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This paper considers the navigation of a three degrees-of-freedom mobile robot equipped with position and tactile sensors in an unknown planar environment. The paper focuses on the contact preserving segments of the robot's path. Any contact preserving path can trace a single or two simultaneous contacts. The paper establishes that motions involving two contacts induce two types of configuration-space curves: contractible loops representing passable gaps, and non- contractible loops representing impassable gaps. The paper identifies a generic class of contact preserving paths which requires only single-contact tracings with efficient transitions at double-contact configurations involving impassable gaps, and at triple-contact configurations involving both passable and impassable gaps. A preliminary tactile-sensor navigation algorithm based on these paths is illustrated with an example.