Tactile perception is a crucial sensing modality in robotics, particularly in scenarios that require precise manipulation and safe interaction with other objects. Previous research in this area has focused extensively on tactile perception of contact poses as this is an important capability needed for tasks such as traversing an object's surface or edge, manipulating an object, or pushing an object along a predetermined path. Another important capability needed for tasks such as object tracking and manipulation is estimation of post-contact shear but this has received much less attention. Indeed, post-contact shear has often been considered a "nuisance variable" and is removed if possible because it can have an adverse effect on other types of tactile perception such as contact pose estimation. This paper proposes a tactile robotic system that can simultaneously estimate both the contact pose and post-contact shear, and use this information to control its interaction with other objects. Moreover, our new system is capable of interacting with other objects in a smooth and continuous manner, unlike the stepwise, position-controlled systems we have used in the past. We demonstrate the capabilities of our new system using several different controller configurations, on tasks including object tracking, surface following, single-arm object pushing, and dual-arm object pushing.

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