Tactile servoing is an important technique because it enables robots to manipulate objects with precision and accuracy while adapting to changes in their environments in real-time. One approach for tactile servo control with high-resolution soft tactile sensors is to estimate the contact pose relative to an object surface using a convolutional neural network (CNN) for use as a feedback signal. In this paper, we investigate how the surface pose estimation model can be extended to include shear, and utilize these combined pose-and-shear models to develop a tactile robotic system that can be programmed for diverse non-prehensile manipulation tasks, such as object tracking, surface following, single-arm object pushing and dual-arm object pushing. In doing this, two technical challenges had to be overcome. Firstly, the use of tactile data that includes shear-induced slippage can lead to error-prone estimates unsuitable for accurate control, and so we modified the CNN into a Gaussian-density neural network and used a discriminative Bayesian filter to improve the predictions with a state dynamics model that utilizes the robot kinematics. Secondly, to achieve smooth robot motion in 3D space while interacting with objects, we used SE(3) velocity-based servo control, which required re-deriving the Bayesian filter update equations using Lie group theory, as many standard assumptions do not hold for state variables defined on non-Euclidean manifolds. In future, we believe that pose and shear-based tactile servoing will enable many object manipulation tasks and the fully-dexterous utilization of multi-fingered tactile robot hands. Video: https://www.youtube.com/watch?v=xVs4hd34ek0
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