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Control of a perturbed satellite formation antenna array, with dual quaternion dynamics, is considered. The perturbations and their derivatives are assumed bounded with unknown bounds. The objective of this article is to employ continuous control algorithms which feature adaptive gain nonoverestimation. In this work, three novel dual quaternion-based adaptive continuous sliding mode control algorithms to control a perturbed satellite antenna array are assessed. These methods of adaptive sliding mode control are caspable of handling coupled perturbed systems, such as dual quaternion models. The efficacy of the proposed algorithms is verified via simulations and comparison to the available traditional PD Plus controller and classical sliding mode control methods. [ABSTRACT FROM AUTHOR]

This article aims to investigate the coupled attitude and orbit tracking control problem of rigid spacecraft motion. A proportional-integral (PI)-type event-triggered active disturbance rejection control scheme is proposed for spacecraft coupled attitude and orbit control under the unknown internal uncertainties and external disturbances. First, the relative kinematics and dynamics are established using error dual quaternions to describe the attitude and orbit coupled motion of rigid spacecraft. Then, the PI-type event-triggering schemes are designed to reduce the communication rates between the pose sensors and the observers. Finally, the asymptotic stability of the closed-loop control system is proved. The simulation results show that the proposed closed-loop control system can achieve satisfactory tracking performance and reduce the occupancy of on-board communication resources to ensure the stable operation of the spacecraft. [ABSTRACT FROM AUTHOR]

This article is concerned with the development of two novel Kalman filters for satellite relative pose estimation. The relative pose, which is represented by a dual quaternion, is estimated from noisy lines-of-sight via a single camera, along with biases of linear velocity and angular rate measurements. The constraints on the dual quaternion are handled by brute-force and virtual measurement techniques. The partial reset analysis shows how to propagate the estimation error biases and covariances. Closed-form expressions for the Jacobians are provided. A quantitative observability analysis for the position states is provided. Compared with traditional representations, the dual quaternion model increases the position observability by a factor of four for each line-of-sight. The additive dual quaternion model enhances the observability of the rotation states thanks to a specific coupling term in the pose dynamics. Extensive Monte-Carlo simulations of a flight formation case verify that the proposed novel filters are asymptotically unbiased and statistically consistent for all practical purposes. They outperform the other candidate estimators in particular during the transient phase. The numerical simulations validate the observability analysis. [ABSTRACT FROM AUTHOR]

Rigid motion computation or estimation is a cornerstone in numerous fields. Attitude computation can be achieved by integrating the angular velocity measured by gyroscopes, the accuracy of which is crucially important for the dead-reckoning inertial navigation. The state-of-the-art attitude algorithms have unexceptionally relied on the simplified differential equation of the rotation vector to obtain the attitude. This paper proposes a functional iteration technique with the Rodrigues vector (named the RodFIter method) to analytically reconstruct the attitude from gyroscope measurements. The RodFIter method is provably exact in reconstructing the incremental attitude as long as the angular velocity is exact. Notably, the Rodrigues vector is analytically obtained and can be used to update the attitude over the considered time interval. The proposed method gives birth to an ultimate attitude algorithm scheme that can be naturally extended to the general rigid motion computation. It is extensively evaluated under the attitude coning motion and compares favorably in accuracy with the mainstream attitude algorithms. This paper is believed having eliminated the long-standing theoretical barrier in exact motion integration from inertial measurements. [ABSTRACT FROM AUTHOR]