LMI Methods for Extended ℋ∞ Filters for Landmark-based Mobile Robot Localization

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Abstract
Localization is still one of the most fundamental tasks for autonomous navigation of mobile robots. However, the existing methods lack robustness when dealing with uncertainties without assuming some characteristics about noise inputs and the nonlinearity of the measurement models. In this work, a theoretical basis for designing two separate extended robust filters based on linear matrix inequalities is proposed to solve the localization problem. The first approach is based on the design of an ℋ ∞ observer-based filter through a two-step prediction correction structure. In this way, a convex optimization problem needs to be solved at each time step to determine the observer-gain that corrects the predicted pose of a differential wheeled robot. The second approach considers the advantages of a full-order filter which guarantees a better performance under the ℋ ∞ robust requirements. Besides, satisfactory results that validate theoretical remarks were performed in real and virtual scenarios through simulation frameworks.

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