| Summary: | This paper investigates the global convergence problem of SLAM algorithms, a problem that has been subject to topological obstacles. This is due to the fact that state-space of attitude kinematics, <inline-formula> <tex-math notation="LaTeX">$SO(3)$ </tex-math></inline-formula>, is a non-contractible manifold. Hence, <inline-formula> <tex-math notation="LaTeX">$SO(3)$ </tex-math></inline-formula> is not diffeomorphic to Euclidean space. Therefore, existing SLAM algorithms can only guarantee almost global convergence. In order to overcome topological obstructions, this paper introduces a gradient-based hybrid observer that ensures global asymptotic convergence of estimation errors to zero. Moreover, integral action is augmented into the proposed observer to estimate unknown constant bias. Accordingly, a projection scheme is designed to cope with the integral action. Lyapunov stability theorem is used to prove the global asymptotic convergence of the proposed algorithm. Experimental and simulation results are provided to evaluate the performance and demonstrate the effectiveness and robustness of the proposed observer.
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