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, VisPRM and VisRRT, designed to tackle visibility-based tasks. VisPRM 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 VisRRT to "glance" in the direction of the target at opportune moments, facilitating the rapid discovery of key configurations. We show that VisPRM and VisRRT 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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