A new form of telexistence is achieved by recording videos with a camera on an Uncrewed aerial vehicle (UAV) and playing the videos to a user via a head-mounted display (HMD). One key problem here is how to let the user freely and naturally control the UAV and thus the viewpoint. In this paper, we develop an HMD-based telexistence technique that achieves full 6- DOF control of the viewpoint. The core of our technique is an improved rate-based control technique with our adaptive origin update (AOU), in which the origin of the coordinate system of the user changes adaptively. This makes the user naturally perceive the origin and thus easily perform the control motion to get his/her desired viewpoint changing. As a consequence, without the aid of any auxiliary equipment, the AOU scheme handles the well known self-centering problem in the rate-based control methods. A real prototype is also built to evaluate this feature of our technique. To explore the advantage of our telexistence technique, we further use it as an interactive tool to perform the task of 3D scene reconstruction. User studies demonstrate that comparing with other telexistence solutions and the widely used joystick-based solutions, our solution largely reduces the workload and saves time and moving distance for the user.