Visibility-constrained path planning refers to problems in which a robot must navigate an environment populated by obstacles and occlusions (e.g. opaque objects) whereby avoiding line-of-sight (LOS) detection by one or more sensors. Example applications are unmanned aerial vehicles (UAVs) used to perform tasks like warehouse inventory monitoring where the UAV must avoid detection by the warehouse security system. This thesis presents a visibility-constrained path planning framework for a quadcopter with an onboard camera to navigate in partially known environments, avoiding collisions with obstacles and LOS detection inside sensor visibility regions created using key concepts of visibility theory. A probabilistic roadmap (PRM) is used to find a path on the prior map with sensor visibility regions. Panoptic segmentation is used to obtain a pixel-wise semantic mask to identify obstacles in the RGB frames captured online. The inverse projection method is then used to map these obstacles on an online map of the workspace using ground truth depth maps and collisions with the quadcopter's path are checked. Additionally, findings on the limitations of machine-learning based monocular depth estimation for online mapping are also discussed. A hybrid path replanning algorithm is used that locally replans the path to avoid collisions with obstacles identified online. If local replanning fails to find a new local path, global replanning is performed using an updated PRM. A simulation environment in Unreal Engine is used to test the visibility-constrained path planning framework with the quadcopter imported from AirSim.