Nonlinear observer for 3D rigid body motion

Finite-time control for spacecraft body-fixed hovering over an asteroid

“…Let (g, ξ ) ∈ SE(3) × R 6 denote the states (configuration and velocities) of the spacecraft. Given the asteroid trajectory generated by (8) and (13), the desired states of the spacecraft are g 0d = g 0 (h f ) and ξ 0d = Ad (h f ) −1 ξ 0 for t ≥ t 0 , (38) and the configuration error between the spacecraft and the asteroid is…”

“…Given η = [ T β T ] T ∈ R 6 , the function G(η) can be expressed as a block-triangular matrix, as follows [38]:…”

“…The desired state trajectory of the spacecraft required to maintain the formation is given by the desired configuration g 0 and its time derivative, which gives the desired velocities ξ 0 = Ad (h f ) −1 ξ 0 as in (38). Let us denote the desired state trajectory for time t ≥ t 0 by the desired position vector in the inertial frame b 0 (t), the desired attitude R 0 (t), and the desired translational and angular velocity in the body frame, ν 0 (t) and 0 (t).…”

“…The feedback system given by (43) and (49) and the control scheme in (50) globally stabilizes (η,ξ ) = (0, 0) ∈ R 6 × R 6 and therefore tracks the trajectory (g, ξ ) = (g 0 , ξ 0 ) given by (38) in finite time. Moreover, the domain of attraction of this trajectory is almost global over the state space…”

Adaptive fuzzy finite-time control for spacecraft formation with communication delays and changing topologies

“…In order to describe the 6-DOF relative-motion in a united framework and facilitate the controller synthesis work, constructing coupled dynamics by the relative position and attitude described on the Lie group SE (3) has been an effective tool and received increasing attention in [2], [10][11][12][13][14][15]. In [2], a sliding mode control scheme on the coupled dynamics on SE(3) was presented to achieve the desired formation with respect to the virtual leader whose trajectory was computed offline.…”