In this work we are investigating reactive avoidance techniques which can be used on board of a small quadcopter and which do not require absolute localization. We propose a local map representation which can be updated with proprioceptive sensors. The local map is centred around the robot and uses spherical coordinates to represent a point cloud. The local map is updated using a depth sensor, the Inertial Measurement Unit and a registration algorithm. We propose an extension of the Dynamic Window Approach to compute a velocity vector based on the current local map. We propose to use an OctoMap structure to compute a 2-pass A* which provide a path which is converted to a velocity vector. Both approaches are reactive as they only make use of local information. The algorithms were evaluated in a simulator which offers a realistic environment, both in terms of control and sensors. The results obtained were also validated by running the algorithms on a real platform.