Unscented Kalman filter and control on TSE(3)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathsf {TSE(3)}$$\end{document} with application to spacecraft dynamics

This paper presents a novel rigid-body navigation and control architecture within the framework of special Euclidean group SE(3)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathsf {SE(3)}$$\end{document} and its tangent bundle TSE(3)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathsf {TSE(3)}$$\end{document} while considering stochastic processes in the system. The proposed framework combines the orbit-attitude motions of the rigid body into a single, compact set. The stochastic state filter is designed based on the unscented Kalman filter (UKF) which uses a special retraction function to encode the sigma points onto the manifold. The navigation system is then integrated and evaluated with two different control techniques on TSE(3)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathsf {TSE(3)}$$\end{document}: An almost globally asymptotically stabilizing Morse–Lyapunov-based control system with backstepping and a robust sliding mode-based control system. Also, the performance of the UKF in TSE(3)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathsf {TSE(3)}$$\end{document} proposed here is compared with similar filters in the literature to demonstrate the robustness and accuracy of the proposed filter in a realistic setting. Numerical simulations are conducted to demonstrate the effectiveness of the proposed navigation filter for the full state estimation. In addition, the navigation and control systems are tested in the nonlinear gravity field of a small celestial body with an irregular shape. In particular, the performance of the closed-loop systems is studied in a tracking problem of spacecraft motion near the asteroid Bennu based on OSIRIS-REx mission data.