This paper proposes the use of path-planning algorithms for hovering autonomous underwater vehicles (AUVs) in applications where the robot needs to adapt online its trajectory for inspection or safety purposes. In particular, it proposes the platform Sparus II AUV and a set of planning algorithms to conduct these new AUV capabilities. These algorithms generate trajectories under motion constraints, which can be followed without deviations, to ensure the safety even when passing close to obstacles. View planning algorithms are also combined to decide the movements to be executed to discover the unexplored seabed or target, and to cover it with a camera or sonar. Online mapping with profiling sonars and online planning with fast sampling-base...