We propose a shared control and active perception framework combining the skills of a human operator in accomplishing complex tasks with the capabilities of a mobile robot in autonomously maximizing the information acquired by the onboard sensors for improving its state estimation. The human operator modifies at runtime some suitable properties of a persistent cyclic path followed by the robot and, at the same time, the path is concurrently adjusted by the robot with the aim of maximizing the collected information. This combined behavior enables the human operator to control the high-level task while the robot autonomously improves its state estimation. The user is also provided with guidance feedback pointing in the direction that would maximize an information metric. We evaluated our approach in human subject studies, testing the effectiveness of including the active perception in a task priority framework, as well as of providing a user feedback (either visual or haptic).