Miaomiao Wang,et al.  Globally asymptotically stable hybrid observers design on SE (3) , 2017, 2017 IEEE 56th Annual Conference on Decision and Control (CDC).

[6]  Robert E. Mahony,et al.  Observers for invariant systems on Lie groups with biased input measurements and homogeneous outputs , 2015, Autom..

[7]  Roland Siegwart,et al.  The EuRoC micro aerial vehicle datasets , 2016, Int. J. Robotics Res..

[8]  Abdelhamid Tayebi,et al.  Hybrid Pose and Velocity-Bias Estimation on $SE(3)$ Using Inertial and Landmark Measurements , 2019, IEEE Transactions on Automatic Control.

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

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

[11]  Minh-Duc Hua,et al.  Riccati Observer Design for Pose, Linear Velocity and Gravity Direction Estimation Using Landmark Position and IMU Measurements , 2018, 2018 IEEE Conference on Control Technology and Applications (CCTA).

[12]  Richard S. Bucy,et al.  The Riccati Equation and Its Bounds , 1972, J. Comput. Syst. Sci..

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

[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]  Tarek Hamel,et al.  Riccati Observers for the Nonstationary PnP Problem , 2018, IEEE Transactions on Automatic Control.

[16]  Stergios I. Roumeliotis,et al.  A Multi-State Constraint Kalman Filter for Vision-aided Inertial Navigation , 2007, Proceedings 2007 IEEE International Conference on Robotics and Automation.

[17]  Abdelkader Abdessameud,et al.  Hybrid Attitude and Gyro-Bias Observer Design on $SO(3)$ , 2017, IEEE Transactions on Automatic Control.

[18]  Stergios I. Roumeliotis,et al.  Vision-Aided Inertial Navigation for Spacecraft Entry, Descent, and Landing , 2009, IEEE Transactions on Robotics.

[19]  Richard S. Bucy,et al.  Global Theory of the Riccati Equation , 1967, J. Comput. Syst. Sci..

[20]  Abdelhamid Tayebi,et al.  Hybrid Nonlinear Observers for Inertial Navigation Using Landmark Measurements , 2019, IEEE Transactions on Automatic Control.

[21]  Axel Barrau,et al.  The Invariant Extended Kalman Filter as a Stable Observer , 2014, IEEE Transactions on Automatic Control.

[22]  Tarek Hamel,et al.  Observers for Position Estimation Using Bearing and Biased Velocity Information , 2017 .