In most robotic applications, tactile sensors are modeled as rigid matrices of adjacent pressure sensing elements so that the geometric deformations of their surfaces are neglected. This paper proposes to define these deformations as rotational and translational compliances that are later used as new tactile features for tactile servoing tasks. In fact, a novel two-layered inverse tactile Jacobian matrix is developed in order to map errors of these features into cartesian errors required for touch-driven exploration and manipulation robotic tasks. The performance of this new tactile servoing approach is demonstrated in several real experiments with a 6 × 14 tactile array mounted on a 7-dof robotic manipulator.