Abstract
In this paper, a reaching law-based adaptive fixed-time terminal sliding mode control law, which is used for coupled spacecraft tracking maneuver in the presence of large inertia parametric uncertainties and external disturbances, is proposed. The coupled 6-DOF kinematics and dynamics for spacecraft motion are modeled on Lie group SE(3). The relative configuration is expressed by a local coordinate (exponential coordinate) of SE(3). In order to estimate the inertia parameters and external disturbances, we also propose a novel adaptive update law, which can make the control law be applied without the inertia parameters of the spacecraft a priori. Fixed-time convergence property of the closed-loop feedback system is proved in the framework of Lyapunov. Numerical simulations are performed to demonstrate the performances of the proposed control scheme for coupled spacecraft tracking maneuver.
Highlights
Spacecraft proximity operation plays an important role in a variety of space missions such as space debris removal, space station maintenance and installation, on-orbit spacecraft service, large structure assembly, and spacecraft networking [1, 2], in which position and attitude tracking maneuvers are the key steps requiring to be performed with high control precision
Modeling of coupled rotational and translational relative motions of rigid spacecraft has been receiving great interests in recent years based on different forms, such as dual quaternion [4,5,6,7], three-dimensional (3-D) Euclidean space (Lie group SE(3)) [8,9,10,11], 6-DOF Euler-Lagrange form [12]
In this study, inspired by the adaptive asymptotic stabilization of position and attitude tracking problem that modeled by dual quaternion in Ref. [6], we extend the asymptotic stable control law with dual quaternion to the adaptive fixed-time terminal sliding mode control law on SE(3)
Summary
Spacecraft proximity operation plays an important role in a variety of space missions such as space debris removal, space station maintenance and installation, on-orbit spacecraft service, large structure assembly, and spacecraft networking [1, 2], in which position and attitude tracking maneuvers are the key steps requiring to be performed with high control precision. The proposed adaptive control law and update law can be applied without inertia parameters and upper bounds of external disturbances, which guarantees the relative pose and velocities converging to the origins in fixed time from any given initial state, except that the initial relative error of principal rotation angle is exactly π radian. The contributions of this research are as follows: An adaptive modified fixed-time terminal sliding control law (AMFixed) is proposed for coupled spacecraft tracking maneuver that modeled on SE(3), so that the desired pose and velocities are obtained in fixed time in the presences of large inertia parametric uncertainties and external disturbances. By taking the time derivative of equation (16) and substituting (14) into (8), the velocity tracking error of the follower spacecraft with respect to the leader spacecraft, which is expressed in the follower’s body-fixed frame, is obtained. The coupled translational and rotational error tracking system is composed of the relative kinematics expressed by exponential coordinate (21) and the relative acceleration equation (25)
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