Distributed formation control of the special Euclidean group SE(2) via global orientation control

On the state independency and log-linearity of error propagation for discrete group affine systems with application to attitude estimation

“…Motivated by the estimation and control of engineering physical systems in aerospace and robotics applications, the study of analytical dynamics on Lie groups has been an active topic for past two decades Barfoot and Furgale (2017); Zhang et al (2021aZhang et al ( , 2021b. Many physical dynamical models carry symmetric structures that are invariant under transformation by a symmetry group, which is expressed as the invariance property of systems on matrix Lie groups Mahony et al (2013) and Lee et al (2020). Taking into account this geometry property of Lie groups would lead to well-posed problems and boost the estimation and control performance for physical systems on matrix Lie groups Vasconcelos et al (2010), Grip et al (2015); Menegaz et al (2019).…”

Covariance regulation based invariant Kalman filtering for attitude estimation on matrix Lie groups

“…Attitude estimation is a benchmark problem in aerospace, satellite and robotics engineering and, recently, building the attitude dynamics and kinematics on matrix Lie groups has been actively investigated [1][2][3][4]. In the past decades, researchers have defined Lie groups states to describe the attitude motion of rigid targets and develop various Kalman filters for Lie groups systems [1,5].…”

“…Attitude estimation is a benchmark problem in aerospace, satellite and robotics engineering and, recently, building the attitude dynamics and kinematics on matrix Lie groups has been actively investigated [1][2][3][4]. In the past decades, researchers have defined Lie groups states to describe the attitude motion of rigid targets and develop various Kalman filters for Lie groups systems [1,5]. Note that, practical attitude systems are usually corrupted by noisy disturbances; the observation noise statistics can be obtained by offline tests, but it is difficult to accurately determine the statistics parameter of process noise covariance in advance, which makes great trouble for the implementation of Kalman type Lie groups estimators [6,7].…”

Adaptive invariant Kalman filtering for attitude estimation on SO (3) thorough feedback calibration of prior error covariance

“…Motivated by the navigation and control of aerospace engineering and robotics applications, the dynamics and kinematics of Lie groups have been actively studied for the past decade [1][2][3][4][5][6].…”

“…Motivated by the navigation and control of aerospace engineering and robotics applications, the dynamics and kinematics of Lie groups have been actively studied for the past decade [1][2][3][4][5][6]. The attitude estimation problem whose states evolve into Lie groups with invariance properties is a benchmark and motivating application, and various Kalman type filtering methods have been developed by researchers for attitude estimation [7,8], target tracking and so on [9,10].…”