Robot Task and Motion Planning (TAMP) algorithms enable autonomous operation by incorporating the specific functions and constraints of end-effector tools, such as grippers or soldering irons, directly into the planning process. In this paper, we explore sampling-based TAMP algorithms specifically designed for a critical subset of devices whose unique properties make traditional planning methods ineffective. Visibility-based instruments, such as exteroceptive sensors, cameras, flashlights and directional antennas, are essential across a vast array of human activities. The unique properties of these devices, and particularly, their field-of-view, render many widely used heuristics and distance metrics less effective. We introduce two new sampling-based algorithms, FOV-PRM and FOV-RRT, designed to tackle visibility-based tasks. FOV-PRM employs a hierarchical decomposition of the environment, leveraging the concept of visibility integrity, to efficiently sample configurations with a clear line-of-sight to the target. A specialized Inverse Kinematics solver enables FOV-RRT to "glance" in the direction of the target at opportune moments, facilitating the rapid discovery of key configurations. We show that FOV-PRM and FOV-RRT achieve a higher success rate and faster runtimes compared to adaptations of RRT, PRM and VIR, through both simulated and physical experiments.

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