Obstacle avoidance methods approach the problem of mobile robot autonomous navigation by steering the robot in real-time according to the most recent sensor readings, being suitable to dynamic or unknown environments. However, real-time performance is commonly gained by ignoring the robot shape and some or all of its kinematic restrictions which may lead to poor navigation performance in many practical situations. In this paper we propose a framework where a kinematically constrained and any-shape robot is transformed in real-time into a free-flying point in a new space where well-known obstacle avoidance methods are applicable. Our contribution with this framework is twofold: the definition of generalized space transformations that cover most of the existing transformational approaches, and a reactive navigation system where multiple transformations can be applied concurrently in order to optimize robot motion decisions. As a result, these transformations allow existing obstacle avoi...