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This paper examines the global convergence problem of SLAM algorithms, an issue that faces topological obstructions. This is because the state-space for attitude kinematics is defined on a noncontractible manifold: the special orthogonal group of order three SO(3). Therefore, this paper presents a novel, gradient-based hybrid observer to overcome these topological obstacles. Moreover, the integral action is applied into the proposed observer to estimate unknown constant bias, which results in an increase in bias estimation. Accordingly, a new projection scheme is defined to cope with the integral action. The Lyapunov stability theorem is used to prove the globally asymptotic convergence of the proposed algorithm. Experimental and simulation results are provided to evaluate the performance and to demonstrate the effectiveness and robustness of the proposed scheme.

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The main purpose of this paper is to introduce a hybrid controller for global attitude tracking of a quadrotor. This controller globally exponentially stabilizes the desired attitude, a task that is impossible to accomplish with memoryless discontinuous or continuous state feedback owing to topological obstruction. Thereafter, this paper presents a new centrally synergistic potential function to construct hybrid feedback that defeats the topological obstruction. This function induces a gradient vector field to globally asymptotically stabilize the reference attitude and produces the synergy gap to generate a switching control law. The proposed control structure is consisting of two major parts. In the first part, a synergetic controller is designed to cooperate with the hybrid controller, whereas it exponentially stabilizes the origin of the error dynamics. In the second part, a hybrid controller is introduced to globally stabilize the attitude of the quadrotor, where an average dwell constraint is considered with the switching control law to guarantee the exponential stability of the switched system. Finally, the effectiveness and superiority of the proposed control technique are validated by a comparative analysis in simulations.

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