Despite the growing impact of Unmanned Aerial Vehicles (UAVs) across various industries, most of current available solutions lack for a robust autonomous navigation system to deal with the appearance of obstacles safely. This work presents an approach to perform autonomous UAV planning and navigation in scenarios in which a safe and high maneuverability is required, due to the cluttered environment and the narrow rooms to move. The system combines an RRT* global planner with a newly proposed reactive planner, DWA-3D, which is the extension of the well known DWA method for 2D robots. We provide a theoretical-empirical method for adjusting the parameters of the objective function to optimize, easing the classical difficulty for tuning them. An onboard LiDAR provides a 3D point cloud, which is projected on an Octomap in which the planning and navigation decisions are made. There is not a prior map; the system builds and updates the map online, from the current and the past LiDAR information included in the Octomap. Extensive real-world experiments were conducted to validate the system and to obtain a fine tuning of the involved parameters. These experiments allowed us to provide a set of values that ensure safe operation across all the tested scenarios. Just by weighting two parameters, it is possible to prioritize either horizontal path alignment or vertical (height) tracking, resulting in enhancing vertical or lateral avoidance, respectively. Additionally, our DWA-3D proposal is able to navigate successfully even in absence of a global planner or with one that does not consider the drone's size. Finally, the conducted experiments show that computation time with the proposed parameters is not only bounded but also remains stable around 40 ms, regardless of the scenario complexity.