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This paper proposes an optimization-based task and motion planning framework, named “Logic Network Flow”, to integrate signal temporal logic (STL) specifications into efficient mixed-binary linear programmings. In this framework, temporal predicates are encoded as polyhedron constraints on each edge of the network flow, instead of as constraints between the nodes as in the traditional Logic Tree formulation. Synthesized with Dynamic Network Flows, Logic Network Flows render a tighter convex relaxation compared to Logic Trees derived from these STL specifications. Our formulation is evaluated on several multi-robot motion planning case studies. Empirical results demonstrate that our formulation outperforms Logic Tree formulation in terms of computation time for several planning problems. As the problem size scales up, our method still discovers better lower and upper bounds by exploring fewer number of nodes during the branch-andbound process, although this comes at the cost of increased computational load for each node when exploring branches. 

Tactile sensing is pivotal for enhancing robot manipulation abilities by providing crucial feedback for localized information. However, existing sensors often lack the necessary resolution and bandwidth required for intricate tasks. To address this gap, we introduce VibTac, a novel multi-modal tactile sensing finger designed to offer high-resolution and high-bandwidth tactile sensing simultaneously. VibTac seamlessly integrates vision-based and vibration-based tactile sensing modes to achieve high-resolution and high-bandwidth tactile sensing respectively, leveraging a streamlined human-inspired design for versatility in tasks. This paper outlines the key design elements of VibTac and its fabrication methods, highlighting the significance of the Elastomer Gel Pad (EGP) in its sensing mechanism. The sensor’s multi-modal performance is validated through 3D reconstruction and spectral analysis to discern tactile stimuli effectively. In experimental trials, VibTac demonstrates its efficacy by achieving over 90% accuracy in insertion tasks involving objects emitting distinct sounds, such as ethernet connectors. Leveraging vision-based tactile sensing for object localization and employing a deep learning model for “click” sound classification, VibTac showcases its robustness in real-world scenarios. Video of the sensor working can be accessed at https://youtu.be/kmKIUlXGroo.